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ThreeColumnLayout_leftColumn__Tf0iY"> <div> <div> <div id="article-table-of-contents" data-ismobile="false"> <div class="TableOfContents_tableOfContents__tmWzJ"> <div class="TableOfContents_tableOfContents__title__sU5vH"> 在这一页上</d我v> <a class="TableOfContents_tableOfContents__item__zC0yd" href="#abstract">文摘</一个><一个cl一个年代年代="TableOfContents_tableOfContents__item__zC0yd" href="#introduction">介绍</一个><一个cl一个年代年代="TableOfContents_tableOfContents__item__zC0yd" href="#conclusion">结论</一个><一个cl一个年代年代="TableOfContents_tableOfContents__item__zC0yd" href="#references">引用</一个><一个cl一个年代年代="TableOfContents_tableOfContents__item__zC0yd" href="#copyright">版权</一个><一个cl一个年代年代="TableOfContents_tableOfContents__item__zC0yd" href="#related-articles">相关文章</一个></d我v> </div> </div> </div> </div> <div class="ant-col ThreeColumnLayout_middleColumn__Pn_ys"> <div class="ArticleMiddleSection_articleMiddleSection__DtVY3"> <div class="articleHeader"> <strong>研究文章|<gydF4y2Ba!-- -->开放获取</年代trong> <div class="articleHeader__meta"> <span>体积<gydF4y2Ba!-- -->2008年<gydF4y2Ba!-- -->|</年代p一个n><年代p一个n>文章的ID<gydF4y2Ba!-- -->426080年<gydF4y2Ba!-- -->|</年代p一个n><年代p一个ncl一个年代s="articleHeader__meta_doiLink"><a href="https://doi.org/10.1155/2008/426080" aria-label="Doi-link" target="_blank" rel="noreferrer">https://doi.org/10.1155/2008/426080</一个></年代p一个n></d我v> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示引用</gydF4y2Babutton> </div> <h1 class="articleHeader__title">通过无参数不对称变量代双重神经学习算法</h1><d我v class="articleHeader__authors"> <span class="articleHeader__authors_author"><strong>西蒙·菲奥里</年代trong><a href="//www.newsama.com/cdn-cgi/l/email-protection" aria-label="Mail Option"><span role="img" class="anticon"> <svg version="1.0" xmlns="http://www.w3.org/2000/svg" width="1em" height="1em" viewbox="0 0 1401 1101"> <path fill="#6ba439" d="M132.5 2.1C101.4 6 71.1 20.5 48.3 42.4c-22.7 21.7-37.5 48.3-44.6 80l-2.2 10.1v837l2.2 10.1c6.7 30 19.3 53.9 39.8 75.3 23.3 24.3 56.4 40.9 90 45 12.8 1.6 1122.2 1.6 1135 0 38.9-4.8 75.9-25.6 100-56.4 15-19.3 24.2-39 29.8-63.9l2.2-10.1v-837l-2.2-10.1c-7.1-31.8-21.9-58.3-44.6-80.1-20.2-19.2-43.9-31.7-73.6-38.5l-9.6-2.3L705 1.4c-321.9-.1-568.5.2-572.5.7zm1123.4 99.5c1.7.4 3.1 1 3.1 1.4 0 .5-125.6 87.7-279 194L700.9 490.2 422 297C268.5 190.7 143 103.4 143 103c0-.5 1-1.1 2.3-1.3 3.5-.7 1107.1-.8 1110.6-.1zM401 404c164.4 113.8 299.4 207 300 207 .6 0 135.6-93.2 300.1-207 164.5-113.9 299.3-207 299.5-207 .2 0 .4 170.9.4 379.7 0 417.9.5 386-6.1 398.3-6.2 11.6-19 21.4-31.9 24.4-5.8 1.4-67.4 1.6-562 1.6s-556.2-.2-562-1.6c-12.9-3-25.7-12.8-31.9-24.4-6.6-12.3-6.1 19.6-6.1-398.3 0-208.8.2-379.7.5-379.7S236.6 290.1 401 404z"></path> </svg></span></a><sup>1</年代up></年代p一个n></div> <div class="simpleShowMore"> <button class="simpleShowMore__button">显示更多</gydF4y2Babutton> </div> <div class="articleHeader__academicEditor"> <strong>学术编辑器:</年代trong> <span>美国Cruces-Alvarez</年代p一个n></d我v> <div class="articleHeader__timeline"> <div class="articleHeader__timeline_item "> <strong>收到了</年代trong> <span>2007年6月16日</年代p一个n></d我v> <div class="articleHeader__timeline_item "> <strong>接受</年代trong> <span>2007年9月19日</年代p一个n></d我v> <div class="articleHeader__timeline_item articleHeader__timeline_item_sticky"> <strong>发表</年代trong> <span>2008年4月24日</年代p一个n></d我v> </div> </div> <div class="articleBody"> <div class="xml-content"> <h4 class="header" id="abstract">文摘</h4><p>gydF4y2Ba在以前的工作(s .菲奥里,2006),我们提出了一个随机数发生器基于可调非线性神经系统,其学习规则设计基本方程的基础上实现基于查找表的统计数据和(附近地区)。目前的手稿的目的是改善上述随机数生成方法通过改变学习的原则,同时保留有效LUT-based实现。这里提出证明新方法更容易实现和放松一些以前的限制。</p><年代p一个ncl一个年代年代="end-abs"></span> <h4 id="introduction">1。介绍</h4><p>gydF4y2Ba随机数是目前用于各种目的,如:密钥生成、游戏,一些种类的科学实验以及蒙特卡罗方法在物理学和计算机科学(<一个href="#B2">1</一个>- - - - - -<一个href="#B13">6</一个>]。标准编程环境被赋予统一等基本伪随机信号发生器和高斯的,而通常所需的分布比均匀涉及/高斯。一个简单的示例应用程序的密码生成:随机密码生成器是一个软件,输入从一个随机或伪随机数生成器,并自动生成一个密码。的一个示例应用程序,需要涉及到概率分布在独立分量分析(ICA),<一个href="#B1">7</一个>)测试:作为ICA算法的行为可能取决于来源的统计分布,ICA-algorithm测试工具可能需要随机序列发生器能产生随机数按涉及概率分配法。</p><p>gydF4y2Ba主要方法在文献获取一批样品具有任意分布从一批样品有一个简单的“转换法”和“反对方法”(<一个href="#B6">8</一个>]。在本文中,我们专注于转换的方法,这可能是通过一个可调的神经系统实现,因为一个随机数源的可用性和可调的非线性系统,在一个适当的学习过程,可以获得广泛的伪随机信号发生器类。</p><p>gydF4y2Ba著名的非线性神经系统的影响是经其输入的统计分布。特别是,我们假设考虑中的系统所描述的非线性自适应结构转移<年代vg height="13.6125" id="M1" style="vertical-align:-2.34499pt;width:54.9375px;" version="1.1" viewbox="0 0 54.9375 13.6125" width="54.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6648188" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.705208" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.644373" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.807873" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.684521" y="0"> )</t年代p一个n></text> </g> </g> </svg>,在那里<年代vg height="12.475" id="M2" style="vertical-align:-1.29163pt;width:73.099998px;" version="1.1" viewbox="0 0 73.099998 12.475" width="73.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.475)"> <g transform="translate(72,-62.02)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.996376" y="0"> ⊆</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.036766" y="0"> ℝ</t年代p一个n></text> </g> </g> </svg>表示系统输入随机信号概率密度函数<年代vg height="14.7" id="M3" style="vertical-align:-3.21404pt;width:33.412498px;" version="1.1" viewbox="0 0 33.412498 14.7" width="33.412498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.52,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.3875" id="M4" style="vertical-align:-2.83405pt;width:72.800003px;" version="1.1" viewbox="0 0 72.800003 14.3875" width="72.800003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6648188" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.705208" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.75882" y="0"> ⊆</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.79921" y="0"> ℝ</t年代p一个n></text> </g> </g> </svg>表示输出信号概率密度函数<年代vg height="16.6" id="M5" style="vertical-align:-4.74141pt;width:31.975px;" version="1.1" viewbox="0 0 31.975 16.6" width="31.975" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n></text> </g> </g> </svg>,如图<一个href="//www.newsama.com/journals/cin/2008/426080/fig1/" target="_blank">1</一个>。假设神经系统中的移情是严格单调,即<年代vg height="15.5625" id="M6" style="vertical-align:-2.34499pt;width:61.224998px;" version="1.1" viewbox="0 0 61.224998 15.5625" width="61.224998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.5625)"> <g transform="translate(72,-59.55)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.51,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.04,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.679482" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.707369" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,尽管<年代vg height="11.2875" id="M7" style="vertical-align:-0.33858pt;width:42.037498px;" version="1.1" viewbox="0 0 42.037498 11.2875" width="42.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.2875)"> <g transform="translate(72,-62.97)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> </t年代p一个n></text> </g> </g> </svg>输入分布之间的关系,输出分布,系统传递函数是(<一个href="#B12">9</一个>]<gydF4y2Ba年代p一个ncl一个年代年代="equation" id="Eq1"> <svg height="39.950001" id="M8" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 39.950001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,39.95)"> <g transform="translate(72,-40.04)"> <text transform="matrix(1,0,0,-1,128.32,54.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,134.43,51.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,139.27,54.28)"> <tspan style="font-size: 12.50px; " x="31.48" y="-9.2200003"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.991817" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.86,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,182.17,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> <g> <path d="m 170.5,57.41 27.12,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,170.5,44.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,178.94,49.57)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,182.42,44.5)"> <tspan style="font-size: 12.50px; " x="16.4" y="-9.7799997"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.32,41.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.8136001" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.80872" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,218.03,45.23)"> <tspan style="font-size: 6.25px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 6.25px; " x="4.28262" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.94,41.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.9144161" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.2554078" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,236.61,54.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.518623" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.546509" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.686684" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="237.50999" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="241.67349" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="247.925" y="0"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="16.775" id="M9" style="vertical-align:-2.34499pt;width:39.137501px;" version="1.1" viewbox="0 0 39.137501 16.775" width="39.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>表示函数的倒数<年代vg height="13.6125" id="M10" style="vertical-align:-2.34499pt;width:23.674999px;" version="1.1" viewbox="0 0 23.674999 13.6125" width="23.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.678522" y="0"> )</t年代p一个n></text> </g> </g> </svg>。通常,(<一个href="#Eq1">1</一个>)被解释为一个分析公式,使计算输出分布当输入分布和系统传递函数是已知的。然而,基本方程(<一个href="#Eq1">1</一个>)也可以被解释为一个公式时,允许设计非线性系统分布<年代vg height="14.7" id="M11" style="vertical-align:-3.21404pt;width:29.2875px;" version="1.1" viewbox="0 0 29.2875 14.7" width="29.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.52,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>是已知的和期望的系统响应根据期望的分布<年代vg height="16.6" id="M12" style="vertical-align:-4.74141pt;width:28.700001px;" version="1.1" viewbox="0 0 28.700001 16.6" width="28.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>。事实上,(<一个href="#Eq1">1</一个>)微分方程可以写成:<年代p一个ncl一个年代年代="equation" id="Eq2"> <svg height="50.75" id="M13" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.75" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.75)"> <g transform="translate(72,-31.4)"> <text transform="matrix(1,0,0,-1,135.92,54.28)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,144.36,59.35)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,147.84,54.28)"> <tspan style="font-size: 12.50px; " x="42.619999" y="-9.2200003"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.666979" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.58,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.89,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> <g> <path d="m 179.75,57.41 48.06,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,179.75,39.86)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,185.86,36.73)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,190.7,34.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.51" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3600001" y="-4.9200001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.299165" y="-4.9200001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.462664" y="-4.9200001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.339314" y="-4.9200001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.299999" y="-19.34"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.466141" y="-19.34"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.818623" y="-19.34"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.859009" y="-19.34"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.999184" y="-19.34"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="283.42001" y="-19.34"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="287.5835" y="-19.34"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="293.83499" y="-19.34"> )</t年代p一个n></text> </g> </g> </svg></span>一般来说,这样的设计操作相当困难,因为(<一个href="#Eq2">2</一个>在未知的<年代vg height="13.6125" id="M14" style="vertical-align:-2.34499pt;width:23.674999px;" version="1.1" viewbox="0 0 23.674999 13.6125" width="23.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.678522" y="0"> )</t年代p一个n></text> </g> </g> </svg>涉及非线性微分方程的解决方案,提供了一个一致的边界条件是确定的。</p><d我v class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-e076880412fe78cd6ced8f2193042bf1"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.001.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-e076880412fe78cd6ced8f2193042bf1 partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.001_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-e076880412fe78cd6ced8f2193042bf1 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图1</年代p一个n><一个一个r我一个-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2008/426080/fig1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>神经系统中,神经双系统,输入/输出样本空间及其统计分布。</td></tr></tbody> </table> </div> </div> </div> </div> <p>在最近的贡献(<一个href="#B3">10</一个>),我们提出了一个伪随机样本发生器基于非线性单调神经系统的传递函数是用<年代vg height="13.6125" id="M15" style="vertical-align:-2.34499pt;width:23.674999px;" version="1.1" viewbox="0 0 23.674999 13.6125" width="23.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.678522" y="0"> )</t年代p一个n></text> </g> </g> </svg>微分方程的基础上,调整(<一个href="#Eq2">2</一个>)。红衣主教的设计方程(<一个href="#Eq2">2</一个>)提出了要解决通过(relaxation-type)定点算法。关键的优势的方法<一个href="#B3">10</一个>)如下。(一)为了获得fully-tunable神经传递函数,选择查阅表表示。它保证高灵活性在神经传递的形状以及从容的表示和处理涉及数量。(b)定点学习算法表现出快速收敛在基于其他可能的方法,如梯度:不同于这些方法,定点学习算法不需要计算相关函数的导数。</p><p>gydF4y2Ba产生的随机数生成方法应该因此阅读作为一个两阶段的过程。第一阶段由红衣主教在解决微分方程(<一个href="#Eq2">2</一个>未知函数)<年代vg height="13.6125" id="M16" style="vertical-align:-2.34499pt;width:23.674999px;" version="1.1" viewbox="0 0 23.674999 13.6125" width="23.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.678522" y="0"> )</t年代p一个n></text> </g> </g> </svg>考虑到分布,<年代vg height="14.7" id="M17" style="vertical-align:-3.21404pt;width:29.2875px;" version="1.1" viewbox="0 0 29.2875 14.7" width="29.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.52,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>和<年代vg height="16.6" id="M18" style="vertical-align:-4.74141pt;width:28.700001px;" version="1.1" viewbox="0 0 28.700001 16.6" width="28.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>作为数据。第二阶段包括在生成输入随机样本的分布<年代vg height="14.7" id="M19" style="vertical-align:-3.21404pt;width:29.2875px;" version="1.1" viewbox="0 0 29.2875 14.7" width="29.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.52,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>让这种随机抽样,然后通过学习非线性神经系统通过计算输出值<年代vg height="13.6125" id="M20" style="vertical-align:-2.34499pt;width:54.9375px;" version="1.1" viewbox="0 0 54.9375 13.6125" width="54.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6648188" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.705208" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.644373" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.807873" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.684521" y="0"> )</t年代p一个n></text> </g> </g> </svg>。随机样本<年代vg height="9.8625002" id="M21" style="vertical-align:-2.29482pt;width:7.875px;" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.8625)"> <g transform="translate(72,-64.11)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>保证是根据概率密度分布函数<年代vg height="16.6" id="M22" style="vertical-align:-4.74141pt;width:28.700001px;" version="1.1" viewbox="0 0 28.700001 16.6" width="28.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba然而,我们认识到的方法<一个href="#B3">10</一个>)也遭受一些缺点,即以下。(一)数值收敛的目的,fixed-point-type调优算法的每一步都需要一些标准化的步骤。也就是说,从(<一个href="#Eq2">2</一个>),它是很容易看到,当函数<年代vg height="16.6" id="M23" style="vertical-align:-4.74141pt;width:51.900002px;" version="1.1" viewbox="0 0 51.900002 16.6" width="51.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.266163" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.142813" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.306313" y="0"> )</t年代p一个n></text> </g> </g> </svg>方法<年代vg height="10.9125" id="M24" style="vertical-align:-0.17555pt;width:7.9375px;" version="1.1" viewbox="0 0 7.9375 10.9125" width="7.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 0</t年代p一个n></text> </g> </g> </svg>的计算<年代vg height="15.5625" id="M25" style="vertical-align:-2.34499pt;width:34.025002px;" version="1.1" viewbox="0 0 34.025002 15.5625" width="34.025002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.5625)"> <g transform="translate(72,-59.55)"> <text transform="matrix(1,0,0,-1,-71.95,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.51,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.04,61.94)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> </g> </g> </svg>变得坏脾气的,因此数量<年代vg height="16.6" id="M26" style="vertical-align:-4.74141pt;width:51.900002px;" version="1.1" viewbox="0 0 51.900002 16.6" width="51.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.266163" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.142813" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.306313" y="0"> )</t年代p一个n></text> </g> </g> </svg>被取代了<年代vg height="16.6" id="M27" style="vertical-align:-4.74141pt;width:77.5px;" version="1.1" viewbox="0 0 77.5 16.6" width="77.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.266163" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.142813" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.306313" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.245476" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.585697" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.6125" id="M28" style="vertical-align:-2.34499pt;width:35.262501px;" version="1.1" viewbox="0 0 35.262501 13.6125" width="35.262501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.8148546" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.855244" y="0"> 0</t年代p一个n></text> </g> </g> </svg>作为一个小的常数是正确的大小。同时,为了改进学习,每个迭代步骤后,解决方案<年代vg height="13.6125" id="M29" style="vertical-align:-2.34499pt;width:27.799999px;" version="1.1" viewbox="0 0 27.799999 13.6125" width="27.799999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.979315" y="0"> )</t年代p一个n></text> </g> </g> </svg>需要规范化通过仿射尺度,为了控制变量的范围<年代vg height="9.8625002" id="M30" style="vertical-align:-2.29482pt;width:7.875px;" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.8625)"> <g transform="translate(72,-64.11)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>由线性扩展,或者为了匹配输出分布的真实价值的时刻预选的秩序。反过来,这需要提前计算感兴趣的(封闭形式)时刻输出的分布。(b)尽管仿射尺度,它是不容易控制输出值的范围<年代vg height="9.8625002" id="M31" style="vertical-align:-2.29482pt;width:7.875px;" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.8625)"> <g transform="translate(72,-64.11)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,仿射尺度收敛并不能保证在任何情况下感兴趣的,因此不能在任何情况下。(c)开发过程是自定义生成输出分布是对称的(即<年代vg height="16.6" id="M32" style="vertical-align:-4.74141pt;width:93.925003px;" version="1.1" viewbox="0 0 93.925003 16.6" width="93.925003" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.728054" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.929543" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.568874" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.59676" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-16.28,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-11.44,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n></text> </g> </g> </svg>)或完全向右倾斜(即<年代vg height="16.6" id="M33" style="vertical-align:-4.74141pt;width:59.174999px;" version="1.1" viewbox="0 0 59.174999 16.6" width="59.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.00432" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.032206" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,尽管<年代vg height="13.55" id="M34" style="vertical-align:-2.29482pt;width:35.075001px;" version="1.1" viewbox="0 0 35.075001 13.55" width="35.075001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6648188" y="0"> <</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.705208" y="0"> 0</t年代p一个n></text> </g> </g> </svg>只)。不对称或外形分布没有考虑。</p><p>gydF4y2Ba在本文中,我们考虑的问题扩展前面的方法生成通过删除约束对称或不对称分布skewedness到右边。同时,我们提出一个方法来避免概率密度函数。选择的解决方案意味着改变的观点基本方程(<一个href="#Eq1">1</一个>):不是转换公式(<一个href="#Eq1">1</一个>)到微分方程(<一个href="#Eq2">2</一个>),我们将它转换成一个新的微分方程,以下简称<我>双重基本方程</我>,这将被证明是容易解决和更灵活的运用在实践中,同时保留前面的数字表示/优势。因此,我们将保留相关的有效的数值表示数量已经介绍了工作(<一个href="#B3">10</一个>,<gydF4y2Ba一个href="#B4">11</一个>),基于“查表”(附近地区)神经激活功能的实现以及有效的数值算法来解决双重基本方程。附近地区被证明是提供一个有效的方式来表示和处理的变量出现在设计了随机数生成算法。过程的突出优势是缺乏硬计算需求除了附近地区处理,由列表的排序、搜索和一些简单的代数操作的号码。</p><p>gydF4y2Ba该方法将评估的有效性通过数值实验。特别是,设计实验遵循逻辑,开始时提出的基本评估方法应用于bi-Gaussian分布,然后跟着相对困难些分布,即广义高斯分布和非对称伽马分布。</p><p>gydF4y2Ba现有的方法(<一个href="#B10">3</一个>是值得讨论。它关注neural-networks-type算法生成随机向量具有任意边际分布和相关矩阵,基于交互的方法。“normal-to-anything”(交互)方法(见,例如,<一个href="#B5">12</一个>])是最有效的方法之一,随机向量的一代。在[<一个href="#B10">3</一个>),提出了一种技术来生成正态随机向量的相关矩阵基于人工神经网络的方法。以以下方式交互算法生成随机抽样与规定的概率密度函数。首先,生成零均值unit-variance随机样本<年代vg height="11.05" id="M35" style="vertical-align:-3.2316pt;width:12.75px;" version="1.1" viewbox="0 0 12.75 11.05" width="12.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.575" id="M36" style="vertical-align:-2.26974pt;width:89.5px;" version="1.1" viewbox="0 0 89.5 13.575" width="89.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3517642" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.392153" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.393593" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.645094" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.858845" y="0"> ⋯</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.512119" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.725872" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.490715" y="0"> }</t年代p一个n></text> </g> </g> </svg>。然后,生成所需的随机样本<年代vg height="19.674999" id="M37" style="vertical-align:-4.74141pt;width:101.8625px;" version="1.1" viewbox="0 0 101.8625 19.674999" width="101.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.675)"> <g transform="translate(72,-56.26)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.06,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-37.72,66.03)"> <tspan style="font-size: 8.75px; " x="-1.87" y="8.1199999"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-26.85,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> Φ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.703288" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.866787" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-2.1,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,1.12,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> )</t年代p一个n></text> </g> </g> </svg>,在那里<年代vg height="13.45" id="M38" style="vertical-align:-2.21957pt;width:26.924999px;" version="1.1" viewbox="0 0 26.924999 13.45" width="26.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Φ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.5397892" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.703288" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.279146" y="0"> )</t年代p一个n></text> </g> </g> </svg>表示标准正态随机变量的累积分布函数<年代vg height="16.6" id="M39" style="vertical-align:-4.74141pt;width:30.3375px;" version="1.1" viewbox="0 0 30.3375 16.6" width="30.3375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.68,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>表示所需的累积分布函数,<年代vg height="19.674999" id="M40" style="vertical-align:-4.74141pt;width:180.05px;" version="1.1" viewbox="0 0 180.05 19.674999" width="180.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.675)"> <g transform="translate(72,-56.26)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.65,66.03)"> <tspan style="font-size: 8.75px; " x="-1.87" y="8.1199999"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-51.78,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.089921" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.716751" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.757139" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.232975" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.484474" y="0"> f</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.986275" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.987713" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.702545" y="0"> ∣</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.491676" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,25.15,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,29.99,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.402496" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.029325" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.069715" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.996136" y="0"> }</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.125" id="M41" style="vertical-align:-1.95624pt;width:55.5625px;" version="1.1" viewbox="0 0 55.5625 13.125" width="55.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.125)"> <g transform="translate(72,-61.5)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3897533" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.430141" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.593641" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.933144" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.184643" y="0"> ]</t年代p一个n></text> </g> </g> </svg>。似乎,因此,作为一个转换方法。</p><p>gydF4y2Ba大多数已知的随机向量的方法生成的文学强加约束随机向量的大小,其中许多适用只equidistributed的二元分布组件。相反,在交互框架中,边际概率分布向量组件以及它们的相关矩阵可以被指定。获得规定的随机向量生成相关矩阵需要求解一个非线性方程组,这是最严重的问题在这样的方法。文献[<一个href="#B10">3</一个>]利用多层感知器神经网络估计正态随机向量的相关性矩阵,因此可以克服NORTA方程涉及的分析算法。而这里的方法是更一般的交互,它适用于任何类型的可用发生器不仅(高斯),它是少将军与规定不允许生成多元随机变量联合统计数据。</p><h4gydF4y2Baid="dual-cardinal-equation-and-its-numerical-solution">2。双重基本方程及其数值解</h4><p>gydF4y2Ba目前部分正式学习问题和演示了一个fixed-point-based数值算法解决双重基本方程。</p><h5gydF4y2Baid="subsec2.1">2.1。双重基本方程和神经系统</h5><p>gydF4y2Ba新方法的关键在于学习逆函数<年代vg height="16.775" id="M42" style="vertical-align:-2.34499pt;width:39.137501px;" version="1.1" viewbox="0 0 39.137501 16.775" width="39.137501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.775)"> <g transform="translate(72,-58.58)"> <text transform="matrix(1,0,0,-1,-71.95,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-63.51,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.64,60.96)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>而不是函数<年代vg height="13.6125" id="M43" style="vertical-align:-2.34499pt;width:23.674999px;" version="1.1" viewbox="0 0 23.674999 13.6125" width="23.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.678522" y="0"> )</t年代p一个n></text> </g> </g> </svg>。将在接下来的部分澄清,这个选择简化了学习问题而增加轻微的计算负担学习神经系统的使用生成模型。</p><p>gydF4y2Ba我们表示<年代vg height="24.3375" id="M44" style="vertical-align:-2.34499pt;width:118.9125px;" version="1.1" viewbox="0 0 118.9125 24.3375" width="118.9125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,24.3375)"> <g transform="translate(72,-52.53)"> <text transform="matrix(1,0,0,-1,-71.95,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.339981" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.380369" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.531845" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.695347" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.896832" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-25.41,63.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.2618876" y="0"> f</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-24.1,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.328198" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-2.32,59.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="5.99512" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,8.55,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n></text> </g> </g> </svg>实际神经传递函数的逆函数和参考新的神经系统,拥有<年代vg height="13.6125" id="M45" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>传递函数,如“双神经系统”(如图<一个href="//www.newsama.com/journals/cin/2008/426080/fig1/" target="_blank">1</一个>)。这里的目的是学习一个弯曲的双神经系统<年代vg height="16.6" id="M46" style="vertical-align:-4.74141pt;width:28.700001px;" version="1.1" viewbox="0 0 28.700001 16.6" width="28.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>成<年代vg height="14.7" id="M47" style="vertical-align:-3.21404pt;width:29.2875px;" version="1.1" viewbox="0 0 29.2875 14.7" width="29.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.52,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>约束条件下<年代vg height="15.475" id="M48" style="vertical-align:-2.34499pt;width:58.150002px;" version="1.1" viewbox="0 0 58.150002 15.475" width="58.150002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.475)"> <g transform="translate(72,-59.62)"> <text transform="matrix(1,0,0,-1,-71.95,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.3,67.01)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61.82,62)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.991817" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.032206" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,尽管<年代vg height="14.3875" id="M49" style="vertical-align:-2.83405pt;width:41.737499px;" version="1.1" viewbox="0 0 41.737499 14.3875" width="41.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6648188" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.705208" y="0"> </t年代p一个n></text> </g> </g> </svg>。我们表示对生成的随机变量的区间<年代vg height="20.174999" id="M50" style="vertical-align:-6.43292pt;width:62.5px;" version="1.1" viewbox="0 0 62.5 20.174999" width="62.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.175)"> <g transform="translate(72,-55.86)"> <text transform="matrix(1,0,0,-1,-71.95,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.041109" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.081497" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.244997" y="0"> </t年代p一个n></text> <g> <path d="m -40.7,57.15 6.2,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <g> <path d="m -32.41,70.71 6.2,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-32.41,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.201488" y="0"> ]</t年代p一个n></text> </g> </g> </svg>。这个假设在非线性双重神经传递函数,基本方程(<一个href="#Eq1">1</一个>)可以写成<年代p一个ncl一个年代年代="equation" id="Eq3"> <svg height="52.650002" id="M51" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 52.650002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,52.65)"> <g transform="translate(72,-29.88)"> <text transform="matrix(1,0,0,-1,111.86,52.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,118.51,57.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,121.98,52.76)"> <tspan style="font-size: 12.50px; " x="42.029999" y="-10.74"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.991817" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,170.13,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,174.97,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n></text> <g> <path d="m 153.22,55.88 47.07,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,153.22,38.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,159.33,35.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,164.64,33.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.049999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3699999" y="-4.9200001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.521476" y="-4.9200001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.684975" y="-4.9200001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.886463" y="-4.9200001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.849998" y="-19.35"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.01614" y="-19.35"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="58.167614" y="-19.35"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.331116" y="-19.35"> </t年代p一个n></text> <g> <path d="m 226.97,47.58 6.2,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,233.17,52.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.918718" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.295967" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.973289" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.01368" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.591461" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="240.95" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="245.11349" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="251.36501" y="0"> )</t年代p一个n></text> </g> </g> </svg></span>这将是以后称为“双重基本方程。“值得注意的是,边界条件<年代vg height="18.7125" id="M52" style="vertical-align:-6.43292pt;width:53.174999px;" version="1.1" viewbox="0 0 53.174999 18.7125" width="53.174999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.7125)"> <g transform="translate(72,-57.03)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> </t年代p一个n></text> <g> <path d="m -61.64,58.32 6.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-55.43,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6268301" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.667219" y="0"> 0</t年代p一个n></text> </g> </g> </svg>是完全任意的。尽管没有理论原因设置边界条件在任何特定的方式,上面的选择是出于观察,它简化了定点适应算法对之前的版本提出了(<一个href="#B3">10</一个>]。</p><p>gydF4y2Ba一般来说,封闭的解(<一个href="#Eq3">3</一个>)可能没有意识到,因此我们应该采取迭代学习算法来寻找一个解决方案。正式,这意味着设计一个算法,生成一个连续的函数<年代vg height="14.6875" id="M53" style="vertical-align:-3.20526pt;width:32.037498px;" version="1.1" viewbox="0 0 32.037498 14.6875" width="32.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.8,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n></text> </g> </g> </svg>,<年代vg height="10.8875" id="M54" style="vertical-align:-0.33858pt;width:38.1875px;" version="1.1" viewbox="0 0 38.1875 10.8875" width="38.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8875)"> <g transform="translate(72,-63.29)"> <text transform="matrix(1,0,0,-1,-71.95,63.67)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6773224" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.71771" y="0"> ℕ</t年代p一个n></text> </g> </g> </svg>,其限制一致的解决方案(<一个href="#Eq3">3</一个>)。产生一系列的方法是采用定点算法:<年代p一个ncl一个年代年代="equation" id="Eq4"> <svg height="52.650002" id="M55" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 52.650002" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,52.65)"> <g transform="translate(72,-29.88)"> <text transform="matrix(1,0,0,-1,105.23,52.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,111.38,49.63)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,126.6,52.76)"> <tspan style="font-size: 12.50px; " x="30.040001" y="7.6999998"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.991817" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,163.64,66.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.530001"> </t年代p一个n></text> <g> <path d="m 162.39,37.64 4.84,0" style="fill:none;stroke:#000000;stroke-width:0.57800001;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,179.69,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,185.81,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,190.65,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.240437" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.892033" y="0"> </t年代p一个n></text> <g> <path d="m 171.76,55.88 49.63,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,171.76,38.33)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,177.87,35.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,183.18,33.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3699999" y="-4.9200001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,196.7,35.21)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.55,38.33)"> <tspan style="font-size: 12.50px; " x="12.24" y="4.9200001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.030001" y="-14.43"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.19614" y="-14.43"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.885963" y="-14.43"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="57.926353" y="-14.43"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.177856" y="-14.43"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.555099" y="-14.43"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.232422" y="-14.43"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="95.260307" y="-14.43"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="106.83809" y="-14.43"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="272.57001" y="-14.43"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="276.73349" y="-14.43"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="282.98499" y="-14.43"> )</t年代p一个n></text> </g> </g> </svg></span>figure-of-convergence的学习过程,我们考虑函数的加权的区别<年代vg height="13.6125" id="M56" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>在两个连续的迭代,即<年代p一个ncl一个年代年代="equation" id="Eq5"> <svg height="38.599998" id="M57" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 38.599998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,38.6)"> <g transform="translate(72,-41.12)"> <text transform="matrix(1,0,0,-1,98.5,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,113.68,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,122,63.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.2618876" y="0"> f</t年代p一个n></text> <text transform="matrix(1,0,0,-1,123.31,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.34" y="7.6999998"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,142.4,43.14)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,153.09,61.56)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="10.67"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="13.83"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5" y="6.9200001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,161.74,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,166.59,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.304152" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.644373" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,201.39,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,216.61,54.64)"> <tspan style="font-size: 12.50px; " x="14.53" y="-6.9200001"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.53" y="3.75"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.53" y="6.9099998"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.030001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.75,51.51)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,244.59,54.64)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.528486" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.180082" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.381571" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.54771" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.237534" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.277924" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.529427" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="229.53" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="233.6935" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="239.94499" y="0"> )</t年代p一个n></text> </g> </g> </svg></span>作为最初的猜测,我们假设<年代vg height="14.75" id="M58" style="vertical-align:-3.25793pt;width:59.275002px;" version="1.1" viewbox="0 0 59.275002 14.75" width="59.275002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.75)"> <g transform="translate(72,-60.2)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.8,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.92,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.991817" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.032206" y="0"> 0</t年代p一个n></text> </g> </g> </svg>,尽管<年代vg height="14.3875" id="M59" style="vertical-align:-2.83405pt;width:41.737499px;" version="1.1" viewbox="0 0 41.737499 14.3875" width="41.737499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6648188" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.705208" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba在学习一个逆函数<年代vg height="13.6125" id="M60" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>,数值程序计算实际的非线性函数<年代vg height="13.6125" id="M61" style="vertical-align:-2.34499pt;width:23.674999px;" version="1.1" viewbox="0 0 23.674999 13.6125" width="23.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.678522" y="0"> )</t年代p一个n></text> </g> </g> </svg>通过数值反演。在下一节将会澄清,框架内提出,这样的操作涉及很少的计算工作。</p><h5gydF4y2Baid="subsec2.2">2.2。学习过程的数值实现</h5><p>gydF4y2Ba从实现角度看,该算法(<一个href="#Eq4">4</一个>)需要离散为了获得一个版本适用于在计算机上实现。</p><p>gydF4y2Ba我们选择代表函数<年代vg height="14.6875" id="M62" style="vertical-align:-3.20526pt;width:32.037498px;" version="1.1" viewbox="0 0 32.037498 14.6875" width="32.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.8,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n></text> </g> </g> </svg>通过一个数值向量:在实践中,我们假设的间隔<年代vg height="20.174999" id="M63" style="vertical-align:-6.43292pt;width:59.900002px;" version="1.1" viewbox="0 0 59.900002 20.174999" width="59.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.175)"> <g transform="translate(72,-55.86)"> <text transform="matrix(1,0,0,-1,-71.95,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.041109" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.081497" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.244997" y="0"> </t年代p一个n></text> <g> <path d="m -40.7,57.15 6.2,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <g> <path d="m -34.5,70.71 6.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-34.5,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.201488" y="0"> ]</t年代p一个n></text> </g> </g> </svg>感兴趣的划分<年代vg height="12.3" id="M64" style="vertical-align:-1.29163pt;width:40.625px;" version="1.1" viewbox="0 0 40.625 12.3" width="40.625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.3)"> <g transform="translate(72,-62.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.103384" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.143772" y="0"> 1</t年代p一个n></text> </g> </g> </svg>离散的垃圾箱。这就产生了vector类型表示<年代vg height="16.975" id="M65" style="vertical-align:-2.5707pt;width:61.900002px;" version="1.1" viewbox="0 0 61.900002 16.975" width="61.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.975)"> <g transform="translate(72,-58.42)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7148314" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.75522" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-40.85,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.4479518" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.443072" y="0"> 1</t年代p一个n></text> </g> </g> </svg>支持的输出序列的概率密度函数,在那里<年代vg height="10.5375" id="M66" style="vertical-align:-2.5707pt;width:8.25px;" version="1.1" viewbox="0 0 8.25 10.5375" width="8.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>包含<年代vg height="11.325" id="M67" style="vertical-align:-0.51414pt;width:38.887501px;" version="1.1" viewbox="0 0 38.887501 11.325" width="38.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.325)"> <g transform="translate(72,-62.94)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> 1</t年代p一个n></text> </g> </g> </svg>定期间隔的值在<年代vg height="14.3875" id="M68" style="vertical-align:-2.83405pt;width:14.6px;" version="1.1" viewbox="0 0 14.6 14.3875" width="14.6" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>与spacing-width表示<年代vg height="16.5625" id="M69" style="vertical-align:-4.74141pt;width:17.4625px;" version="1.1" viewbox="0 0 17.4625 16.5625" width="17.4625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5625)"> <g transform="translate(72,-58.75)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。然后<年代vg height="14.6875" id="M70" style="vertical-align:-3.20526pt;width:32.037498px;" version="1.1" viewbox="0 0 32.037498 14.6875" width="32.037498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6875)"> <g transform="translate(72,-60.25)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.8,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n></text> </g> </g> </svg>可能是由一个数值向量<年代vg height="17.762501" id="M71" style="vertical-align:-3.20526pt;width:67.962502px;" version="1.1" viewbox="0 0 67.962502 17.762501" width="67.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,17.7625)"> <g transform="translate(72,-57.79)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.38,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.4479518" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.443072" y="0"> 1</t年代p一个n></text> </g> </g> </svg>现在的神经输入输出转移由离散的关系<年代vg height="16.987499" id="M72" style="vertical-align:-2.58324pt;width:138.14999px;" version="1.1" viewbox="0 0 138.14999 16.987499" width="138.14999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.9875)"> <g transform="translate(72,-58.41)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.616247" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.867746" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.50708" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.54747" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.06,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.4479518" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.443072" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,0.04,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.765083" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,20.16,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.4479518" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.443072" y="0"> 1</t年代p一个n></text> </g> </g> </svg>,即一个数值<我>查表</我>。一个向量的条目<年代vg height="11.5" id="M73" style="vertical-align:-3.20526pt;width:14px;" version="1.1" viewbox="0 0 14 11.5" width="14" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.5)"> <g transform="translate(72,-62.8)"> <text transform="matrix(1,0,0,-1,-71.95,66.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,62.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>可以用一个额外的页脚,也就是说,<年代vg height="12.4625" id="M74" style="vertical-align:-4.37273pt;width:22.5375px;" version="1.1" viewbox="0 0 22.5375 12.4625" width="22.5375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.4625)"> <g transform="translate(72,-62.03)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.8,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.537744" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.575" id="M75" style="vertical-align:-2.26974pt;width:109.6875px;" version="1.1" viewbox="0 0 109.6875 13.575" width="109.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.239957" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.280346" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.281786" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.533287" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.747036" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.998535" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.199783" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.790787" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.004539" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.644592" y="0"> }</t年代p一个n></text> </g> </g> </svg>。的时间间隔<年代vg height="16.5625" id="M76" style="vertical-align:-4.74141pt;width:17.4625px;" version="1.1" viewbox="0 0 17.4625 16.5625" width="17.4625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5625)"> <g transform="translate(72,-58.75)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>与整数<年代vg height="10.325" id="M77" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>并可能被定义为<年代vg height="29.424999" id="M78" style="vertical-align:-6.43292pt;width:102.725px;" version="1.1" viewbox="0 0 102.725 29.424999" width="102.725" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,29.425)"> <g transform="translate(72,-48.46)"> <text transform="matrix(1,0,0,-1,-71.95,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.92,51.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-54.61,63.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.2618876" y="0"> f</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.3,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.328198" y="0"> (</t年代p一个n></text> <g> <path d="m -35.8,63.31 6.2,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-35.8,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.9771538" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.317375" y="0"> </t年代p一个n></text> <g> <path d="m -15.47,49.74 6.2,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-9.27,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> /</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba为了将学习规则(<一个href="#Eq4">4</一个>)到一个版本适用于数值表示,我们应该考虑数值积分微分方程的固有局限性。以下笔记是值得考虑的。(一)<我>选择输出支持</我>:在建随机数生成方法的最终目的是生成随机抽样与期望的概率分布<我>感兴趣的范围内</我>与价值观在一个时间间隔,即被认为是适用于随机样本生成启动的目的。因此,输出范围<年代vg height="20.174999" id="M79" style="vertical-align:-6.43292pt;width:59.900002px;" version="1.1" viewbox="0 0 59.900002 20.174999" width="59.900002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,20.175)"> <g transform="translate(72,-55.86)"> <text transform="matrix(1,0,0,-1,-71.95,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.041109" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.081497" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.244997" y="0"> </t年代p一个n></text> <g> <path d="m -40.7,57.15 6.2,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <g> <path d="m -34.5,70.71 6.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-34.5,62.32)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.201488" y="0"> ]</t年代p一个n></text> </g> </g> </svg>是根据需要自由选择要生成的随机样本。然后,上述向量<年代vg height="10.5375" id="M80" style="vertical-align:-2.5707pt;width:8.25px;" version="1.1" viewbox="0 0 8.25 10.5375" width="8.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>有项<年代vg height="11.025" id="M81" style="vertical-align:-3.2316pt;width:14.425px;" version="1.1" viewbox="0 0 14.425 11.025" width="14.425" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.025)"> <g transform="translate(72,-63.18)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>计算为<年代vg height="18.674999" id="M82" style="vertical-align:-6.43292pt;width:96.4375px;" version="1.1" viewbox="0 0 96.4375 18.674999" width="96.4375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.675)"> <g transform="translate(72,-57.06)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-57.03,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <g> <path d="m -45,58.35 6.21,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,-36.02,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.892513" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.244038" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,0.26,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.575" id="M83" style="vertical-align:-2.26974pt;width:109.6875px;" version="1.1" viewbox="0 0 109.6875 13.575" width="109.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.239957" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.280346" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.281786" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.533287" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.747036" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.998535" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.199783" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.790787" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.004539" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.644592" y="0"> }</t年代p一个n></text> </g> </g> </svg>。(b)<我>输入支持选择</我>:为了防止分母的数量<年代vg height="21.775" id="M84" style="vertical-align:-4.58821pt;width:45px;" version="1.1" viewbox="0 0 45 21.775" width="45" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,21.775)"> <g transform="translate(72,-54.58)"> <text transform="matrix(1,0,0,-1,-71.95,59.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.3,67.71)"> <tspan style="font-size: 6.25px; " x="0" y="0"> ′</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.8,54.99)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.58,59.21)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n></text> </g> </g> </svg>在(<一个href="#Eq4">4</一个>)变得太接近于零,明智的选择是精心选择的支持<年代vg height="11.1" id="M85" style="vertical-align:-0.1881pt;width:14.05px;" version="1.1" viewbox="0 0 14.05 11.1" width="14.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。在本文中,我们考虑输入概率密度函数(对称)高斯或制服,我们集<年代vg height="14.8625" id="M86" style="vertical-align:-3.21404pt;width:90.962502px;" version="1.1" viewbox="0 0 90.962502 14.8625" width="90.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.8625)"> <g transform="translate(72,-60.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.603504" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.643892" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.807392" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.371948" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-23.32,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-18.01,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-8.75,60.23)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-3.44,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ]</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.7" id="M87" style="vertical-align:-3.21404pt;width:45.537498px;" version="1.1" viewbox="0 0 45.537498 14.7" width="45.537498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.7,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-53.91,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ></t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n></text> </g> </g> </svg>。不变的价值<年代vg height="14.3375" id="M88" style="vertical-align:-3.21404pt;width:18.325001px;" version="1.1" viewbox="0 0 18.325001 14.3375" width="18.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>这样选择<年代vg height="14.7" id="M89" style="vertical-align:-3.21404pt;width:74.099998px;" version="1.1" viewbox="0 0 74.099998 14.7" width="74.099998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.52,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-47.11,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-41.8,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.6393328" y="0"> ≫</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.767963" y="0"> 0</t年代p一个n></text> </g> </g> </svg>。值得回顾的是,输入分布的支持可能是任意选择的,因为它不影响输出分布的支持。(c)<我>迭代范围扩展</我>:每个学习步骤后,执行一个仿射规范化操作,线性尺度的条目公认的解决方案<年代vg height="11.5" id="M90" style="vertical-align:-3.20526pt;width:14px;" version="1.1" viewbox="0 0 14 11.5" width="14" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.5)"> <g transform="translate(72,-62.8)"> <text transform="matrix(1,0,0,-1,-71.95,66.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.7,62.92)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>这<年代vg height="15.775" id="M91" style="vertical-align:-4.37273pt;width:70.375px;" version="1.1" viewbox="0 0 70.375 15.775" width="70.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.775)"> <g transform="translate(72,-59.38)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.8,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.537744" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-50.91,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.592442" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.06,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>和<年代vg height="15.775" id="M92" style="vertical-align:-4.37273pt;width:64.5px;" version="1.1" viewbox="0 0 64.5 15.775" width="64.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.775)"> <g transform="translate(72,-59.38)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.8,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.537744" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-47.05,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-25.76,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba为了描述数值算法,下面的操作符被定义为一个通用的查表<年代vg height="16.975" id="M93" style="vertical-align:-2.5707pt;width:139.02499px;" version="1.1" viewbox="0 0 139.02499 16.975" width="139.02499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.975)"> <g transform="translate(72,-58.42)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.115167" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="16.316416" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.567915" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.207249" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.247639" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-20.36,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.4479518" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.443072" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,0.74,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.765083" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,20.86,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.4479518" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.443072" y="0"> 1</t年代p一个n></text> </g> </g> </svg>:<年代p一个ncl一个年代年代="equation" id="Eqx"> <svg height="102.1125" id="M94" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 102.1125" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,102.1125)"> <g transform="translate(72,9.69)"> <text transform="matrix(1,0,0,-1,85.91,50.29)"> <tspan style="font-size: 12.50px; " x="42.380001" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.23" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.18" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.530167" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.393833" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.645332" y="0"> 米</t年代p一个n></text> <text transform="matrix(1,0,0,-1,146.94,45.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,155.29,50.29)"> <tspan style="font-size: 12.50px; " x="89.970001" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="95.82" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="102.77" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.367388" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.586418" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.137749" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.389252" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="69.116585" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.980247" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="80.23175" y="0"> 米</t年代p一个n></text> <text transform="matrix(1,0,0,-1,263.91,45.29)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,272.62,58.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.2618876" y="0"> f</t年代p一个n></text> <text transform="matrix(1,0,0,-1,273.93,50.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,287.27,63.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.7435842" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.738704" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,289.12,50.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∑</t年代p一个n></text> <text transform="matrix(1,0,0,-1,288.28,39.24)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="2.7218721" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.7169924" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,302.39,50.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,308.54,47.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,311.76,50.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,320.79,47.17)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,327.71,50.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-205.50999" y="47.299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-168.45" y="47.299999"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-243.62" y="44.790001"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-238.06866" y="44.790001"> ff</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-230.50435" y="44.790001"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-225.64069" y="44.790001"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-220.08936" y="44.790001"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-214.53802" y="44.790001"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-211.06219" y="44.790001"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-198.32001" y="44.790001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-191.36833" y="44.790001"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-185.817" y="44.790001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-179.5405" y="44.790001"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-174.32674" y="44.790001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,166.45,0.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,175.17,14.08)"> <tspan style="font-size: 8.75px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.2618876" y="0"> f</t年代p一个n></text> <text transform="matrix(1,0,0,-1,176.47,5.5)"> <tspan style="font-size: 12.50px; " x="34.939999" y="-9.5100002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.299999" y="-14.43"> ℎ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.340701" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.392874" y="0"> +</t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.99,16.8)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,234.01,19.93)"> <tspan style="font-size: 12.50px; " x="30.799999" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.990002" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.939999" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.130001" y="4.9200001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.067554" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.543388" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.73" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.893497" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="72.545578" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.885796" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="90.1623" y="0"> )</t年代p一个n></text> <g> <path d="m 211.41,8.63 116.93,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,220.99,-5.07)"> <tspan style="font-size: 12.50px; " x="21.530001" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.719999" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.669998" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.440002" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.629997" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="90.580002" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="108.55" y="-10.57"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.727334" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.278666" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.639999" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.980221" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.707558" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.183388" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="253.13" y="-33.099998"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="257.29349" y="-33.099998"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="263.54501" y="-33.099998"> )</t年代p一个n></text> </g> </g> </svg></span>其中下标<年代vg height="10.7375" id="M95" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>表示<年代vg height="10.7375" id="M96" style="vertical-align:-0.13794pt;width:8.6000004px;" version="1.1" viewbox="0 0 8.6000004 10.7375" width="8.6000004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>输入的向量<年代vg height="13.45" id="M97" style="vertical-align:-2.21957pt;width:72.1875px;" version="1.1" viewbox="0 0 72.1875 13.45" width="72.1875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.530167" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.393833" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.645332" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.372665" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.536167" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="53.487835" y="0"> )</t年代p一个n></text> </g> </g> </svg>和<年代vg height="13.625" id="M98" style="vertical-align:-2.26974pt;width:100.1125px;" version="1.1" viewbox="0 0 100.1125 13.625" width="100.1125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.625)"> <g transform="translate(72,-61.1)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> ff</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.115647" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.979315" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.530645" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.081978" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.557812" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.109142" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.110584" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.062252" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.613583" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="62.890091" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="68.103844" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="73.980247" y="0"> }</t年代p一个n></text> </g> </g> </svg>。的行为“cumsum”操作符如图<一个href="//www.newsama.com/journals/cin/2008/426080/fig2/" target="_blank">2</一个>,它还提供了一个可视化表示的查找表。在实践中,认为数字版本的学习规则(<一个href="#Eq4">4</一个>)写道<年代p一个ncl一个年代年代="equation" id="Eq6"> <svg height="123.5875" id="M99" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 123.5875" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,123.5875)"> <g transform="translate(72,26.87)"> <text transform="matrix(1,0,0,-1,110.03,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.190665" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.442165" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.769163" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,144.06,60.07)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,152.4,63.2)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.3890328" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.429422" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.680922" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-42.369999" y="29.370001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-38.206501" y="29.370001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-29.179335" y="29.370001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-22.927835" y="29.370001"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-14.600837" y="29.370001"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-8.3493366" y="29.370001"> ′</t年代p一个n></text> <text transform="matrix(1,0,0,-1,147.67,30.7)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,166.36,33.83)"> <tspan style="font-size: 12.50px; " x="29.15" y="-10.74"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.3890328" y="0"> =</t年代p一个n></text> <text transform="matrix(1,0,0,-1,202.47,41.44)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <g> <path d="m 185.98,36.95 30.86,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,185.98,25.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,192.1,21.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,197.41,25.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.82,21.95)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,212.67,25.07)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.3600001" y="-8.7600002"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.526138" y="-8.7600002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.215963" y="-8.7600002"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.256351" y="-8.7600002"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.507854" y="-8.7600002"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-102.64" y="22.98"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-98.476501" y="22.98"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-89.449333" y="22.98"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-83.197838" y="22.98"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-74.870834" y="22.98"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,144.06,-1.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,162.75,2.09)"> <tspan style="font-size: 12.50px; " x="60.799999" y="2.52"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.3890328" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.41692" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.96825" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.219751" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.947086" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.810753" y="0"> u</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.062252" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.989998" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="74.241501" y="0"> ′</t年代p一个n></text> <text transform="matrix(1,0,0,-1,240.6,-1.04)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,255.82,-0.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.2700005" y="-2.52"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-145.78999" y="21.83"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-141.6265" y="21.83"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-132.59933" y="21.83"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-126.34783" y="21.83"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-118.02084" y="21.83"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,144.06,-25.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,162.75,-22.26)"> <tspan style="font-size: 12.50px; " x="56.529999" y="2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="63.720001" y="3.5527137e-015"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.3890328" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.41692" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.96825" y="0"> ff</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.532566" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.396233" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.947563" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="47.498898" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.974731" y="0"> e</t年代p一个n></text> <text transform="matrix(1,0,0,-1,232.73,-25.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,247.94,-22.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ;</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.5638351" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.12839" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,271.32,-25.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,276.63,-22.26)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2012482" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,291.09,-25.38)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,296.41,-24.77)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.2700005" y="-2.51"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="177.71001" y="-44.209999"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="181.8735" y="-44.209999"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="188.125" y="-44.209999"> )</t年代p一个n></text> </g> </g> </svg></span>在象征<年代vg height="8.4750004" id="M100" style="vertical-align:-0.16302pt;width:18.8125px;" version="1.1" viewbox="0 0 18.8125 8.4750004" width="18.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,8.475)"> <g transform="translate(72,-65.22)"> <text transform="matrix(1,0,0,-1,-71.95,65.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.3890328" y="0"> =</t年代p一个n></text> </g> </g> </svg>表示向量赋值和值<年代vg height="13.425" id="M101" style="vertical-align:-4.74141pt;width:14.8625px;" version="1.1" viewbox="0 0 14.8625 13.425" width="14.8625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.425)"> <g transform="translate(72,-61.26)"> <text transform="matrix(1,0,0,-1,-71.95,66.04)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65,62.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>表示的向量<年代vg height="11.325" id="M102" style="vertical-align:-0.51414pt;width:38.887501px;" version="1.1" viewbox="0 0 38.887501 11.325" width="38.887501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.325)"> <g transform="translate(72,-62.94)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.415719" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.755939" y="0"> 1</t年代p一个n></text> </g> </g> </svg>条目包含的值<年代vg height="16.6" id="M103" style="vertical-align:-4.74141pt;width:28.700001px;" version="1.1" viewbox="0 0 28.700001 16.6" width="28.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>对应的值<年代vg height="10.5375" id="M104" style="vertical-align:-2.5707pt;width:8.25px;" version="1.1" viewbox="0 0 8.25 10.5375" width="8.25" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.5375)"> <g transform="translate(72,-63.57)"> <text transform="matrix(1,0,0,-1,-71.95,66.19)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>可以表示为,其条目<年代vg height="12.925" id="M105" style="vertical-align:-4.74141pt;width:19.75px;" version="1.1" viewbox="0 0 19.75 12.925" width="19.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.340992" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.575" id="M106" style="vertical-align:-2.26974pt;width:109.6875px;" version="1.1" viewbox="0 0 109.6875 13.575" width="109.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.239957" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.280346" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.281786" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.533287" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.747036" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.998535" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.199783" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.790787" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.004539" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.644592" y="0"> }</t年代p一个n></text> </g> </g> </svg>。</p><d我v class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-ba79a897bc90f0f8c01e164b4da54b3a"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.002.jpg"> <br> <strong></strong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-ba79a897bc90f0f8c01e164b4da54b3a partial-carousel-thumbnail"> <button aria-label="Slide to " class="partial-carousel-dot"><img loading="lazy" alt="" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.002_th.jpg"><br><strong></strong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-ba79a897bc90f0f8c01e164b4da54b3a partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图2</年代p一个n><一个一个r我一个-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2008/426080/fig2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>行为“cumsum”操作符的查找表。</td></tr></tbody> </table> </div> </div> </div> </div> <p>look-up-tables条目而言,学习放松指数<年代vg height="14.65" id="M107" style="vertical-align:-3.20526pt;width:25.1625px;" version="1.1" viewbox="0 0 25.1625 14.65" width="25.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.65)"> <g transform="translate(72,-60.28)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.77,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>的定义(<一个href="#Eq5">5</一个>)可以近似<年代p一个ncl一个年代年代="equation" id="Eq7"> <svg height="50.700001" id="M108" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 50.700001" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,50.7)"> <g transform="translate(72,-31.44)"> <text transform="matrix(1,0,0,-1,112.36,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,127.54,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,135.86,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≈</t年代p一个n></text> <text transform="matrix(1,0,0,-1,151.86,63.76)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,147.9,41.27)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,148.42,34.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.7435842" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.738704" y="0"> 0</t年代p一个n></text> <text transform="matrix(1,0,0,-1,164.05,54.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="10.67"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="13.83"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5" y="6.9200001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,172.71,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="6.537744" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.26,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,204.76,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3497438" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.344864" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="14.720864" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="16.908863" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,226.91,54.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="10.67"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="13.83"> |</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="2.5" y="6.9200001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,235.52,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,239.86,42.5)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,244.25,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,253.28,44.69)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,258.12,47.82)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.166139" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.84346" y="0"> ≥</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.88385" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.135349" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="216" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="220.1635" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="226.41499" y="0"> )</t年代p一个n></text> </g> </g> </svg></span></p> <h5 id="subsec2.3">2.3。使用神经系统生成模型</h5><p>gydF4y2Ba当一个合适的双神经系统所描述的移情<年代vg height="13.6125" id="M109" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>一直学习,它可以有效地用于生成随机样本来自所需的统计分布。可用输入样本的数量(恰逢生成输出样本的数量)是以后用<年代vg height="12.925" id="M110" style="vertical-align:-1.90608pt;width:12.325px;" version="1.1" viewbox="0 0 12.325 12.925" width="12.325" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,63.61)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。这里的困难是,输入样本<年代vg height="7.1624999" id="M111" style="vertical-align:-0.11285pt;width:8.7250004px;" version="1.1" viewbox="0 0 8.7250004 7.1624999" width="8.7250004" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,7.1625)"> <g transform="translate(72,-66.27)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>众所周知,输出的产品陈列室吗<年代vg height="9.8625002" id="M112" style="vertical-align:-2.29482pt;width:7.875px;" version="1.1" viewbox="0 0 7.875 9.8625002" width="7.875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.8625)"> <g transform="translate(72,-64.11)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>应该是作为计算<年代vg height="13.6125" id="M113" style="vertical-align:-2.34499pt;width:54.9375px;" version="1.1" viewbox="0 0 54.9375 13.6125" width="54.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6648188" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.705208" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.644373" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.807873" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.684521" y="0"> )</t年代p一个n></text> </g> </g> </svg>。然而,不像在<一个href="#B3">10</一个>),这个函数<年代vg height="13.6125" id="M114" style="vertical-align:-2.34499pt;width:23.674999px;" version="1.1" viewbox="0 0 23.674999 13.6125" width="23.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.9391651" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.102664" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.678522" y="0"> )</t年代p一个n></text> </g> </g> </svg>不知道在目前设定为逆<年代vg height="13.6125" id="M115" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>只有学会了。然而,函数的反演<年代vg height="13.6125" id="M116" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>不需要为了使用双神经系统生成模型,提供了一个适当的使用查表代表<年代vg height="13.6125" id="M117" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>是由。首先,它是必要的生产实现<年代vg height="14.775" id="M118" style="vertical-align:-3.2316pt;width:27.75px;" version="1.1" viewbox="0 0 27.75 14.775" width="27.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.07,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.85,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.575" id="M119" style="vertical-align:-2.26974pt;width:90.650002px;" version="1.1" viewbox="0 0 90.650002 13.575" width="90.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3517642" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.392153" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.393593" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.645094" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.858845" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.437344" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.651093" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.415939" y="0"> }</t年代p一个n></text> </g> </g> </svg>来自available-generator分布<年代vg height="14.7" id="M120" style="vertical-align:-3.21404pt;width:29.2875px;" version="1.1" viewbox="0 0 29.2875 14.7" width="29.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.52,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>(有,例如,零均值高斯分布或均匀概率密度函数)不等<年代vg height="11.1" id="M121" style="vertical-align:-0.1881pt;width:14.05px;" version="1.1" viewbox="0 0 14.05 11.1" width="14.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。关于代的输入样本,因为它们是通过使用一个可用的生成器生成的范围是广泛的<年代vg height="11.1" id="M122" style="vertical-align:-0.1881pt;width:14.05px;" version="1.1" viewbox="0 0 14.05 11.1" width="14.05" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,一些生成输入样本将必然丢弃。丢弃的输入样本可能被量化。让我们表示的<年代vg height="14.7" id="M123" style="vertical-align:-3.21404pt;width:30.924999px;" version="1.1" viewbox="0 0 30.924999 14.7" width="30.924999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.52,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.21,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>输入的累积分布函数,即<年代p一个ncl一个年代年代="equation" id="EqH"> <svg height="36.849998" id="M124" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 36.849998" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,36.85)"> <g transform="translate(72,-42.52)"> <text transform="matrix(1,0,0,-1,154.41,54.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,161.83,50.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,167.14,54.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,185.82,62.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.2618876" y="0"> f</t年代p一个n></text> <text transform="matrix(1,0,0,-1,187.13,54.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.34" y="7.6900001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,207.47,68.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="-1.25" y="25.52"> −</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.74512" y="25.52"> ∞</t年代p一个n></text> <text transform="matrix(1,0,0,-1,222.9,54.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,229.02,50.94)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,234.33,54.06)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.0769377" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.240437" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.892033" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.88097" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="239.78999" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="243.95351" y="0"> 9</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="250.205" y="0"> )</t年代p一个n></text> </g> </g> </svg></span>这一比率<年代vg height="9.875" id="M125" style="vertical-align:-2.29482pt;width:7.9749999px;" version="1.1" viewbox="0 0 7.9749999 9.875" width="7.9749999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,9.875)"> <g transform="translate(72,-64.1)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 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x="62.676491" y="-8.7299995"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.003487" y="-8.7299995"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="75.867157" y="-8.7299995"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="81.418488" y="-8.7299995"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="91.120811" y="-8.7299995"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="97.372314" y="-8.7299995"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="100.84815" y="-8.7299995"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="106.39948" y="-8.7299995"> 年代</t年代p一个n></text> <g> <path d="m 142.05,57.81 96.97,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,142.05,45.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> #</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> g</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.315455" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="17.866787" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.118286" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.669619" y="0"> r</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.808113" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.359444" y="0"> t</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.835278" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="48.386608" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.713608" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.577274" y="0"> 一个</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="67.128609" y="0"> 米</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.830933" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="83.082436" y="0"> l</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="86.558266" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="92.109604" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="101.64" y="-8.75"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="113.66788" y="-8.75"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="122.69505" y="-8.75"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="134.03528" y="-8.75"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="140.28677" y="-8.75"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,289.78,51.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,295.09,49.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3600001" y="-4.9200001"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,311.7,51.56)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,317.02,49.76)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.6800003" y="-4.9200001"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="150.85001" y="-4.9200001"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="155.0135" y="-4.9200001"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="161.265" y="-4.9200001"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="167.51649" y="-4.9200001"> )</t年代p一个n></text> </g> </g> </svg></span>的参数<年代vg height="14.3375" id="M127" style="vertical-align:-3.21404pt;width:18.325001px;" version="1.1" viewbox="0 0 18.325001 14.3375" width="18.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg><i></i>可能因此被选择为了调整的价值吗<年代vg height="14.7" id="M128" style="vertical-align:-3.21404pt;width:36.587502px;" version="1.1" viewbox="0 0 36.587502 14.7" width="36.587502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7)"> <g transform="translate(72,-60.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2765059" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-52.26,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-46.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> </g> </g> </svg>设计的需要。然后,需要地址正确的学会了查找表中的值<年代vg height="16.987499" id="M129" style="vertical-align:-2.58324pt;width:138.14999px;" version="1.1" viewbox="0 0 138.14999 16.987499" width="138.14999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.9875)"> <g transform="translate(72,-58.41)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.616247" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.867746" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.50708" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.54747" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-21.06,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.4479518" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.443072" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,0.04,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ×</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.765083" y="0"> ℝ</t年代p一个n></text> <text transform="matrix(1,0,0,-1,20.16,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="7.4479518" y="0"> +</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="13.443072" y="0"> 1</t年代p一个n></text> </g> </g> </svg><i></i>对应的值<年代vg height="14.775" id="M130" style="vertical-align:-3.2316pt;width:27.75px;" version="1.1" viewbox="0 0 27.75 14.775" width="27.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.07,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.85,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.575" id="M131" style="vertical-align:-2.26974pt;width:90.650002px;" version="1.1" viewbox="0 0 90.650002 13.575" width="90.650002" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.575)"> <g transform="translate(72,-61.14)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.3517642" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="19.392153" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.393593" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.645094" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.858845" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="51.437344" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.651093" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.415939" y="0"> }</t年代p一个n></text> </g> </g> </svg>通过指针<年代vg height="14.775" id="M132" style="vertical-align:-3.2316pt;width:111.6125px;" version="1.1" viewbox="0 0 111.6125 14.775" width="111.6125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.775)"> <g transform="translate(72,-60.18)"> <text transform="matrix(1,0,0,-1,-71.95,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.85,60.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-60.16,63.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.040389" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.041828" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.293329" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.494577" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="35.746078" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="40.959827" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="55.550831" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="60.752075" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.392128" y="0"> }</t年代p一个n></text> </g> </g> </svg>这样<年代vg height="14.275" id="M133" style="vertical-align:-5.39853pt;width:47.962502px;" version="1.1" viewbox="0 0 47.962502 14.275" width="47.962502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.275)"> <g transform="translate(72,-60.58)"> <text transform="matrix(1,0,0,-1,-71.95,66.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.8,62.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.23,60.7)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.81,66.01)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ≈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-36.9,62.89)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。这意味着搜索,在整个查表,最亲密的的价值<我></我><年代vg height="13.6125" id="M134" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>样品<年代vg height="11.05" id="M135" style="vertical-align:-3.2316pt;width:12.75px;" version="1.1" viewbox="0 0 12.75 11.05" width="12.75" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.07,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。这样的操作应该执行在一个有效的方法。最后,所需的设置<年代vg height="15.875" id="M136" style="vertical-align:-3.2316pt;width:26.9px;" version="1.1" viewbox="0 0 26.9 15.875" width="26.9" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,15.875)"> <g transform="translate(72,-59.3)"> <text transform="matrix(1,0,0,-1,-71.95,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.6013441" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.00144" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.75,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.53,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> }</t年代p一个n></text> </g> </g> </svg>输出样本,大约分布的概率密度函数<年代vg height="16.6" id="M137" style="vertical-align:-4.74141pt;width:28.700001px;" version="1.1" viewbox="0 0 28.700001 16.6" width="28.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>,可以通过设置<年代vg height="18.575001" id="M138" style="vertical-align:-5.39853pt;width:152.21249px;" version="1.1" viewbox="0 0 152.21249 18.575001" width="152.21249" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,18.575)"> <g transform="translate(72,-57.14)"> <text transform="matrix(1,0,0,-1,-72.35,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0.400096" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-59.06,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ∶</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.3890328" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.429422" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-34.43,59.45)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-30.86,57.26)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-27.92,62.57)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.2137508" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.565515" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.605904" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.607344" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="36.858845" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="42.072594" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.651093" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.864845" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="71.629684" y="0"> }</t年代p一个n></text> </g> </g> </svg>,在那里<年代vg height="13.725" id="M139" style="vertical-align:-5.39853pt;width:16.012501px;" version="1.1" viewbox="0 0 16.012501 13.725" width="16.012501" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.725)"> <g transform="translate(72,-61.02)"> <text transform="matrix(1,0,0,-1,-71.95,66.45)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.75,63.32)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.18,61.13)"> <tspan style="font-size: 6.25px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>表示<年代vg height="11.05" id="M140" style="vertical-align:-3.2316pt;width:10.525px;" version="1.1" viewbox="0 0 10.525 11.05" width="10.525" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.05)"> <g transform="translate(72,-63.16)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-66.85,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>查找表的条目<年代vg height="13.9125" id="M141" style="vertical-align:-2.58324pt;width:32.674999px;" version="1.1" viewbox="0 0 32.674999 13.9125" width="32.674999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.9125)"> <g transform="translate(72,-60.87)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.616247" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.867746" y="0"> )</t年代p一个n></text> </g> </g> </svg>。(评论MATLAB代码可以请求。)</p><h4gydF4y2Baid="computer-based-numerical-experiments">3所示。基于计算机的数值试验</h4><p>gydF4y2Ba在接下来的实验中,我们考虑生成随机单变量和样品感兴趣的规定范围内规定的密度函数,假设一个原型高斯随机数生成器是可用的。原型高斯分布为零均值和统一的方差。的参数<年代vg height="14.3375" id="M142" style="vertical-align:-3.21404pt;width:18.325001px;" version="1.1" viewbox="0 0 18.325001 14.3375" width="18.325001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3375)"> <g transform="translate(72,-60.53)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-62.7,60.66)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在所有的实验设置为1,对应于一个比<年代vg height="13.55" id="M143" style="vertical-align:-2.29482pt;width:70.337502px;" version="1.1" viewbox="0 0 70.337502 13.55" width="70.337502" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.7398367" y="0"> ≈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.780226" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.031727" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.157476" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.408978" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.660477" y="0"> 7</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.911976" y="0"> 3</t年代p一个n></text> </g> </g> </svg>生成的输入样本,允许保留约70%。实验运行在1.86 GHz, 512 mb ram的平台。</p><h5gydF4y2Baid="subsec3.1">3.1。实验“bi-Gaussian”分布</h5><p>gydF4y2Ba第一个案例的生成一个随机变量问题定义为“bi-Gaussian”分布<年代p一个ncl一个年代年代="equation" id="Eq8"> <svg height="131.83749" id="M144" preserveaspectratio="xMaxYMin" style="vertical-align:-0pt;width:700.9375px;" version="1.1" viewbox="0 0 700.9375 131.83749" width="700.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,131.8375)"> <g transform="translate(72,33.47)"> <text transform="matrix(1,0,0,-1,95.3,40.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,104.48,37.11)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,109.35,37.72)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.8600001" y="-2.51"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.06" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.379999" y="-2.51"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="34.619999" y="-9.7700005"> 1</t年代p一个n></text> <g> <path d="m 143.97,43.36 6.25,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,143.97,31.48)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.4400001" y="-8.75"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.51" y="-16.01"> 1</t年代p一个n></text> <g> <path d="m 156.77,43.36 37.67,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,156.77,27.48)"> <tspan style="font-size: 12.50px; " x="0" y="0"> √</t年代p一个n></text> <g> <path d="m 168.37,39.23 13.86,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,168.37,26.87)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.853324" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,189.57,23.75)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,197.72,40.23)"> <tspan style="font-size: 12.50px; " x="34.060001" y="-9.5100002"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.129829" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.293329" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.43" y="-14.43"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.407154" y="-14.43"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.747375" y="-14.43"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,267.08,51.53)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,271.96,49.74)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,279.56,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <g> <path d="m 231.78,43.36 52.66,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,248.88,30.05)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,262.47,34.55)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.21"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,285.63,40.23)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-113.91" y="57.16"> +</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-85.660004" y="49.91"> 1</t年代p一个n></text> <g> <path d="m 184.26,-13.81 37.67,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,184.26,-29.69)"> <tspan style="font-size: 12.50px; " x="0" y="0"> √</t年代p一个n></text> <g> <path d="m 195.86,-17.93 13.86,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,195.86,-30.29)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.853324" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,217.06,-33.42)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,225.21,-16.93)"> <tspan style="font-size: 12.50px; " x="34.060001" y="-9.5"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="0" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="5.551332" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.802832" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.129829" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.293329" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="41.43" y="-14.42"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.407154" y="-14.42"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="61.747375" y="-14.42"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,294.58,-5.64)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,299.45,-7.43)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,307.05,8.87)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <g> <path d="m 259.27,-13.81 52.66,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path> </g> <text transform="matrix(1,0,0,-1,276.37,-27.11)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.2515001" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,289.96,-22.61)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.2200003"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,313.12,-16.93)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ]</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="154.75" y="-33.07"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="158.9135" y="-33.07"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="165.16499" y="-33.07"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="171.4165" y="-33.07"> )</t年代p一个n></text> </g> </g> </svg></span>可能认为相当不对称形状。</p><p>gydF4y2Ba下面给出的数值结果与价值观<年代vg height="14.6" id="M145" style="vertical-align:-3.13504pt;width:54.3125px;" version="1.1" viewbox="0 0 54.3125 14.6" width="54.3125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.26,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.405136" y="0"> 3</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.7875" id="M146" style="vertical-align:-3.13504pt;width:65.362503px;" version="1.1" viewbox="0 0 65.362503 14.7875" width="65.362503" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.7875)"> <g transform="translate(72,-60.17)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.34,60.22)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.99,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="20.592442" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.843941" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.96969" y="0"> 5</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.6" id="M147" style="vertical-align:-3.13504pt;width:42.599998px;" version="1.1" viewbox="0 0 42.599998 14.6" width="42.599998" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.61,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.26,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 1</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.6" id="M148" style="vertical-align:-3.13504pt;width:54.662498px;" version="1.1" viewbox="0 0 54.662498 14.6" width="54.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.6)"> <g transform="translate(72,-60.32)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-64.34,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-55.99,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="12.027886" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.279387" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.405136" y="0"> 8</t年代p一个n></text> </g> </g> </svg>。感兴趣的时间间隔设置为输出变量<年代vg height="14.4125" id="M149" style="vertical-align:-2.83405pt;width:87.662498px;" version="1.1" viewbox="0 0 87.662498 14.4125" width="87.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.4125)"> <g transform="translate(72,-60.47)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.041109" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.081497" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.244997" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.809551" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="46.06105" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="49.186802" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="59.601803" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="65.853302" y="0"> ]</t年代p一个n></text> </g> </g> </svg>。生成的输出样本数量的总数<年代vg height="13.1875" id="M150" style="vertical-align:-1.90608pt;width:70.787498px;" version="1.1" viewbox="0 0 70.787498 13.1875" width="70.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.1875)"> <g transform="translate(72,-61.45)"> <text transform="matrix(1,0,0,-1,-71.95,63.4)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.228174" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.268562" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.520063" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.771564" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.023064" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.274563" y="0"> 9</t年代p一个n></text> </g> </g> </svg>。点的数量的函数<年代vg height="13.6125" id="M151" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>是计算<年代vg height="10.9125" id="M152" style="vertical-align:-0.17555pt;width:64.074997px;" version="1.1" viewbox="0 0 64.074997 10.9125" width="64.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.103384" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.143772" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.395271" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.646774" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.898273" y="0"> 0</t年代p一个n></text> </g> </g> </svg>。通过运行学习算法获得的结果(<一个href="#Eq6">7</一个>)如图<一个href="//www.newsama.com/journals/cin/2008/426080/fig3/" target="_blank">3</一个>。该指数的值<年代vg height="14.65" id="M153" style="vertical-align:-3.20526pt;width:25.1625px;" version="1.1" viewbox="0 0 25.1625 14.65" width="25.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.65)"> <g transform="translate(72,-60.28)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.77,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>显示5次迭代后定点算法可能会停止。在图<一个href="//www.newsama.com/journals/cin/2008/426080/fig3/" target="_blank">3</一个>,直方图估计(50箱)的生成高斯数据和bi-Gaussian输出——取得了双系统可以观察到。</p><d我v class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-9fd5bac3c022a64f32b828cfd50cb9e1"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.003a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.003b.jpg"> <br> <strong>(b)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(c)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.003c.jpg"> <br> <strong>(c)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(d)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.003d.jpg"> <br> <strong>(d)</年代trong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-9fd5bac3c022a64f32b828cfd50cb9e1 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.003a_th.jpg"><br><strong>(一)</年代trong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.003b_th.jpg"><br><strong>(b)</年代trong></button> <button aria-label="Slide to (c) " class="partial-carousel-dot"><img loading="lazy" alt="(c)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.003c_th.jpg"><br><strong>(c)</年代trong></button> <button aria-label="Slide to (d) " class="partial-carousel-dot"><img loading="lazy" alt="(d)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.003d_th.jpg"><br><strong>(d)</年代trong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-9fd5bac3c022a64f32b828cfd50cb9e1 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图3</年代p一个n><一个一个r我一个-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2008/426080/fig3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>由于双神经系统适应高斯输入和bi-Gaussian输出。</td></tr></tbody> </table> </div> </div> </div> </div> <p>独立重复试验累积的结果。算法的迭代次数(<一个href="#Eq6">7</一个>)设置为10,而其他数据保持不变之前的单道实验。数量<年代vg height="10.325" id="M154" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>点的功能<年代vg height="13.6125" id="M155" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg><i></i>计算范围从200年<我></我>到2000年<我></我>步骤200,为了获得一些关于算法的灵敏度信息的选择分域的数量<年代vg height="14.3875" id="M156" style="vertical-align:-2.83405pt;width:14.6px;" version="1.1" viewbox="0 0 14.6 14.3875" width="14.6" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg><i></i>和数量的影响<我></我><年代vg height="10.325" id="M157" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>在算法的计算复杂度。特别是,该算法对数字的敏感性<年代vg height="10.325" id="M158" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>通过差异指数DSC测量计算如下。(a)的基于直方图估计概率密度函数生成的样本计算箱子的数量等于50。这样的估计是用的离散值<年代vg height="16.5625" id="M159" style="vertical-align:-4.74141pt;width:18.9625px;" version="1.1" viewbox="0 0 18.9625 16.5625" width="18.9625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.5625)"> <g transform="translate(72,-58.75)"> <text transform="matrix(1,0,0,-1,-65.07,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> ̂</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="-6.8766499" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.340992" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.7" id="M160" style="vertical-align:-2.26974pt;width:110.8875px;" version="1.1" viewbox="0 0 110.8875 13.7" width="110.8875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7)"> <g transform="translate(72,-61.04)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3397408" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.380131" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.381571" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.633072" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.846821" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.09832" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.299568" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.890572" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="70.104324" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="76.35582" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="82.607323" y="0"> }</t年代p一个n></text> </g> </g> </svg>。(b)的真实值概率密度函数<我></我><年代vg height="16.6" id="M161" style="vertical-align:-4.74141pt;width:28.700001px;" version="1.1" viewbox="0 0 28.700001 16.6" width="28.700001" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,16.6)"> <g transform="translate(72,-58.72)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,60.37)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.739357" y="0"> )</t年代p一个n></text> </g> </g> </svg>在对应的直方图bin-centers计算。离散值的概率密度函数是用<年代vg height="12.925" id="M162" style="vertical-align:-4.74141pt;width:20.7875px;" version="1.1" viewbox="0 0 20.7875 12.925" width="20.7875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,12.925)"> <g transform="translate(72,-61.66)"> <text transform="matrix(1,0,0,-1,-71.95,66.44)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,63.31)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.340992" y="0"> </t年代p一个n></text> </g> </g> </svg>,<年代vg height="13.7" id="M163" style="vertical-align:-2.26974pt;width:113.5px;" version="1.1" viewbox="0 0 113.5 13.7" width="113.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.7)"> <g transform="translate(72,-61.04)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.3397408" y="0"> ∈</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="21.380131" y="0"> {</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.381571" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="33.633072" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.846821" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="45.09832" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.299568" y="0"> …</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="66.978569" y="0"> ,</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="72.179817" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="78.43132" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="84.682816" y="0"> }</t年代p一个n></text> </g> </g> </svg>。(c) weighted-square-difference-type差异指数计算的表达式<年代vg height="27.325001" id="M164" style="vertical-align:-4.74141pt;width:179.45px;" version="1.1" viewbox="0 0 179.45 27.325001" width="179.45" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,27.325)"> <g transform="translate(72,-50.14)"> <text transform="matrix(1,0,0,-1,-71.95,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> D</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.978834" y="0"> C</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-44.16,63.5)"> <tspan style="font-size: 8.75px; " x="0" y="0"> d</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="8.2618876" y="0"> f</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-42.85,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.34" y="0.029999999"> ∑</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-18.08,61.15)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.3759999" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="0" y="9.9300003"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.11344" y="9.9300003"> =</t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="10.10856" y="9.9300003"> 1</t年代p一个n></text> <text transform="matrix(1,0,0,-1,-3.1,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.040149" y="0"> ̂</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.176002" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,7.18,51.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.340992" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,18.91,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.340221" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,36.37,51.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.340992" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,45.32,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> )</t年代p一个n></text> <text transform="matrix(1,0,0,-1,49.48,60.09)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,54.36,54.92)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,60.47,51.79)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 8.75px; " x="4.340992" y="0"> </t年代p一个n></text> </g> </g> </svg>。</p><p>gydF4y2Ba生成样本的平均数对68250年和68290年之间的变化。结果在表中进行了总结<一个href="//www.newsama.com/journals/cin/2008/426080/tab1/" target="_blank"></a>和<一个href="//www.newsama.com/journals/cin/2008/426080/tab2/" target="_blank"></a>。学习所需的表显示平均运行时(用秒表示),生成所需的运行时平均样本(使用学习系统的生成模型)和平均DSC索引值。容易理解,计算复杂度由于学习阶段的数量取决于点用于近似非线性转移<年代vg height="13.6125" id="M165" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>正如预期的那样,而计算复杂度仅略取决于由于生成阶段<年代vg height="10.325" id="M166" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。方法的灵敏度差异指数衡量DSC高对低参数的值<年代vg height="10.325" id="M167" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>,而变得很低的值<年代vg height="10.325" id="M168" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>大于1000。</p><d我v class="floats-partial-section partial-other-wrapper" data-section="tab1"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表1</年代p一个n><一个一个r我一个-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2008/426080/tab1/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 对实验的平均结果bi-Gaussian随机数生成;平均计算在100个独立的实验中,当算法(<一个href="#Eq6">7</一个>)迭代10次(第一批结果)。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/cin/2008/426080/tab1" target="_blank" aria-label="View full page"></a> </div> </div> <div class="floats-partial-section partial-other-wrapper" data-section="tab2"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表2</年代p一个n><一个一个r我一个-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2008/426080/tab2/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 对实验的平均结果bi-Gaussian随机数生成;平均计算在100个独立的实验中,当算法(<一个href="#Eq6">7</一个>)迭代10次(第二批的结果)。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/cin/2008/426080/tab2" target="_blank" aria-label="View full page"></a> </div> </div> <h5 id="subsec3.2">3.2。广义高斯分布的实验</h5><p>gydF4y2Ba随机抽样生成的第二个例子是关于一个广义高斯分布(<一个href="#B14">13</一个>]:<gydF4y2Ba年代p一个ncl一个年代年代="equation" id="Eq9"> <svg height="13.5625" id="M171" preserveaspectratio="xMaxYMin" style="vertical-align:-2.21957pt;width:43.662498px;" version="1.1" viewbox="0 0 43.662498 13.5625" width="43.662498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5625)"> <g transform="translate(72,-61.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.863667" y="0"> 我</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="8.3395014" y="0"> n</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.591001" y="0"> h</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.917999" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.081497" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="30.657356" y="0"> )</t年代p一个n></text> </g> </g> </svg></span>在哪里<年代vg height="13.5625" id="M172" style="vertical-align:-2.21957pt;width:45.375px;" version="1.1" viewbox="0 0 45.375 13.5625" width="45.375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.5625)"> <g transform="translate(72,-61.15)"> <text transform="matrix(1,0,0,-1,-71.95,63.41)"> <tspan style="font-size: 12.50px; " x="0" y="0"> 年代</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.863667" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.414999" y="0"> c</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.041828" y="0"> h</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="24.293329" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.456827" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.032684" y="0"> )</t年代p一个n></text> </g> </g> </svg>表示双曲正弦函数和<年代vg height="19.674999" id="M173" style="vertical-align:-4.74141pt;width:133.8px;" version="1.1" viewbox="0 0 133.8 19.674999" width="133.8" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,19.675)"> <g transform="translate(72,-56.26)"> <text transform="matrix(1,0,0,-1,-71.95,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-65.84,57.91)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-61,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="18.00432" y="0"> ∝</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.120209" y="0"> e</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.671539" y="0"> x</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="43.923038" y="0"> p</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="52.262539" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.426041" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="64.990593" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,11.42,66.03)"> <tspan style="font-size: 8.75px; " x="0" y="0"> 2</t年代p一个n></text> <text transform="matrix(1,0,0,-1,16.29,61.03)"> <tspan style="font-size: 12.50px; " x="0" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="4.1634989" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.364987" y="0"> )</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.528486" y="0"> )</t年代p一个n></text> </g> </g> </svg>表示双曲余弦函数的倒数(即双曲正割函数)目前的广义高斯分布(GGD)标准GGD模型中遇到不同的文学(见,例如,<一个href="#B7">14</一个>])。它属于一般的指数族分布类型<年代vg height="13.45" id="M174" style="vertical-align:-2.21957pt;width:24.2875px;" version="1.1" viewbox="0 0 24.2875 13.45" width="24.2875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.45)"> <g transform="translate(72,-61.24)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="7.414279" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.577778" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.153636" y="0"> )</t年代p一个n></text> </g> </g> </svg>,<年代vg height="10.8625" id="M175" style="vertical-align:-0.13794pt;width:36.5px;" version="1.1" viewbox="0 0 36.5 10.8625" width="36.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.8625)"> <g transform="translate(72,-63.31)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.802592" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.842981" y="0"> 1</t年代p一个n></text> </g> </g> </svg>满足适当条件的兼容性。分布(<一个href="#Eq9">12</一个>)以及GGD (<一个href="#B7">14</一个>)属于上述指数的家庭。</p><p>gydF4y2Ba下面给出的数值结果与价值观<年代vg height="13.55" id="M176" style="vertical-align:-2.29482pt;width:48.5625px;" version="1.1" viewbox="0 0 48.5625 13.55" width="48.5625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="11.077658" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="23.118048" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="29.369547" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.495296" y="0"> 8</t年代p一个n></text> </g> </g> </svg>,<年代vg height="11.125" id="M177" style="vertical-align:-0.20064pt;width:47.5px;" version="1.1" viewbox="0 0 47.5 11.125" width="47.5" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.125)"> <g transform="translate(72,-63.1)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.227454" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.267843" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.519342" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.645094" y="0"> 5</t年代p一个n></text> </g> </g> </svg>,<年代vg height="14.3875" id="M178" style="vertical-align:-2.83405pt;width:75.9375px;" version="1.1" viewbox="0 0 75.9375 14.3875" width="75.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.041109" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.081497" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.244997" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.809551" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.224552" y="0"> 4</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.476051" y="0"> ]</t年代p一个n></text> </g> </g> </svg>。感兴趣的时间间隔设置为输出变量<年代vg height="13.25" id="M179" style="vertical-align:-1.90608pt;width:70.787498px;" version="1.1" viewbox="0 0 70.787498 13.25" width="70.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.25)"> <g transform="translate(72,-61.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.228174" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.268562" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.520063" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.771564" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.023064" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.274563" y="0"> 5</t年代p一个n></text> </g> </g> </svg>。生成的输出样本数量的总数<年代vg height="13.6125" id="M180" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>。点的数量的函数<我></我><年代vg height="10.9125" id="M181" style="vertical-align:-0.17555pt;width:64.074997px;" version="1.1" viewbox="0 0 64.074997 10.9125" width="64.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.103384" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.143772" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.395271" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.646774" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.898273" y="0"> 0</t年代p一个n></text> </g> </g> </svg>是计算<年代vg height="14.65" id="M182" style="vertical-align:-3.20526pt;width:25.1625px;" version="1.1" viewbox="0 0 25.1625 14.65" width="25.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.65)"> <g transform="translate(72,-60.28)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.77,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。通过运行学习算法获得的结果(<一个href="#Eq6">7</一个>)如图<一个href="//www.newsama.com/journals/cin/2008/426080/fig4/" target="_blank">4</一个>。该指数的值<年代vg height="10.325" id="M183" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>表明,定点算法可以安全地5次迭代后再停止。在图<一个href="//www.newsama.com/journals/cin/2008/426080/fig4/" target="_blank">4</一个>,直方图估计(50箱)生成的广义高斯分布的高斯数据和输出可能会观察到。</p><d我v class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-212aef05124bf3a1d2f6816fe80732fa"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.004a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.004b.jpg"> <br> <strong>(b)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(c)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.004c.jpg"> <br> <strong>(c)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(d)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.004d.jpg"> <br> <strong>(d)</年代trong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-212aef05124bf3a1d2f6816fe80732fa partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.004a_th.jpg"><br><strong>(一)</年代trong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.004b_th.jpg"><br><strong>(b)</年代trong></button> <button aria-label="Slide to (c) " class="partial-carousel-dot"><img loading="lazy" alt="(c)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.004c_th.jpg"><br><strong>(c)</年代trong></button> <button aria-label="Slide to (d) " class="partial-carousel-dot"><img loading="lazy" alt="(d)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.004d_th.jpg"><br><strong>(d)</年代trong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-212aef05124bf3a1d2f6816fe80732fa partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图4</年代p一个n><一个一个r我一个-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2008/426080/fig4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>由于双神经系统适应高斯输入和广义高斯输出。</td></tr></tbody> </table> </div> </div> </div> </div> <p>累积的结果也说明了。算法的迭代次数(<一个href="#Eq6">7</一个>)设置为10,而其他数据保持不变之前的单道实验。数量<年代vg height="10.325" id="M184" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg><i></i>点范围从200年到1000年的200步。生成样本的平均数对68250年和68290年之间的变化。结果在表中做了总结<一个href="//www.newsama.com/journals/cin/2008/426080/tab3/" target="_blank"></a>。</p><d我v class="floats-partial-section partial-other-wrapper" data-section="tab3"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表3</年代p一个n><一个一个r我一个-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2008/426080/tab3/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 对实验的平均结果广义高斯随机数生成;平均计算在100个独立的实验中,当算法(<一个href="#Eq6">7</一个>)迭代10次。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/cin/2008/426080/tab3" target="_blank" aria-label="View full page"></a> </div> </div> <h5 id="subsec3.3">3.3。伽马分布实验</h5><p>gydF4y2Ba第三个例子是重复的(<一个href="#B3">10</一个>]:我们考虑的一代(对称)伽马分布:<年代p一个ncl一个年代年代="equation" id="Eq10"> <svg height="10.9125" id="M186" preserveaspectratio="xMaxYMin" style="vertical-align:-0.17555pt;width:47.862499px;" version="1.1" viewbox="0 0 47.862499 10.9125" width="47.862499" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.9125)"> <g transform="translate(72,-63.27)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.515023" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.555412" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="28.806911" y="0"> 。</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.932661" y="0"> 8</t年代p一个n></text> </g> </g> </svg></span>这个选择是出于观察的随机数生成算法(<一个href="#B3">10</一个>)产生最不准确的结果当伽马分布测试。</p><p>gydF4y2Ba下面给出的数值结果与价值观<年代vg height="13.55" id="M187" style="vertical-align:-2.29482pt;width:36.049999px;" version="1.1" viewbox="0 0 36.049999 13.55" width="36.049999" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.55)"> <g transform="translate(72,-61.16)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.440005" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="22.480394" y="0"> 4</t年代p一个n></text> </g> </g> </svg>和<年代vg height="14.3875" id="M188" style="vertical-align:-2.83405pt;width:75.9375px;" version="1.1" viewbox="0 0 75.9375 14.3875" width="75.9375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.3875)"> <g transform="translate(72,-60.49)"> <text transform="matrix(1,0,0,-1,-71.95,63.36)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="15.041109" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="27.081497" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.244997" y="0"> −</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="39.809551" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.224552" y="0"> 2</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="56.476051" y="0"> ]</t年代p一个n></text> </g> </g> </svg>。感兴趣的时间间隔设置为输出变量<年代vg height="13.25" id="M189" style="vertical-align:-1.90608pt;width:70.787498px;" version="1.1" viewbox="0 0 70.787498 13.25" width="70.787498" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.25)"> <g transform="translate(72,-61.4)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.228174" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="25.268562" y="0"> 6</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="31.520063" y="0"> 8</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="37.771564" y="0"> 3</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.023064" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="50.274563" y="0"> 5</t年代p一个n></text> </g> </g> </svg>。生成的输出样本数量的总数<年代vg height="13.6125" id="M190" style="vertical-align:-2.34499pt;width:22.6875px;" version="1.1" viewbox="0 0 22.6875 13.6125" width="22.6875" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,13.6125)"> <g transform="translate(72,-61.11)"> <text transform="matrix(1,0,0,-1,-71.95,63.5)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="6.1514759" y="0"> (</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="10.314975" y="0"> ⋅</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="13.890833" y="0"> )</t年代p一个n></text> </g> </g> </svg>。点的数量的函数<年代vg height="11.1" id="M191" style="vertical-align:-0.17555pt;width:64.074997px;" version="1.1" viewbox="0 0 64.074997 11.1" width="64.074997" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,11.1)"> <g transform="translate(72,-63.12)"> <text transform="matrix(1,0,0,-1,-71.95,63.35)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="14.103384" y="0"> =</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="26.143772" y="0"> 1</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="32.395271" y="0"> 5</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="38.646774" y="0"> 0</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="44.898273" y="0"> 0</t年代p一个n></text> </g> </g> </svg>是计算<年代vg height="14.65" id="M192" style="vertical-align:-3.20526pt;width:25.1625px;" version="1.1" viewbox="0 0 25.1625 14.65" width="25.1625" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,14.65)"> <g transform="translate(72,-60.28)"> <text transform="matrix(1,0,0,-1,-71.95,63.52)"> <tspan style="font-size: 12.50px; " x="0" y="0"> Δ</t年代p一个n><t年代p一个n style="font-size: 12.50px; " x="9.0271664" y="0"> </t年代p一个n></text> <text transform="matrix(1,0,0,-1,-56.77,60.4)"> <tspan style="font-size: 8.75px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>。通过运行学习算法获得的结果(<一个href="#Eq6">7</一个>)如图<一个href="//www.newsama.com/journals/cin/2008/426080/fig5/" target="_blank">5</一个>。该指数的值<年代vg height="10.325" id="M193" style="vertical-align:-0.0pt;width:14.8375px;" version="1.1" viewbox="0 0 14.8375 10.325" width="14.8375" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.325)"> <g transform="translate(72,-63.74)"> <text transform="matrix(1,0,0,-1,-71.95,63.79)"> <tspan style="font-size: 12.50px; " x="0" y="0"> </t年代p一个n></text> </g> </g> </svg>表明,定点算法可以安全地5次迭代后再停止。图<一个href="//www.newsama.com/journals/cin/2008/426080/fig5/" target="_blank">5</一个>显示了直方图估计(50箱)的生成高斯数据和Gamma-distributed输出。</p><d我v class="partial-carousel-wrapper"> <div class="floats-partial-section"> <div class="floats-partial-content"> <div class="partial-carousel--full-image partial-carousel-0bf0e0ded26ab64a63a5c208fa6d2eb5"> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(一)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.005a.jpg"> <br> <strong>(一)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(b)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.005b.jpg"> <br> <strong>(b)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(c)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.005c.jpg"> <br> <strong>(c)</年代trong> </div> <div class="partial-carousel--single-image"> <img loading="lazy" alt="(d)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/figures/426080.fig.005d.jpg"> <br> <strong>(d)</年代trong> </div> </div> </div> <div class="floats-partial-middle"> <div class="floats-partial-middle--thumbs"> <div class="partial-carousel-dots-0bf0e0ded26ab64a63a5c208fa6d2eb5 partial-carousel-thumbnail"> <button aria-label="Slide to (a) " class="partial-carousel-dot"><img loading="lazy" alt="(一)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.005a_th.jpg"><br><strong>(一)</年代trong></button> <button aria-label="Slide to (b) " class="partial-carousel-dot"><img loading="lazy" alt="(b)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.005b_th.jpg"><br><strong>(b)</年代trong></button> <button aria-label="Slide to (c) " class="partial-carousel-dot"><img loading="lazy" alt="(c)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.005c_th.jpg"><br><strong>(c)</年代trong></button> <button aria-label="Slide to (d) " class="partial-carousel-dot"><img loading="lazy" alt="(d)gydF4y2Ba" src="https://static.hindawi.com/articles/cin/volume-2008/426080/thumbnails/426080.fig.005d_th.jpg"><br><strong>(d)</年代trong></button> </div> </div> <div class="floats-partial-middle--nav"> <div class="partial-carousel-next-prev-0bf0e0ded26ab64a63a5c208fa6d2eb5 partial-carousel-next-prev"> <button aria-label="Previous" class="carousel-prev"></button> <button aria-label="Next" class="carousel-next"></button> </div> </div> </div> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">图5</年代p一个n><一个一个r我一个-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2008/426080/fig5/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> <table> <tbody> <tr> <td>由于双神经系统适应与高斯输入和伽马输出。</td></tr></tbody> </table> </div> </div> </div> </div> <p>累积的结果通过设置算法的迭代次数(<一个href="#Eq6">7</一个>)到20,而前面的同一次实验的其他数据保持不变。数量<年代p一个ncl一个年代年代="inline" id="M194"></span><i></i>点从1000年到1800年不等<我></我>200步。生成样本的平均数之间的差异<我></我>68230年和68280年。结果在表中做了总结<一个href="//www.newsama.com/journals/cin/2008/426080/tab4/" target="_blank"></a>。</p><d我v class="floats-partial-section partial-other-wrapper" data-section="tab4"> <div class="floats-partial-footer"> <div class="floats-partial-caption"> <span class="caption-text">表4</年代p一个n><一个一个r我一个-label="View full page" class="caption-partial-url" href="//www.newsama.com/journals/cin/2008/426080/tab4/" title="" target="_blank"></a> </div> <div class="floats-partial-caption-text"> 对实验的平均结果伽马随机数生成;平均计算在100个独立的实验中,当算法(<一个href="#Eq6">7</一个>)是重复20次。</d我v> <a class="table-thumb-overlay" href="//www.newsama.com/journals/cin/2008/426080/tab4" target="_blank" aria-label="View full page"></a> </div> </div> <h4 id="conclusion">4所示。结论</h4><p>gydF4y2Ba目前的手稿的目的是提出一个新颖的随机数生成技术基于双神经系统学习。我们阐述了我们最近的工作<一个href="#B3">10</一个>)为了获得一个新的免费学习算法选择参数和normalization-criteria的需要。主要的思想是将学习范式从基本方程的角度解决双重基本方程求解,这似乎更容易赚钱。</p><p>gydF4y2Ba提出的数值结果证实了协议的期望和获得分布生成的变量。分析计算负担,在运行时间方面,表明该算法不需要计算。</p></d我v> </div> <div class="ArticleReferences_xmlContent__TZqgx"> <h4 class="ArticleReferences_references__dHBcT" id="references">引用</h4><gydF4y2Baol class="ArticleReferences_orderedReferences__K1TM4"> <li class="ArticleReferences_articleReference__7aCxy" id="B1"> <div class="referenceContent"> <p class="referenceText">p L 'Ecuyer“随机数生成”<我>模拟的手册</我>Ed, j .银行,页93 - 137年,约翰·威利& Sons,纽约,纽约,美国,1998年,第4章。</p>gydF4y2Ba视图:<gydF4y2Ba!-- --> <a 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Lagarias“伪随机数生成器在密码学和数论,”<我>密码学和计算数论、座谈会在应用数学学报》上</我>,c。Pomerance Ed, 42卷,页115 - 143,美国数学学会,普罗维登斯,国际扶轮,美国,1990年。</p>gydF4y2Ba视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=Pseudorandom%20number%20generators%20in%20cryptography%20and%20number%20theory&author=J.%20C.%20Lagarias&publication_year=1990" target="_blank" rel="noreferrer">谷歌学术搜索</一个></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B3"> <div class="referenceContent"> <p class="referenceText">s . t . a . Niaki和b . Abbasi交互和基于神经网络的方法来生成随机向量具有任意边际分布和相关矩阵,”<我>学报17适国际会议上建模和仿真</我>加拿大蒙特利尔,页234 - 239,,2006年5月。</p>gydF4y2Ba视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=NORTA%20and%20neural%20networks%20based%20method%20to%20generate%20RANDOM%20vectors%20with%20arbitrary%20marginal%20distributions%20and%20correlation%20matrix&author=S.%20T.%20A.%20Niaki&author=B.%20Abbasi" target="_blank" rel="noreferrer">谷歌学术搜索</一个></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B4"> <div class="referenceContent"> <p class="referenceText">g .马“随机数生成器的当前视图”<我>计算机科学和统计:接口</我>l。台球,艾德。,页3 - 10,爱思唯尔,阿姆斯特丹,荷兰,1985年。</p>gydF4y2Ba视图:<gydF4y2Ba!-- --> <a href="https://scholar.google.com/scholar_lookup?title=A%20current%20view%20of%20random%20number%20generators&author=G.%20Marsaglia&publication_year=1985" target="_blank" rel="noreferrer">谷歌学术搜索</一个></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B5"> <div class="referenceContent"> <p class="referenceText">h . Niederreiter<我>随机数生成和Quasi-Monte卡洛方法</我>、暹罗、费城,宾夕法尼亚州,美国,1992年。</p></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B6"> <div class="referenceContent"> <p class="referenceText">b·d·里普利”对伪随机数生成器的想法。”<我>计算和应用数学杂志》上</我>没有,卷。31日。1,第163 - 153页,1990。</p>gydF4y2Ba视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1016/0377-0427(90)90346-2" target="_blank" rel="noreferrer">出版商的网站</一个><年代p一个ncl一个年代年代="sep">|</年代p一个n><一个href="https://scholar.google.com/scholar_lookup?title=Thoughts%20on%20pseudorandom%20number%20generators&author=B.%20D.%20Ripley&publication_year=1990" target="_blank" rel="noreferrer">谷歌学术搜索</一个></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B7"> <div class="referenceContent"> <p class="referenceText">答:Cichocki和siv。、<我>自适应盲信号和图像处理:学习算法和应用程序</我>约翰·威利& Sons,纽约,纽约,美国,2002年。</p></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B8"> <div class="referenceContent"> <p class="referenceText">d·e·Knuth<我>计算机编程的艺术:Seminumerical算法</我>,卷2,addison - wesley,阅读,质量,美国第3版,1997年版。</p></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B9"> <div class="referenceContent"> <p class="referenceText">a . Papoulis<我>概率和统计</我>新世纪,恩格尔伍德悬崖,新泽西,美国,1996年。</p></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B10"> <div class="referenceContent"> <p class="referenceText">美国菲奥里,”神经系统numerically-matched输入-输出数据:变量的一代,”<我>神经处理信件</我>,23卷,不。2、143 - 170年,2006页。</p>gydF4y2Ba视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1007/s11063-005-4016-6" target="_blank" rel="noreferrer">出版商的网站</一个><年代p一个ncl一个年代年代="sep">|</年代p一个n><一个href="https://scholar.google.com/scholar_lookup?title=Neural%20systems%20with%20numerically-matched%20input-output%20statistic%3A%20variate%20generation&author=S.%20Fiori&publication_year=2006" target="_blank" rel="noreferrer">谷歌学术搜索</一个></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B11"> <div class="referenceContent"> <p class="referenceText">美国菲奥里,”神经系统数值匹配输入-输出数据:等渗二元统计建模、”<我>计算智能和神经科学</我>文章ID 71859卷,2007年,p。23页,2007。</p>gydF4y2Ba视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1155/2007/71859" target="_blank" rel="noreferrer">出版商的网站</一个><年代p一个ncl一个年代年代="sep">|</年代p一个n><一个href="https://scholar.google.com/scholar_lookup?title=Neural%20systems%20with%20numerically%20matched%20input-output%20statistic%3A%20isotonic%20bivariate%20statistical%20modeling&author=S.%20Fiori&publication_year=2007" target="_blank" rel="noreferrer">谷歌学术搜索</一个></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B12"> <div class="referenceContent"> <p class="referenceText">Ghosh和s g·亨德森,”在更高的维度属性交互方法的<我>冬季模拟研讨会论文集(WSC的02)</我>、大肠Yucesan学术界。陈,j·l·斯诺登峰,j . m . Charnes Eds。,vol. 1, pp. 263–269, San Diego, Calif, USA, December 2002.</p>视图:<gydF4y2Ba!-- --> <a href="https://doi.org/10.1109/WSC.2002.1172894" target="_blank" rel="noreferrer">出版商的网站</一个><年代p一个ncl一个年代年代="sep">|</年代p一个n><一个href="https://scholar.google.com/scholar_lookup?title=Properties%20of%20the%20NORTA%20method%20in%20higher%20dimensions&author=S.%20Ghosh&author=S.%20G.%20Henderson" target="_blank" rel="noreferrer">谷歌学术搜索</一个></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B13"> <div class="referenceContent"> <p class="referenceText">a·c·蔡,2006年1月,个人通信。</p></d我v></li> <li class="ArticleReferences_articleReference__7aCxy" id="B14"> <div class="referenceContent"> <p class="referenceText">k . 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