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<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6262fc464f8811599e0341d9/bg1.jpg"><div class="c x0 y1 w2 h2"><div class="t m0 x1 h3 y2 ff1 fs0 fc0 sc0 ls0 ws0"><span class="fc0 sc2">书</span><span class="_ _0"></span><span class="sc1"><span class="fc0 sc2">书</span><span class="_ _0"></span><span class="fc1 sc2"><span class="fc0 sc2">书</span></span></span></div><div class="t m0 x2 h4 y3 ff2 fs1 fc2 sc2 ls0 ws0">收稿<span class="_ _1"></span>日期</div><div class="t m0 x3 h4 y4 ff3 fs1 fc2 sc2 ls0 ws0">：<span class="_ _2"> </span><span class="ff4">2014<span class="_ _1"></span>-<span class="_ _3"></span>05<span class="_ _1"></span>-<span class="_ _3"></span>28<span class="_ _1"></span><span class="ff5">；</span></span></div><div class="t m0 x4 h4 y3 ff2 fs1 fc2 sc2 ls0 ws0">修回<span class="_ _1"></span>日期</div><div class="t m0 x5 h4 y4 ff3 fs1 fc2 sc2 ls0 ws0">：<span class="_ _2"> </span><span class="ff4">2014<span class="_ _1"></span>-<span class="_ _3"></span>08<span class="_ _1"></span>-<span class="_ _3"></span>06</span></div><div class="t m0 x6 h4 y3 ff2 fs1 fc2 sc2 ls0 ws0">基金<span class="_ _1"></span>项目</div><div class="t m0 x7 h4 y4 ff3 fs1 fc2 sc2 ls0 ws0">：</div><div class="t m0 x8 h4 y3 ff6 fs1 fc2 sc2 ls1 ws0">国家自然科学基金资助项目</div><div class="t m0 x9 h4 y4 ff5 fs1 fc2 sc2 ls0 ws0">（<span class="_ _4"> </span><span class="ff4">61170159<span class="_ _1"></span></span>）<span class="_ _5"> </span>；</div><div class="t m0 xa h4 y3 ff6 fs1 fc2 sc2 ls1 ws0">国防科学技术大学优秀研究生创新</div><div class="t m0 xb h4 y5 ff6 fs1 fc2 sc2 ls0 ws0">项目</div><div class="t m0 x2 h4 y6 ff5 fs1 fc2 sc2 ls0 ws0">（<span class="_ _5"> </span><span class="ff4">S<span class="_ _6"></span>130501<span class="_ _1"></span><span class="ff5">）</span></span></div><div class="t m0 x2 h4 y7 ff2 fs1 fc2 sc2 ls0 ws0">作者<span class="_ _1"></span>简介</div><div class="t m0 x3 h4 y8 ff3 fs1 fc2 sc2 ls0 ws0">：</div><div class="t m0 xc h4 y7 ff6 fs1 fc2 sc2 ls0 ws0">李硕<span class="_ _1"></span>豪</div><div class="t m0 xd h4 y8 ff5 fs1 fc2 sc2 ls0 ws0">（<span class="_ _4"> </span><span class="ff4">1990<span class="_ _1"></span>-<span class="_ _6"></span><span class="ff5">）<span class="_ _5"> </span>，</span></span></div><div class="t m0 xe h4 y7 ff6 fs1 fc2 sc2 ls0 ws0">男</div><div class="t m0 xf h4 y8 ff5 fs1 fc2 sc2 ls0 ws0">，</div><div class="t m0 x10 h4 y7 ff6 fs1 fc2 sc2 ls0 ws0">河南<span class="_ _1"></span>许昌<span class="_ _1"></span>人</div><div class="t m0 x11 h4 y8 ff5 fs1 fc2 sc2 ls0 ws0">，</div><div class="t m0 x12 h4 y7 ff6 fs1 fc2 sc2 ls0 ws0">博士<span class="_ _1"></span>研究<span class="_ _1"></span>生</div><div class="t m0 x13 h4 y8 ff5 fs1 fc2 sc2 ls0 ws0">，</div><div class="t m0 x14 h4 y7 ff6 fs1 fc2 sc2 ls2 ws0">主<span class="_ _6"></span>要研究方向为信息系统工程</div><div class="t m0 x15 h5 y8 ff7 fs1 fc2 sc2 ls0 ws0">、</div><div class="t m0 x16 h4 y7 ff6 fs1 fc2 sc2 ls0 ws0">人<span class="_ _1"></span>工<span class="_ _1"></span>智<span class="_ _7"></span>能</div><div class="t m0 x17 h4 y8 ff5 fs1 fc2 sc2 ls0 ws0">（<span class="_ _5"> </span><span class="ff4">lishuohao<span class="_ _1"></span>@<span class="_ _5"> </span>nudt．<span class="_ _5"> </span>edu．<span class="_ _5"> </span>cn<span class="_ _1"></span></span>）<span class="_ _5"> </span>；</div><div class="t m0 x18 h4 y7 ff6 fs1 fc2 sc2 ls0 ws0">张<span class="_ _1"></span>军</div><div class="t m0 x19 h4 y8 ff5 fs1 fc2 sc2 ls0 ws0">（<span class="_ _8"> </span><span class="ff4">1975<span class="_ _1"></span>-</span>）<span class="_ _5"> </span>，</div><div class="t m0 xb h4 y9 ff6 fs1 fc2 sc2 ls0 ws0">女</div><div class="t m0 x1a h4 ya ff5 fs1 fc2 sc2 ls0 ws0">，</div><div class="t m0 x1b h4 y9 ff6 fs1 fc2 sc2 ls0 ws0">湖南<span class="_ _1"></span>邵阳<span class="_ _1"></span>人</div><div class="t m0 xc h4 ya ff5 fs1 fc2 sc2 ls0 ws0">，</div><div class="t m0 x1c h4 y9 ff6 fs1 fc2 sc2 ls0 ws0">教授</div><div class="t m0 x1d h4 ya ff5 fs1 fc2 sc2 ls0 ws0">，</div><div class="t m0 xd h4 y9 ff6 fs1 fc2 sc2 ls0 ws0">博士</div><div class="t m0 x1e h4 ya ff5 fs1 fc2 sc2 ls0 ws0">，</div><div class="t m0 x1f h4 y9 ff6 fs1 fc2 sc2 ls0 ws0">主要<span class="_ _1"></span>研究<span class="_ _1"></span>方向<span class="_ _1"></span>为模<span class="_ _1"></span>式识<span class="_ _1"></span>别</div><div class="t m0 x20 h5 ya ff7 fs1 fc2 sc2 ls0 ws0">、</div><div class="t m0 x21 h4 y9 ff6 fs1 fc2 sc2 ls0 ws0">人工<span class="_ _1"></span>智能</div><div class="t m0 x22 h5 ya ff7 fs1 fc2 sc2 ls0 ws0">、</div><div class="t m0 x23 h4 y9 ff6 fs1 fc2 sc2 ls0 ws0">决策<span class="_ _1"></span>支持<span class="_ _1"></span>系统</div><div class="t m0 x24 h6 ya ff4 fs1 fc2 sc2 ls0 ws0">．</div><div class="t m0 x25 h7 yb ff2 fs2 fc2 sc2 ls3 ws0">贝叶斯网络结构学习综述</div><div class="t m0 x26 h8 yc ff4 fs3 fc2 sc2 ls0 ws0">*</div><div class="t m0 x14 h9 yd ff1 fs4 fc2 sc2 ls0 ws0">李硕<span class="_ _1"></span>豪</div><div class="t m0 x27 h9 ye ff1 fs4 fc2 sc2 ls0 ws0">，</div><div class="t m0 x28 h9 yd ff1 fs4 fc2 sc2 ls0 ws0">张<span class="_ _9"> </span>军</div><div class="t m0 x29 ha yf ff5 fs5 fc2 sc2 ls0 ws0">（</div><div class="t m0 x2a ha y10 ff6 fs5 fc2 sc2 ls4 ws0">国防科学技术大学<span class="_ _a"> </span>信息系统与管理学院</div><div class="t m0 x2b ha yf ff5 fs5 fc2 sc2 ls0 ws0">，</div><div class="t m0 x2c ha y10 ff6 fs5 fc2 sc2 ls0 ws0">长沙</div><div class="t m0 x2d ha yf ff4 fs5 fc2 sc2 ls0 ws0">410073<span class="ff5">）</span></div><div class="t m0 x2e ha y11 ff2 fs5 fc2 sc2 ls0 ws0">摘<span class="_ _b"> </span>要</div><div class="t m0 xc ha y12 ff3 fs5 fc2 sc2 ls0 ws0">：</div><div class="t m0 x2f ha y11 ff6 fs5 fc2 sc2 ls4 ws0">贝叶斯网络是一种有效的不确定性知识表达和推<span class="_ _1"></span>理工<span class="_ _1"></span>具</div><div class="t m0 x30 ha y12 ff5 fs5 fc2 sc2 ls0 ws0">，</div><div class="t m0 x31 ha y11 ff6 fs5 fc2 sc2 ls5 ws0">在数据挖掘等领域得到了较好的应用</div><div class="t m0 x32 ha y12 ff5 fs5 fc2 sc2 ls0 ws0">，</div><div class="t m0 x33 ha y11 ff6 fs5 fc2 sc2 ls0 ws0">而<span class="_ _1"></span>结</div><div class="t m0 x2e ha y13 ff6 fs5 fc2 sc2 ls4 ws0">构学习是其重要研究内容之一</div><div class="t m0 x34 hb y14 ff7 fs5 fc2 sc2 ls0 ws0">。</div><div class="t m0 x35 ha y15 ff6 fs5 fc2 sc2 ls4 ws0">经过二十多年的发展</div><div class="t m0 x36 ha y14 ff5 fs5 fc2 sc2 ls0 ws0">，</div><div class="t m0 x37 ha y15 ff6 fs5 fc2 sc2 ls5 ws0">已经出<span class="_ _6"></span>现了一些比较成熟的贝叶斯网络结构学习算法</div><div class="t m0 x38 ha y14 ff5 fs5 fc2 sc2 ls0 ws0">，</div><div class="t m0 x2e ha y16 ff6 fs5 fc2 sc2 ls4 ws0">对迄今为止的贝叶斯网络结构学习方法进行了综述</div><div class="t m0 x39 hb y17 ff7 fs5 fc2 sc2 ls0 ws0">。</div><div class="t m0 x36 ha y16 ff6 fs5 fc2 sc2 ls4 ws0">现阶段获得的用于结构学习的观测数据都<span class="_ _1"></span>比较<span class="_ _1"></span>复杂</div><div class="t m0 x32 ha y17 ff5 fs5 fc2 sc2 ls0 ws0">，</div><div class="t m0 x33 ha y16 ff6 fs5 fc2 sc2 ls0 ws0">这<span class="_ _1"></span>些</div><div class="t m0 x2e ha y18 ff6 fs5 fc2 sc2 ls4 ws0">数据分为完备数据和不完备数据两种类型</div><div class="t m0 x3a hb y19 ff7 fs5 fc2 sc2 ls0 ws0">。</div><div class="t m0 x3b ha y18 ff6 fs5 fc2 sc2 ls0 ws0">针对<span class="_ _1"></span>完备<span class="_ _1"></span>数<span class="_ _1"></span>据</div><div class="t m0 x3c ha y19 ff5 fs5 fc2 sc2 ls0 ws0">，</div><div class="t m0 x3d ha y18 ff6 fs5 fc2 sc2 ls5 ws0">分别从基于依赖统计分析的方法</div><div class="t m0 x3e hb y19 ff7 fs5 fc2 sc2 ls0 ws0">、</div><div class="t m0 x3f ha y18 ff6 fs5 fc2 sc2 ls5 ws0">基于评分搜索的</div><div class="t m0 x2e ha y1a ff6 fs5 fc2 sc2 ls4 ws0">方法和混合搜索方法三个方面对已有的算法进行分析</div><div class="t m0 x36 hb y1b ff7 fs5 fc2 sc2 ls0 ws0">。</div><div class="t m0 x40 ha y1a ff6 fs5 fc2 sc2 ls4 ws0">对于不完备数据</div><div class="t m0 x41 ha y1b ff5 fs5 fc2 sc2 ls0 ws0">，</div><div class="t m0 x42 ha y1a ff6 fs5 fc2 sc2 ls4 ws0">给出了数据不完备<span class="ls6">情况下网络结构的</span></div><div class="t m0 x2e ha y1c ff6 fs5 fc2 sc2 ls0 ws0">学习<span class="_ _1"></span>框架</div><div class="t m0 x2f hb y1d ff7 fs5 fc2 sc2 ls0 ws0">。</div><div class="t m0 x43 ha y1e ff6 fs5 fc2 sc2 ls4 ws0">在此基础上归纳总结了贝叶斯网络结构学习各个方向的研究进展</div><div class="t m0 x44 ha y1d ff5 fs5 fc2 sc2 ls0 ws0">，</div><div class="t m0 x45 ha y1e ff6 fs5 fc2 sc2 ls4 ws0">给出了贝叶斯<span class="ls6">网络结构学习未来</span></div><div class="t m0 x2e ha y1f ff6 fs5 fc2 sc2 ls4 ws0">可能的研究方向</div><div class="t m0 x46 hb y20 ff7 fs5 fc2 sc2 ls0 ws0">。</div><div class="t m0 x2e ha y21 ff2 fs5 fc2 sc2 ls0 ws0">关键<span class="_ _1"></span>词</div><div class="t m0 xc ha y22 ff3 fs5 fc2 sc2 ls0 ws0">：</div><div class="t m0 x2f ha y21 ff6 fs5 fc2 sc2 ls0 ws0">贝叶<span class="_ _1"></span>斯网<span class="_ _1"></span>络</div><div class="t m0 xe ha y22 ff5 fs5 fc2 sc2 ls0 ws0">；</div><div class="t m0 xf ha y21 ff6 fs5 fc2 sc2 ls0 ws0">结构<span class="_ _1"></span>学习</div><div class="t m0 x47 ha y22 ff5 fs5 fc2 sc2 ls0 ws0">；</div><div class="t m0 x48 ha y21 ff6 fs5 fc2 sc2 ls0 ws0">数据</div><div class="t m0 x49 ha y22 ff5 fs5 fc2 sc2 ls0 ws0">；</div><div class="t m0 x4a ha y21 ff6 fs5 fc2 sc2 ls0 ws0">统计<span class="_ _1"></span>分析</div><div class="t m0 x4b ha y22 ff5 fs5 fc2 sc2 ls0 ws0">；</div><div class="t m0 x4c ha y21 ff6 fs5 fc2 sc2 ls0 ws0">搜索</div><div class="t m0 x2e ha y23 ff2 fs5 fc2 sc2 ls0 ws0">中图<span class="_ _1"></span>分类<span class="_ _1"></span>号</div><div class="t m0 x43 ha y24 ff3 fs5 fc2 sc2 ls0 ws0">：<span class="_ _c"> </span><span class="ff4">TP<span class="_ _6"></span>181</span></div><div class="t m0 x29 ha y23 ff2 fs5 fc2 sc2 ls0 ws0">文献<span class="_ _1"></span>标志<span class="_ _1"></span>码</div><div class="t m0 x4d ha y24 ff3 fs5 fc2 sc2 ls0 ws0">：<span class="_ _c"> </span><span class="ff4">A</span></div><div class="t m0 x23 ha y23 ff2 fs5 fc2 sc2 ls0 ws0">文章<span class="_ _1"></span>编号</div><div class="t m0 x4e ha y24 ff3 fs5 fc2 sc2 ls0 ws0">：<span class="_ _d"> </span><span class="ff4">1001<span class="_ _1"></span>-<span class="_ _0"></span>3695<span class="_ _1"></span><span class="ff5">（<span class="_ _8"> </span></span>2015<span class="_ _1"></span><span class="ff5">）<span class="_ _8"> </span></span>03<span class="_ _1"></span>-<span class="_ _0"></span>0641<span class="_ _1"></span>-<span class="_ _3"></span>06</span></div><div class="t m0 x2e ha y25 ff4 fs5 fc2 sc2 ls0 ws0">doi<span class="ff3">：<span class="_ _4"> </span></span>1<span class="_ _6"></span>0<span class="_ _1"></span>．<span class="_ _4"> </span>3969<span class="_ _e"> </span>/<span class="_ _7"></span>j<span class="_ _1"></span>．<span class="_ _8"> </span>issn．<span class="_ _4"> </span>1001<span class="_ _1"></span>-<span class="_ _f"></span>3695<span class="_ _1"></span>．<span class="_ _e"> </span>2015<span class="_ _1"></span>．<span class="_ _4"> </span>03<span class="_ _1"></span>．<span class="_ _4"> </span>001</div><div class="t m0 xf hc y26 ff4 fs6 fc2 sc2 ls0 ws0">Ｒeview<span class="_ _2"> </span>of<span class="_ _10"> </span>Bayesian<span class="_ _10"> </span>networks<span class="_ _10"> </span>structure<span class="_ _10"> </span>le<span class="_"> </span>a<span class="_ _1"></span>rning</div><div class="t m0 x4f hd y27 ff4 fs7 fc2 sc2 ls0 ws0">LI<span class="_ _a"> </span>Shuo-<span class="_ _11"></span>hao<span class="ff1">，<span class="_ _0"></span><span class="ff4">Z<span class="_ _6"></span>HANG<span class="_ _a"> </span>Jun</span></span></div><div class="t m0 x50 h4 y28 ff1 fs1 fc2 sc2 ls0 ws0">（<span class="_ _5"> </span><span class="ff8">College<span class="_ _5"> </span>of<span class="_ _a"> </span>I<span class="_ _6"></span>nformation<span class="_ _5"> </span>Systems<span class="_ _5"> </span>＆<span class="_ _a"> </span>Manage<span class="_ _6"></span>ment<span class="ff1">，<span class="_ _0"></span><span class="ff8">National<span class="_ _5"> </span>University<span class="_ _5"> </span>of<span class="_ _5"> </span>Defense<span class="_ _5"> </span>Technology<span class="ff1">，<span class="_ _0"></span><span class="ff8">Changsha<span class="_ _4"> </span><span class="ff4">410073<span class="_ _7"></span><span class="ff1">，<span class="_ _0"></span><span class="ff8">China<span class="ff1">）</span></span></span></span></span></span></span></span></span></div><div class="t m0 x2e he y29 ff9 fs8 fc2 sc2 ls0 ws0">Abs<span class="_ _6"></span>tract<span class="_ _1"></span><span class="ff1">：<span class="_ _c"> </span><span class="ff4">Bayesian<span class="_ _a"> </span>networks<span class="_ _a"> </span>is<span class="_ _a"> </span>an<span class="_ _a"> </span>effective<span class="_ _a"> </span>tool<span class="_ _a"> </span>for<span class="_ _a"> </span>uncertainty<span class="_ _a"> </span>knowledge<span class="_ _a"> </span>expres<span class="_ _6"></span>sion<span class="_ _a"> </span>and<span class="_ _12"> </span>reasoning<span class="ff1">，<span class="_ _13"></span><span class="ff4">has<span class="_ _12"> </span>been<span class="_ _12"> </span>applied<span class="_ _a"> </span>in<span class="_ _12"> </span>the</span></span></span></span></div><div class="t m0 x2e he y2a ff4 fs8 fc2 sc2 ls0 ws0">fields<span class="_ _a"> </span>of<span class="_ _a"> </span>data<span class="_ _a"> </span>mining<span class="_ _a"> </span>etc<span class="_ _1"></span>．<span class="_ _10"> </span>Structure<span class="_ _12"> </span>learning<span class="_ _a"> </span>is<span class="_ _12"> </span>one<span class="_ _12"> </span>of<span class="_ _12"> </span>the<span class="_ _a"> </span>most<span class="_ _12"> </span>important<span class="_ _12"> </span>research<span class="_ _12"> </span>content<span class="_ _1"></span>．<span class="_ _10"> </span>After<span class="_ _12"> </span>twenty<span class="_ _a"> </span>years<span class="_ _12"> </span>of<span class="_ _12"> </span>dev<span class="_ _1"></span>elopment<span class="ff1">，</span></div><div class="t m0 x2e hf y2b ff4 fs8 fc2 sc2 ls0 ws0">there<span class="_ _12"> </span>were<span class="_ _5"> </span>already<span class="_ _12"> </span>some<span class="_ _5"> </span>mature<span class="_ _5"> </span>algorithms<span class="_ _5"> </span>for<span class="_ _5"> </span>Bayesian<span class="_ _5"> </span>net<span class="_"> </span>w<span class="_"> </span>o<span class="_ _1"></span>rks<span class="_ _8"> </span>structure<span class="_ _12"> </span>learning．<span class="_ _10"> </span>This<span class="_ _8"> </span>paper<span class="_ _12"> </span>reviewed<span class="_ _5"> </span>the<span class="_ _12"> </span>Bayesian<span class="_ _5"> </span>networks</div><div class="t m0 x2e he y2c ff4 fs8 fc2 sc2 ls0 ws0">structure<span class="_ _a"> </span>learning<span class="_ _a"> </span>algorithms<span class="_ _5"> </span>up<span class="_ _5"> </span>to<span class="_ _5"> </span>t<span class="_"> </span>he<span class="_ _12"> </span>present．<span class="_ _10"> </span>The<span class="_ _5"> </span>observed<span class="_ _5"> </span>data<span class="_ _5"> </span>for<span class="_ _12"> </span>structure<span class="_ _5"> </span>learning<span class="_ _5"> </span>were<span class="_ _12"> </span>relatively<span class="_ _12"> </span>complex<span class="ff1">，<span class="_ _11"></span><span class="ff4">which<span class="_ _5"> </span>divided</span></span></div><div class="t m0 x2e he y2d ff4 fs8 fc2 sc2 ls0 ws0">into<span class="_ _a"> </span>complete<span class="_ _a"> </span>data<span class="_ _a"> </span>and<span class="_ _a"> </span>incomplete<span class="_ _a"> </span>data<span class="_ _a"> </span>of<span class="_ _a"> </span>two<span class="_ _a"> </span>types<span class="_ _1"></span>．<span class="_ _10"> </span>For<span class="_ _a"> </span>the<span class="_ _a"> </span>complete<span class="_ _a"> </span>data<span class="ff1">，<span class="_ _13"></span><span class="ff4">it<span class="_ _a"> </span>analyzed<span class="_ _12"> </span>t<span class="_"> </span>he<span class="_ _a"> </span>existing<span class="_ _a"> </span>algorithms<span class="_ _12"> </span>which<span class="_ _a"> </span>divided</span></span></div><div class="t m0 x2e hf y2e ff4 fs8 fc2 sc2 ls0 ws0">into<span class="_ _12"> </span>thre<span class="_"> </span>e<span class="_ _14"> </span>types</div><div class="t m0 x51 he y2f ff1 fs8 fc2 sc2 ls0 ws0">，<span class="_ _13"></span><span class="ff4">dependency<span class="_ _1"></span>-<span class="_ _11"></span>bas<span class="_ _6"></span>ed<span class="_ _a"> </span>statistical<span class="_ _a"> </span>analysis<span class="_ _12"> </span>method<span class="_ _1"></span><span class="ff1">，<span class="_ _13"></span><span class="ff4">the<span class="_ _a"> </span>method<span class="_ _a"> </span>based<span class="_ _12"> </span>on<span class="_ _a"> </span>the<span class="_ _14"> </span>score<span class="_ _a"> </span>search<span class="_ _a"> </span>and<span class="_ _14"> </span>hybrid<span class="_ _14"> </span>search．<span class="_ _15"> </span>For</span></span></span></div><div class="t m0 x2e he y30 ff4 fs8 fc2 sc2 ls0 ws0">the<span class="_ _a"> </span>incomplete<span class="_ _a"> </span>data<span class="ff1">，<span class="_ _0"></span><span class="ff4">it<span class="_ _a"> </span>given<span class="_ _a"> </span>the<span class="_ _a"> </span>learning<span class="_ _a"> </span>processing<span class="_ _a"> </span>of<span class="_ _a"> </span>incomplete<span class="_ _a"> </span>data<span class="_ _1"></span>．<span class="_ _10"> </span>On<span class="_ _a"> </span>this<span class="_ _a"> </span>basis<span class="ff1">，<span class="_ _13"></span><span class="ff4">summarized<span class="_ _a"> </span>current<span class="_ _14"> </span>research<span class="_ _a"> </span>work<span class="_ _14"> </span>a-</span></span></span></span></div><div class="t m0 x2e he y31 ff4 fs8 fc2 sc2 ls0 ws0">bout<span class="_ _a"> </span>Bayesian<span class="_ _a"> </span>networks<span class="_ _a"> </span>structure<span class="_ _12"> </span>l<span class="_"> </span>e<span class="_ _1"></span>arning<span class="ff1">，<span class="_ _13"></span><span class="ff4">and<span class="_ _a"> </span>pointed<span class="_ _a"> </span>out<span class="_ _a"> </span>fut<span class="_"> </span>ur<span class="_"> </span>e<span class="_ _14"> </span>research<span class="_ _a"> </span>directions．</span></span></div><div class="t m0 x2e he y32 ff9 fs8 fc2 sc2 ls0 ws0">Key<span class="_ _a"> </span>words<span class="ff1">：<span class="_ _c"> </span><span class="ff4">Bayesian<span class="_ _a"> </span>networks</span>（<span class="_ _a"> </span><span class="ff4">BN</span>）<span class="_ _a"> </span>；<span class="_ _2"> </span><span class="ff4">structure<span class="_ _12"> </span>lear<span class="_ _1"></span>ning</span>；<span class="_ _2"> </span><span class="ff4">data</span>；<span class="_ _2"> </span><span class="ff4">statistical<span class="_ _a"> </span>analysis</span>；<span class="_ _2"> </span><span class="ff4">searching</span></span></div><div class="t m0 xb h10 y33 ff4 fs9 fc2 sc2 ls0 ws0">0</div><div class="t m0 x2 h11 y34 ff2 fs9 fc2 sc2 ls0 ws0">引言</div><div class="t m0 x52 hd y35 ff1 fs7 fc2 sc2 ls7 ws0">随着计算机技术和网络技术的迅猛发展</div><div class="t m0 x53 hd y36 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x54 hd y35 ff1 fs7 fc2 sc2 ls7 ws0">对海量数据的处</div><div class="t m0 xb hd y37 ff1 fs7 fc2 sc2 ls8 ws0">理<span class="_ _3"></span>已<span class="_ _6"></span>经<span class="_ _3"></span>成为计算机科学方面的挑战性任务</div><div class="t m0 x55 h12 y38 ff7 fs7 fc2 sc2 ls0 ws0">。<span class="ff4">1995</span></div><div class="t m0 x4f hd y37 ff1 fs7 fc2 sc2 ls0 ws0">年</div><div class="t m0 x56 hd y38 ff1 fs7 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ff4">Fayyad</span></div><div class="t m0 xb hd y39 ff1 fs7 fc2 sc2 ls0 ws0">等人</div><div class="t m0 x57 h13 y3a ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">1<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 x58 hd y39 ff1 fs7 fc2 sc2 ls0 ws0">给出<span class="_ _1"></span>了数<span class="_ _1"></span>据<span class="_ _1"></span>挖<span class="_ _7"></span>掘<span class="_ _7"></span>的<span class="_ _7"></span>定<span class="_ _7"></span>义</div><div class="t m0 x10 hd y3b ff1 fs7 fc2 sc2 ls0 ws0">：</div><div class="t m0 x59 hd y39 ff1 fs7 fc2 sc2 ls9 ws0">数据挖掘是指从数据中发现</div><div class="t m0 xb hd y3c ff1 fs7 fc2 sc2 ls0 ws0">有效<span class="_ _1"></span>的</div><div class="t m0 x5a h14 y3d ff7 fs7 fc2 sc2 ls0 ws0">、</div><div class="t m0 x5b hd y3c ff1 fs7 fc2 sc2 ls0 ws0">新颖<span class="_ _1"></span>的</div><div class="t m0 x50 h14 y3d ff7 fs7 fc2 sc2 ls0 ws0">、</div><div class="t m0 x5c hd y3c ff1 fs7 fc2 sc2 ls0 ws0">潜在<span class="_ _1"></span>的</div><div class="t m0 x46 h14 y3d ff7 fs7 fc2 sc2 ls0 ws0">、</div><div class="t m0 x5d hd y3c ff1 fs7 fc2 sc2 ls7 ws0">有用的和最终被理解的模式和知识的</div><div class="t m0 xb hd y3e ff1 fs7 fc2 sc2 ls0 ws0">非平<span class="_ _1"></span>凡过<span class="_ _1"></span>程</div><div class="t m0 x5e h14 y3f ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x5f hd y3e ff1 fs7 fc2 sc2 ls0 ws0">近二<span class="_ _1"></span>十<span class="_ _1"></span>年<span class="_ _1"></span>来</div><div class="t m0 x60 hd y3f ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x61 hd y3e ff1 fs7 fc2 sc2 lsa ws0">在众多的数据挖掘模型中</div><div class="t m0 x62 hd y3f ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x63 hd y3e ff1 fs7 fc2 sc2 ls0 ws0">贝<span class="_ _1"></span>叶<span class="_ _7"></span>斯</div><div class="t m0 xb hd y40 ff1 fs7 fc2 sc2 ls0 ws0">网络</div><div class="t m0 x52 hd y41 ff1 fs7 fc2 sc2 ls0 ws0">（<span class="_ _12"> </span><span class="ff4">Bayesian<span class="_ _12"> </span>networks</span>，<span class="_ _16"></span><span class="ff4">BN<span class="_ _1"></span><span class="ff1">）</span></span></div><div class="t m0 x64 h13 y42 ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">2<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 x10 hd y40 ff1 fs7 fc2 sc2 ls9 ws0">作为一种图形化的建模工具</div><div class="t m0 x65 hd y41 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xb hd y43 ff1 fs7 fc2 sc2 ls7 ws0">提供了一种表示变量之间因果关系的方法</div><div class="t m0 x66 hd y44 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x67 hd y43 ff1 fs7 fc2 sc2 ls7 ws0">用来发现隐藏在数</div><div class="t m0 xb hd y45 ff1 fs7 fc2 sc2 ls0 ws0">据中<span class="_ _1"></span>的知<span class="_ _1"></span>识</div><div class="t m0 x5e h14 y46 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x5f hd y45 ff1 fs7 fc2 sc2 ls7 ws0">贝叶斯网络将有向无环图与概率理论有机结合</div><div class="t m0 x65 hd y46 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xb hd y47 ff1 fs7 fc2 sc2 ls7 ws0">在不确定推理方面发挥了很大的优势</div><div class="t m0 x68 h14 y48 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x52 hd y49 ff1 fs7 fc2 sc2 ls7 ws0">贝叶斯网络结构学<span class="lsa">习是目前贝叶斯网络研究中的重点和</span></div><div class="t m0 xb hd y4a ff1 fs7 fc2 sc2 ls0 ws0">难点</div><div class="t m0 x52 hd y4b ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x69 hd y4a ff1 fs7 fc2 sc2 ls7 ws0">是利用观测数据集<span class="_ _1"></span>合</div><div class="t m0 x61 h14 y4b ff7 fs7 fc2 sc2 ls0 ws0">、</div><div class="t m0 xe hd y4a ff1 fs7 fc2 sc2 lsa ws0">通过结合先验知识等相关方法自</div><div class="t m0 xb hd y4c ff1 fs7 fc2 sc2 ls7 ws0">动构建贝叶斯网络结构</div><div class="t m0 x46 hd y4d ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x5d hd y4c ff1 fs7 fc2 sc2 ls7 ws0">克服了单纯依靠专家系统建立的网络</div><div class="t m0 xb hd y4e ff1 fs7 fc2 sc2 ls0 ws0">结构<span class="_ _1"></span>的局<span class="_ _1"></span>限性</div><div class="t m0 x5f h14 y4f ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x5c hd y50 ff1 fs7 fc2 sc2 ls0 ws0">以</div><div class="t m0 x6a h12 y4f ff4 fs7 fc2 sc2 ls0 ws0">Asia</div><div class="t m0 x6b hd y50 ff1 fs7 fc2 sc2 ls0 ws0">数据<span class="_ _1"></span>集</div><div class="t m0 x6c h13 y51 ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">3<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 x6d hd y50 ff1 fs7 fc2 sc2 ls0 ws0">为<span class="_ _1"></span>例</div><div class="t m0 x6e hd y4f ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x6f hd y50 ff1 fs7 fc2 sc2 ls0 ws0">图</div><div class="t m0 x70 hd y4f ff4 fs7 fc2 sc2 ls0 ws0">1<span class="_ _7"></span><span class="ff1">（<span class="_ _12"> </span></span>a<span class="_ _1"></span><span class="ff1">）</span></div><div class="t m0 x20 hd y50 ff1 fs7 fc2 sc2 ls0 ws0">所<span class="_ _1"></span>示<span class="_ _1"></span>为<span class="_ _7"></span>完<span class="_ _1"></span>整<span class="_ _1"></span>的</div><div class="t m0 xb hd y52 ff1 fs7 fc2 sc2 ls0 ws0">贝叶<span class="_ _1"></span>斯网<span class="_ _1"></span>络</div><div class="t m0 x5e hd y53 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x71 hd y52 ff1 fs7 fc2 sc2 lsa ws0">表<span class="_ _6"></span>格中<span class="_ _6"></span>给<span class="_ _6"></span>出了网络节点概率参数</div><div class="t m0 x72 hd y53 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x20 hd y52 ff1 fs7 fc2 sc2 ls0 ws0">节<span class="_ _1"></span>点<span class="_ _1"></span>之<span class="_ _7"></span>间<span class="_ _1"></span>的<span class="_ _1"></span>连</div><div class="t m0 xb hd y54 ff1 fs7 fc2 sc2 ls7 ws0">接表示节点间的相关<span class="_ _1"></span>关系</div><div class="t m0 x60 hd y55 ff1 fs7 fc2 sc2 ls0 ws0">；</div><div class="t m0 x61 hd y54 ff1 fs7 fc2 sc2 lsa ws0">贝叶斯网络结构学习如图</div><div class="t m0 x56 hd y55 ff4 fs7 fc2 sc2 ls0 ws0">1<span class="_ _7"></span><span class="ff1">（<span class="_ _a"> </span></span>b<span class="_ _1"></span><span class="ff1">）</span></div><div class="t m0 x73 hd y54 ff1 fs7 fc2 sc2 ls0 ws0">所</div><div class="t m0 x74 hd y56 ff1 fs7 fc2 sc2 ls0 ws0">示</div><div class="t m0 x75 hd y57 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x24 hd y58 ff1 fs7 fc2 sc2 ls7 ws0">数字表示节点可能出<span class="_ _1"></span>现的<span class="_ _1"></span>状<span class="_ _1"></span>态</div><div class="t m0 x76 hd y57 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x77 hd y58 ff1 fs7 fc2 sc2 lsa ws0">观测数据即为节点出现的</div><div class="t m0 x74 hd y59 ff1 fs7 fc2 sc2 ls0 ws0">历史<span class="_ _1"></span>状态</div><div class="t m0 x31 hd y5a ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x78 hd y59 ff1 fs7 fc2 sc2 ls7 ws0">贝叶斯网络结构学习就是通过学习观测数据得出最</div><div class="t m0 x74 hd y5b ff1 fs7 fc2 sc2 ls0 ws0">优的<span class="_ _1"></span>网络<span class="_ _1"></span>结构</div><div class="t m0 x79 h14 y5c ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x7a hd y5d ff1 fs7 fc2 sc2 ls7 ws0">贝叶斯网络结构学习分<span class="lsa">为完备数据和不完备数据</span></div><div class="t m0 x7b h13 y5e ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">4<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 x7c hd y5d ff1 fs7 fc2 sc2 ls0 ws0">两<span class="_ _1"></span>种</div><div class="t m0 x74 hd y5f ff1 fs7 fc2 sc2 ls0 ws0">情况</div><div class="t m0 x7a h14 y60 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x7d hd y5f ff1 fs7 fc2 sc2 lsb ws0">完<span class="_ _3"></span>备数据下贝叶斯网络结构学习的方法通常分为三</div><div class="t m0 x74 hd y61 ff1 fs7 fc2 sc2 ls0 ws0">类</div><div class="t m0 x7e h13 y62 ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">5<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 x7f hd y63 ff1 fs7 fc2 sc2 ls0 ws0">：<span class="_ _5"> </span><span class="ff4">a<span class="_ _1"></span></span>）</div><div class="t m0 x80 hd y61 ff1 fs7 fc2 sc2 lsa ws0">基于依赖统计分析的方法</div><div class="t m0 x81 hd y63 ff1 fs7 fc2 sc2 ls0 ws0">；<span class="_ _5"> </span><span class="ff4">b<span class="_ _1"></span></span>）</div><div class="t m0 x82 hd y61 ff1 fs7 fc2 sc2 lsa ws0">基于评分搜索的方法</div><div class="t m0 x83 hd y63 ff1 fs7 fc2 sc2 ls0 ws0">；</div><div class="t m0 x74 hd y64 ff4 fs7 fc2 sc2 ls0 ws0">c<span class="ff1">）</span></div><div class="t m0 x75 hd y65 ff1 fs7 fc2 sc2 ls7 ws0">结合上述两种方法的混<span class="_ _1"></span>合<span class="_ _1"></span>搜索<span class="_ _1"></span>算<span class="_ _1"></span>法</div><div class="t m0 x84 h14 y64 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x85 hd y65 ff1 fs7 fc2 sc2 lsa ws0">不完备数据下的贝叶</div><div class="t m0 x74 hd y66 ff1 fs7 fc2 sc2 ls7 ws0">斯网络结构学习算法需要对数据进行修补</div><div class="t m0 x86 hd y67 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x87 hd y66 ff1 fs7 fc2 sc2 ls7 ws0">然后再对贝叶斯网</div><div class="t m0 x74 hd y68 ff1 fs7 fc2 sc2 ls7 ws0">络进行结构学习</div><div class="t m0 x42 h14 y69 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x88 hd y6a ff1 fs7 fc2 sc2 lsa ws0">本<span class="_ _6"></span>文阐述了贝叶斯网络结构学习的研究进</div><div class="t m0 x74 hd y6b ff1 fs7 fc2 sc2 ls0 ws0">展</div><div class="t m0 x75 hd y6c ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x24 hd y6d ff1 fs7 fc2 sc2 ls7 ws0">在对结构学习算法分类的基础上重点分析并评价了三种结</div><div class="t m0 x74 hd y6e ff1 fs7 fc2 sc2 ls7 ws0">构学习方法涉及的相关算法</div><div class="t m0 x89 hd y6f ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x8a hd y6e ff1 fs7 fc2 sc2 ls7 ws0">并给出了不完备数据下结构学习</div><div class="t m0 x74 hd y70 ff1 fs7 fc2 sc2 ls0 ws0">的框<span class="_ _1"></span>架和<span class="_ _1"></span>流程</div><div class="t m0 x79 hd y71 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x41 hd y72 ff1 fs7 fc2 sc2 ls7 ws0">指出当前结构学习研究中尚未解决的难题以及</div><div class="t m0 x74 hd y73 ff1 fs7 fc2 sc2 ls7 ws0">未来可能的研究方向</div><div class="t m0 x8b h14 y74 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x74 h10 y75 ff4 fs9 fc2 sc2 ls0 ws0">1</div><div class="t m0 x8c h11 y76 ff2 fs9 fc2 sc2 lsc ws0">贝叶斯网络及其结构模型</div><div class="t m0 x7a hd y77 ff1 fs7 fc2 sc2 lsb ws0">贝<span class="_ _3"></span>叶<span class="_ _3"></span>斯<span class="_ _3"></span>网<span class="_ _6"></span>络<span class="_ _6"></span>又称为信念网络</div><div class="t m0 x8d hd y78 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x81 hd y77 ff1 fs7 fc2 sc2 ls0 ws0">由</div><div class="t m0 x8e hd y78 ff7 fs7 fc2 sc2 ls0 ws0">〈<span class="_ _3"></span><span class="ff8">X<span class="_ _1"></span><span class="ff1">，<span class="_ _16"></span><span class="ff8">A<span class="_ _1"></span><span class="ff1">，</span></span></span></span></div><div class="t m0 x8f h15 y77 ffa fs7 fc2 sc2 ls0 ws0">Θ</div><div class="t m0 x90 h14 y78 ff7 fs7 fc2 sc2 ls0 ws0">〉</div><div class="t m0 x91 hd y77 ff1 fs7 fc2 sc2 ls0 ws0">三<span class="_ _7"></span>部<span class="_ _17"></span>分<span class="_ _7"></span>组<span class="_ _17"></span>成</div><div class="t m0 x83 h14 y78 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x74 hd y54 ff1 fs7 fc2 sc2 ls0 ws0">其中</div><div class="t m0 x8c hd y55 ff1 fs7 fc2 sc2 ls0 ws0">：<span class="_ _18"> </span><span class="ffb">〈<span class="_ _6"></span><span class="ff8">X<span class="ff1">，<span class="_ _19"></span><span class="ff8">A<span class="_ _7"></span><span class="ff7">〉</span></span></span></span></span></div><div class="t m0 x79 hd y54 ff1 fs7 fc2 sc2 lsd ws0">表示一个有向无环图</div><div class="t m0 x84 hd y55 ff1 fs7 fc2 sc2 ls0 ws0">（<span class="_ _18"> </span><span class="ff4">directed<span class="_ _1a"> </span>acyclic<span class="_ _1a"> </span>graph</span>，</div><div class="t m0 x92 ha y79 ff6 fs5 fc2 sc2 ls0 ws0">第</div><div class="t m0 x2 h16 y7a ff4 fs5 fc2 sc2 ls0 ws0">32</div><div class="t m0 x58 ha y79 ff6 fs5 fc2 sc2 ls0 ws0">卷第</div><div class="t m0 x93 h16 y7a ff4 fs5 fc2 sc2 ls0 ws0">3</div><div class="t m0 x1c ha y79 ff6 fs5 fc2 sc2 ls0 ws0">期</div><div class="t m0 x94 h16 y7b ff4 fs5 fc2 sc2 ls0 ws0">2015</div><div class="t m0 x95 ha y7c ff6 fs5 fc2 sc2 ls0 ws0">年</div><div class="t m0 x96 h16 y7b ff4 fs5 fc2 sc2 ls0 ws0">3</div><div class="t m0 x5e ha y7c ff6 fs5 fc2 sc2 ls0 ws0">月</div><div class="t m0 x4f ha y7d ff6 fs5 fc2 sc2 lse ws0">计算机应用研究</div><div class="t m0 x20 h16 y7e ff4 fs5 fc2 sc2 ls0 ws0">Applicati<span class="_ _6"></span>on<span class="_ _14"> </span>Ｒesearch<span class="_ _a"> </span>of<span class="_ _a"> </span>Computers</div><div class="t m0 x97 h16 y7a ff4 fs5 fc2 sc2 ls0 ws0">Vol．<span class="_ _4"> </span>32<span class="_ _14"> </span>No<span class="_ _1"></span>．<span class="_ _4"> </span>3</div><div class="t m0 x98 h16 y7b ff4 fs5 fc2 sc2 ls0 ws0">Mar．<span class="_ _10"> </span>2015</div></div></div><div class="pi" data-data='{"ctm":[1.612022,0.000000,0.000000,1.612022,0.000000,0.000000]}'></div></div>
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<div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://static.pudn.com/prod/directory_preview_static/6262fc464f8811599e0341d9/bg2.jpg"><div class="t m0 xb hd y7f ff4 fs7 fc2 sc2 ls0 ws0">DAG<span class="ff1">）</span></div><div class="t m0 x69 hd y80 ff1 fs7 fc2 sc2 ls0 ws0">的结<span class="_ _1"></span>构</div><div class="t m0 x99 hd y7f ff8 fs7 fc2 sc2 ls0 ws0">G<span class="ff1">，</span></div><div class="t m0 x9a hd y80 ff1 fs7 fc2 sc2 ls0 ws0">如图</div><div class="t m0 x9b hd y7f ff4 fs7 fc2 sc2 ls0 ws0">1<span class="_ _1"></span><span class="ff1">（<span class="_ _12"> </span></span>b<span class="_ _1"></span><span class="ff1">）</span></div><div class="t m0 x4 hd y80 ff1 fs7 fc2 sc2 ls0 ws0">所<span class="_ _1"></span>示</div><div class="t m0 x10 hd y7f ff1 fs7 fc2 sc2 ls0 ws0">；<span class="_ _5"> </span><span class="ff8">X</span></div><div class="t m0 x9c hd y80 ff1 fs7 fc2 sc2 lsa ws0">是网络中节点的集合</div><div class="t m0 x9d hd y7f ff1 fs7 fc2 sc2 ls0 ws0">，<span class="_ _1b"></span><span class="ff8">X</span></div><div class="t m0 x9e h17 y81 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x73 h18 y80 ffc fs7 fc2 sc2 ls0 ws0">∈</div><div class="t m0 xb h19 y82 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 x1a hd y83 ff1 fs7 fc2 sc2 ls9 ws0">表示一个限制定义域的随机变量</div><div class="t m0 x9f hd y82 ff1 fs7 fc2 sc2 ls0 ws0">；<span class="_ _12"> </span><span class="ff8">A</span></div><div class="t m0 x47 hd y83 ff1 fs7 fc2 sc2 ls0 ws0">是<span class="_ _7"></span>网<span class="_ _7"></span>络<span class="_ _1"></span>中<span class="_ _7"></span>有<span class="_ _7"></span>向<span class="_ _17"></span>边<span class="_ _7"></span>的<span class="_ _7"></span>集</div><div class="t m0 xb hd y84 ff1 fs7 fc2 sc2 ls0 ws0">合</div><div class="t m0 xa0 hd y85 ff1 fs7 fc2 sc2 ls0 ws0">，<span class="_ _1c"></span><span class="ff8">a</span></div><div class="t m0 x52 h17 y86 ff8 fsa fc2 sc2 ls0 ws0">ij</div><div class="t m0 xa1 h18 y84 ffc fs7 fc2 sc2 ls0 ws0">∈</div><div class="t m0 xa2 h19 y85 ff8 fs7 fc2 sc2 ls0 ws0">A</div><div class="t m0 x96 hd y84 ff1 fs7 fc2 sc2 ls7 ws0">表示节点之间的直接依赖关系</div><div class="t m0 x35 hd y85 ff1 fs7 fc2 sc2 ls0 ws0">，<span class="_ _1c"></span><span class="ff8">a</span></div><div class="t m0 x12 h17 y86 ff8 fsa fc2 sc2 ls0 ws0">ij</div><div class="t m0 xa3 hd y84 ff1 fs7 fc2 sc2 ls0 ws0">表<span class="_ _1"></span>示</div><div class="t m0 x4a h19 y85 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 xa4 h17 y86 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 xa5 hd y84 ff1 fs7 fc2 sc2 ls0 ws0">与</div><div class="t m0 xa6 h19 y85 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 x9d h17 y86 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 xa7 hd y84 ff1 fs7 fc2 sc2 ls0 ws0">之<span class="_ _1"></span>间</div><div class="t m0 xb hd y87 ff1 fs7 fc2 sc2 ls0 ws0">的有<span class="_ _1"></span>向连<span class="_ _1"></span>接</div><div class="t m0 x5e hd y88 ff1 fs7 fc2 sc2 ls0 ws0">，<span class="_ _1c"></span><span class="ff8">X</span></div><div class="t m0 x1c h17 y89 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x50 h18 y8a ffc fs7 fc2 sc2 ls0 ws0">←</div><div class="t m0 xa8 h19 y88 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 xa9 h17 y89 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 xd hd y88 ff1 fs7 fc2 sc2 ls0 ws0">；</div><div class="t m0 xaa hd y87 ffa fs7 fc2 sc2 ls0 ws0">Θ<span class="_ _12"> </span><span class="ff1">是<span class="_ _1"></span>网<span class="_ _7"></span>络<span class="_ _7"></span>参<span class="_ _1"></span>数</span></div><div class="t m0 xab hd y88 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x9f hd y87 ff1 fs7 fc2 sc2 ls0 ws0">如<span class="_ _1"></span>图</div><div class="t m0 x48 hd y88 ff4 fs7 fc2 sc2 ls0 ws0">1<span class="_ _7"></span><span class="ff1">（<span class="_ _a"> </span></span>a<span class="_ _1"></span><span class="ff1">）</span></div><div class="t m0 x20 hd y87 ff1 fs7 fc2 sc2 ls0 ws0">中<span class="_ _7"></span>节<span class="_ _7"></span>点<span class="_ _1"></span>的<span class="_ _7"></span>概<span class="_ _7"></span>率</div><div class="t m0 xb hd y8b ff1 fs7 fc2 sc2 ls0 ws0">取值</div><div class="t m0 x52 hd y8c ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x69 h15 y8d ffa fs7 fc2 sc2 ls0 ws0">θ</div><div class="t m0 x95 h17 y8e ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 xac hd y8d ffc fs7 fc2 sc2 ls0 ws0">∈<span class="ffa">Θ<span class="_ _5"> </span><span class="ff1">表<span class="_ _1"></span>示<span class="_ _1"></span>与<span class="_ _7"></span>节<span class="_ _1"></span>点</span></span></div><div class="t m0 xad h19 y8c ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 x4 h17 y8e ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 xae hd y8d ff1 fs7 fc2 sc2 ls9 ws0">相关的条件概率分布函数</div><div class="t m0 x63 h14 y8c ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 xa7 hd y8d ff1 fs7 fc2 sc2 ls0 ws0">贝<span class="_ _7"></span>叶</div><div class="t m0 xb hd y8f ff1 fs7 fc2 sc2 ls7 ws0">斯网络蕴涵了条件独立<span class="_ _1"></span>性假<span class="_ _1"></span>设</div><div class="t m0 x6c hd y90 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xaf hd y8f ff1 fs7 fc2 sc2 lsa ws0">即给定一个节点的父节点集</div><div class="t m0 x65 hd y90 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xb hd y91 ff1 fs7 fc2 sc2 ls7 ws0">该节点独立于它的所有非后代节点</div><div class="t m0 xb0 h14 y92 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x68 hd y91 ff1 fs7 fc2 sc2 ls0 ws0">因此</div><div class="t m0 x66 hd y92 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x67 hd y91 ff1 fs7 fc2 sc2 ls7 ws0">贝叶斯网络所表示</div><div class="t m0 xb hd y93 ff1 fs7 fc2 sc2 ls7 ws0">的所有节点的联合概率就可以表示为各节点条件概率的乘积</div><div class="t m0 x65 hd y94 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xb hd y95 ff1 fs7 fc2 sc2 ls0 ws0">如式</div><div class="t m0 x52 hd y96 ff1 fs7 fc2 sc2 ls0 ws0">（<span class="_ _8"> </span><span class="ff4">1<span class="_ _7"></span></span>）</div><div class="t m0 xb1 hd y95 ff1 fs7 fc2 sc2 ls0 ws0">所示</div><div class="t m0 xc h14 y96 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x96 h4 y97 ff8 fs1 fc2 sc2 ls0 ws0">P<span class="ff1">（<span class="_ _12"> </span></span>X</div><div class="t m0 x99 h1a y98 ff4 fsa fc2 sc2 ls0 ws0">1</div><div class="t m0 x1c h4 y97 ff1 fs1 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ff8">X</span></div><div class="t m0 xb2 h1a y98 ff4 fsa fc2 sc2 ls0 ws0">2</div><div class="t m0 xb3 h4 y97 ff1 fs1 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ffb">…<span class="ff1">，<span class="_ _16"></span><span class="ff8">X</span></span></span></div><div class="t m0 x46 h17 y98 ff8 fsa fc2 sc2 ls0 ws0">n</div><div class="t m0 xb4 h4 y97 ff1 fs1 fc2 sc2 ls0 ws0">）<span class="_ _1a"> </span><span class="ff4">=</span></div><div class="t m0 xb5 h1b y99 ffc fs1 fc2 sc2 ls0 ws0">∏</div><div class="t m0 xe h17 y9a ff8 fsa fc2 sc2 ls0 ws0">n</div><div class="t m0 xb6 h1a y9b ff8 fsa fc2 sc2 ls0 ws0">i<span class="_ _1d"> </span><span class="ff4">=<span class="_ _7"> </span>1</span></div><div class="t m0 xb7 h4 y97 ff8 fs1 fc2 sc2 ls0 ws0">P<span class="ff1">（<span class="_ _12"> </span></span>X</div><div class="t m0 xb8 h17 y98 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x9c h6 y97 ff4 fs1 fc2 sc2 ls0 ws0">|<span class="_ _1d"> </span><span class="ff8">X</span></div><div class="t m0 x9f h1a y98 ff4 fsa fc2 sc2 ls0 ws0">1</div><div class="t m0 x68 h4 y97 ff1 fs1 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ff8">X</span></div><div class="t m0 x47 h1a y98 ff4 fsa fc2 sc2 ls0 ws0">2</div><div class="t m0 xb9 h4 y97 ff1 fs1 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ffb">…<span class="ff1">，<span class="_ _16"></span><span class="ff8">X</span></span></span></div><div class="t m0 x72 h1a y98 ff8 fsa fc2 sc2 ls0 ws0">i<span class="_ _1d"> </span><span class="ff4">－<span class="_ _7"> </span>1</span></div><div class="t m0 x4a h4 y97 ff1 fs1 fc2 sc2 ls0 ws0">）<span class="_ _1a"> </span><span class="ff4">=</span></div><div class="t m0 x1e h1b y9c ffc fs1 fc2 sc2 ls0 ws0">∏</div><div class="t m0 xba h17 y9d ff8 fsa fc2 sc2 ls0 ws0">n</div><div class="t m0 xbb h17 y9e ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 xb4 h1a y9f ff4 fsa fc2 sc2 ls0 ws0">=<span class="_ _7"> </span>1</div><div class="t m0 x60 h4 ya0 ff8 fs1 fc2 sc2 ls0 ws0">P<span class="ff1">（<span class="_ _12"> </span></span>X</div><div class="t m0 xb7 h17 ya1 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x6c h6 ya0 ff4 fs1 fc2 sc2 ls0 ws0">|</div><div class="t m0 xbc h1c y9c ffa fs1 fc2 sc2 ls0 ws0">π</div><div class="t m0 x25 h4 ya0 ff1 fs1 fc2 sc2 ls0 ws0">（<span class="_ _5"> </span><span class="ff8">X</span></div><div class="t m0 xab h17 ya1 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 xbd h4 ya0 ff1 fs1 fc2 sc2 ls0 ws0">）<span class="_ _5"> </span>）<span class="_ _1e"> </span>（<span class="_ _4"> </span><span class="ff4">1<span class="_ _7"></span></span>）</div><div class="t m0 xb hd ya2 ff1 fs7 fc2 sc2 ls0 ws0">其中</div><div class="t m0 x52 hd ya3 ff1 fs7 fc2 sc2 ls0 ws0">：<span class="_ _4"> </span><span class="ff8">i<span class="_ _5"> </span><span class="ff4">=<span class="_ _1d"> </span>1<span class="_ _1"></span></span></span>，<span class="_ _1f"></span><span class="ff4">2<span class="ff1">，<span class="_ _1c"></span><span class="ffb">…<span class="ff1">，<span class="_ _1c"></span><span class="ff8">n<span class="ff1">，</span></span></span></span></span></span></div><div class="t m0 xa9 h15 ya2 ffa fs7 fc2 sc2 ls0 ws0">π</div><div class="t m0 x51 hd ya3 ff1 fs7 fc2 sc2 ls0 ws0">（<span class="_ _12"> </span><span class="ff8">X</span></div><div class="t m0 x46 h17 ya4 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x6b hd ya3 ff1 fs7 fc2 sc2 ls0 ws0">）</div><div class="t m0 xbe hd ya2 ff1 fs7 fc2 sc2 ls0 ws0">表<span class="_ _1"></span>示</div><div class="t m0 xbf h19 ya3 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 xc0 h17 ya4 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x6d hd ya2 ff1 fs7 fc2 sc2 ls0 ws0">的<span class="_ _1"></span>父<span class="_ _1"></span>节<span class="_ _1"></span>点<span class="_ _1"></span>集</div><div class="t m0 xc1 h14 ya3 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 xc2 hd ya2 ff1 fs7 fc2 sc2 ls0 ws0">当<span class="_ _1"></span>给<span class="_ _1"></span>出<span class="_ _1"></span>了<span class="_ _1"></span>网<span class="_ _1"></span>络</div><div class="t m0 xb hd ya5 ff1 fs7 fc2 sc2 ls0 ws0">结构</div><div class="t m0 xc3 hd ya6 ff8 fs7 fc2 sc2 ls0 ws0">G<span class="ff1">，</span></div><div class="t m0 xac hd ya7 ff1 fs7 fc2 sc2 ls0 ws0">节点间的相关关系也就随之<span class="_ _1"></span>确定</div><div class="t m0 x47 h14 ya6 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x66 hd ya7 ff1 fs7 fc2 sc2 ls0 ws0">在这<span class="_ _1"></span>个前<span class="_ _1"></span>提下</div><div class="t m0 x9d hd ya6 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xa7 hd ya7 ff1 fs7 fc2 sc2 ls0 ws0">结合</div><div class="t m0 xb hd ya8 ff1 fs7 fc2 sc2 ls0 ws0">网络参数</div><div class="t m0 x96 h15 ya9 ffa fs7 fc2 sc2 ls0 ws0">Θ</div><div class="t m0 xc4 hd yaa ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x93 hd ya9 ff1 fs7 fc2 sc2 ls0 ws0">一个贝叶斯网<span class="lsf">络就可以唯一地确定节点</span></div><div class="t m0 x13 h19 yaa ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 xc5 hd ya9 ff1 fs7 fc2 sc2 ls0 ws0">的<span class="_ _1"></span>联合</div><div class="t m0 xb hd yab ff1 fs7 fc2 sc2 ls0 ws0">概率分布</div><div class="t m0 xc6 hd yac ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xc7 hd yab ff1 fs7 fc2 sc2 ls0 ws0">得到推理结果</div><div class="t m0 x6b h14 yac ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 xc8 hd yab ff1 fs7 fc2 sc2 ls0 ws0">由于节点间存在条件独立<span class="_ _1"></span>的性<span class="_ _1"></span>质</div><div class="t m0 x4b hd yac ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x73 hd yab ff1 fs7 fc2 sc2 ls0 ws0">贝</div><div class="t m0 xb hd yad ff1 fs7 fc2 sc2 ls0 ws0">叶斯网络的计算效率比其他计算联合概率的方法高很多</div><div class="t m0 xc5 h14 yae ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 xb h10 yaf ff4 fs9 fc2 sc2 ls0 ws0">2</div><div class="t m0 x2 h11 yb0 ff2 fs9 fc2 sc2 lsc ws0">完备数据下贝叶斯网络结构学习相关算法</div><div class="t m0 x52 hd yb1 ff1 fs7 fc2 sc2 ls7 ws0">学习由离散变量构<span class="lsa">成的最优贝叶斯网络结构在几乎所有</span></div><div class="t m0 xb hd yb2 ff1 fs7 fc2 sc2 ls0 ws0">的情<span class="_ _1"></span>况<span class="_ _7"></span>下<span class="_ _1"></span>都<span class="_ _1"></span>是</div><div class="t m0 x50 h12 yb3 ff4 fs7 fc2 sc2 ls0 ws0">NP</div><div class="t m0 x43 hd yb2 ff1 fs7 fc2 sc2 ls0 ws0">问<span class="_ _1"></span>题</div><div class="t m0 xc9 h13 yb4 ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">6<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 x60 hd yb3 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x61 hd yb2 ff1 fs7 fc2 sc2 lsa ws0">所以当未知网络结构的情况下</div><div class="t m0 xca hd yb3 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x73 hd yb2 ff1 fs7 fc2 sc2 ls0 ws0">列</div><div class="t m0 xb hd yb5 ff1 fs7 fc2 sc2 ls7 ws0">举出关于节点的所有网络结构是很困难<span class="_ _1"></span>的</div><div class="t m0 x66 hd yb6 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x67 hd yb5 ff1 fs7 fc2 sc2 ls0 ws0">对<span class="_ _1"></span>于<span class="_ _1"></span>节<span class="_ _1"></span>点<span class="_ _1"></span>个<span class="_ _1"></span>数<span class="_ _1"></span>为</div><div class="t m0 x65 h19 yb6 ff8 fs7 fc2 sc2 ls0 ws0">n</div><div class="t m0 xb hd yb7 ff1 fs7 fc2 sc2 ls0 ws0">的有<span class="_ _1"></span>向无<span class="_ _1"></span>环图</div><div class="t m0 x5f hd yb8 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x50 hd yb7 ff1 fs7 fc2 sc2 ls0 ws0">设</div><div class="t m0 xcb hd yb8 ff8 fs7 fc2 sc2 ls0 ws0">f<span class="ff1">（<span class="_ _a"> </span></span>n<span class="ff1">）</span></div><div class="t m0 xcc hd yb7 ff1 fs7 fc2 sc2 ls0 ws0">是由</div><div class="t m0 xe h19 yb8 ff8 fs7 fc2 sc2 ls0 ws0">n</div><div class="t m0 xb7 hd yb7 ff1 fs7 fc2 sc2 ls10 ws0">节点构成的有向无环图的个数</div><div class="t m0 x65 h14 yb8 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 xb h12 yb9 ff4 fs7 fc2 sc2 ls0 ws0">Ｒobinso<span class="_ _6"></span>n</div><div class="t m0 x5b h13 yba ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">7<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 xcd hd ybb ff1 fs7 fc2 sc2 ls0 ws0">给出<span class="_ _1"></span>了关<span class="_ _1"></span>于</div><div class="t m0 x46 hd yb9 ff8 fs7 fc2 sc2 ls0 ws0">f<span class="ff1">（<span class="_ _a"> </span></span>n<span class="ff1">）</span></div><div class="t m0 xae hd ybb ff1 fs7 fc2 sc2 ls0 ws0">的计<span class="_ _1"></span>算公<span class="_ _1"></span>式</div><div class="t m0 xce hd yb9 ff1 fs7 fc2 sc2 ls0 ws0">：</div><div class="t m0 xcf h4 ybc ff8 fs1 fc2 sc2 ls0 ws0">f<span class="ff1">（<span class="_ _12"> </span></span>n<span class="ff1">）<span class="_ _1a"> </span><span class="ff4">=</span></span></div><div class="t m0 xd0 h1b ybd ffc fs1 fc2 sc2 ls0 ws0">∑</div><div class="t m0 x9b h17 ybe ff8 fsa fc2 sc2 ls0 ws0">n</div><div class="t m0 x51 h1a ybf ff8 fsa fc2 sc2 ls0 ws0">i<span class="_ _1d"> </span><span class="ff4">=<span class="_ _7"> </span>1</span></div><div class="t m0 xcc h4 ybc ff1 fs1 fc2 sc2 ls0 ws0">（<span class="_ _1a"> </span><span class="ff4">－<span class="_ _1d"> </span>1<span class="_ _1"></span></span>）</div><div class="t m0 x64 h1a yc0 ff8 fsa fc2 sc2 ls0 ws0">i<span class="_ _1d"> </span><span class="ff4">+<span class="_ _7"> </span>1</span></div><div class="t m0 x9c h4 yc1 ff8 fs1 fc2 sc2 ls0 ws0">n<span class="ff1">！</span></div><div class="t m0 xd1 h4 yc2 ff1 fs1 fc2 sc2 ls0 ws0">（<span class="_ _5"> </span><span class="ff8">n<span class="_ _8"> </span><span class="ff4">－<span class="_ _e"> </span></span>i<span class="_ _1"></span></span>）<span class="_ _5"> </span>！<span class="_ _a"> </span><span class="ff8">i<span class="_ _1"></span></span>！</div><div class="t m0 xb9 h4 ybc ff8 fs1 fc2 sc2 ls0 ws0">f<span class="ff1">（<span class="_ _12"> </span></span>n<span class="_ _4"> </span><span class="ff4">－<span class="_ _4"> </span></span>i<span class="ff1">）<span class="_ _20"> </span>（<span class="_ _4"> </span><span class="ff4">2<span class="_ _7"></span></span>）</span></div><div class="t m0 x52 hd yc3 ff1 fs7 fc2 sc2 ls0 ws0">由式</div><div class="t m0 xd2 hd yc4 ff1 fs7 fc2 sc2 ls0 ws0">（<span class="_ _8"> </span><span class="ff4">2<span class="_ _7"></span></span>）</div><div class="t m0 xc hd yc3 ff1 fs7 fc2 sc2 ls0 ws0">可以<span class="_ _1"></span>得出</div><div class="t m0 xcc hd yc4 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x1e hd yc3 ff1 fs7 fc2 sc2 ls10 ws0">贝叶<span class="_ _6"></span>斯网络结构空间<span class="lsa">随着节点个数的</span></div><div class="t m0 xb hd yc5 ff1 fs7 fc2 sc2 ls7 ws0">增加呈指数倍地增加</div><div class="t m0 xd3 hd yc6 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xd4 hd yc5 ff1 fs7 fc2 sc2 ls7 ws0">采用确定型精确算法求解最优化的网络</div><div class="t m0 xb hd yc7 ff1 fs7 fc2 sc2 ls7 ws0">结构在有限的时间内得不到精确解</div><div class="t m0 xb0 hd yc8 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xd5 hd yc7 ff1 fs7 fc2 sc2 ls7 ws0">所以一般采用非精确的启</div><div class="t m0 xb hd yc9 ff1 fs7 fc2 sc2 lsb ws0">发<span class="_ _3"></span>式<span class="_ _3"></span>搜<span class="_ _6"></span>索算法来对整个贝叶斯网络结构空间进行求解</div><div class="t m0 xa7 h14 yca ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x73 hd ycb ff1 fs7 fc2 sc2 ls0 ws0">自</div><div class="t m0 xb h12 ycc ff4 fs7 fc2 sc2 ls0 ws0">Spirtes</div><div class="t m0 x95 hd ycd ff1 fs7 fc2 sc2 ls0 ws0">等人</div><div class="t m0 xcd h13 yce ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">8<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 x5f hd ycd ff1 fs7 fc2 sc2 ls0 ws0">提<span class="_ _1"></span>出</div><div class="t m0 xd hd ycc ff4 fs7 fc2 sc2 ls0 ws0">SGS<span class="_ _1"></span><span class="ff1">（<span class="_ _14"> </span></span>peter<span class="_ _14"> </span>spirtes<span class="ff1">，<span class="_ _16"></span><span class="ff4">clark<span class="_ _14"> </span>glymour<span class="_ _14"> </span>and<span class="_ _18"> </span>richard</span></span></div><div class="t m0 xb hd ycf ff4 fs7 fc2 sc2 ls0 ws0">scheines<span class="ff1">）</span></div><div class="t m0 xc6 hd yd0 ff1 fs7 fc2 sc2 ls0 ws0">算法<span class="_ _1"></span>以来</div><div class="t m0 x43 hd ycf ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xd hd yd0 ff1 fs7 fc2 sc2 ls7 ws0">贝叶斯网络结构学习算法的发展<span class="_ _1"></span>大致<span class="_ _1"></span>分为</div><div class="t m0 xb hd yd1 ff1 fs7 fc2 sc2 ls0 ws0">三个<span class="_ _1"></span>阶段</div><div class="t m0 xd2 hd yd2 ff1 fs7 fc2 sc2 ls0 ws0">：<span class="_ _8"> </span><span class="ff4">a</span>）</div><div class="t m0 x71 hd yd1 ff1 fs7 fc2 sc2 ls11 ws0">基<span class="_ _6"></span>于<span class="_ _6"></span>依赖统计分析的方法</div><div class="t m0 x6f hd yd2 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xb9 hd yd1 ff1 fs7 fc2 sc2 ls0 ws0">此<span class="_ _1"></span>种<span class="_ _7"></span>方<span class="_ _7"></span>法<span class="_ _1"></span>将</div><div class="t m0 x62 h12 yd2 ff4 fs7 fc2 sc2 ls0 ws0">BN</div><div class="t m0 xa7 hd yd1 ff1 fs7 fc2 sc2 ls0 ws0">看<span class="_ _1"></span>做</div><div class="t m0 xb hd yd3 ff1 fs7 fc2 sc2 ls7 ws0">是表示独立变量关系的网络模型</div><div class="t m0 x25 hd yd4 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xd6 hd yd3 ff1 fs7 fc2 sc2 ls7 ws0">该方法通过计算节点间的互</div><div class="t m0 x74 hd yd5 ff1 fs7 fc2 sc2 ls7 ws0">信息和条件独立性来找出各个节点之间的关系</div><div class="t m0 x90 hd y7f ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x97 hd y80 ff1 fs7 fc2 sc2 ls0 ws0">最终<span class="_ _1"></span>寻求<span class="_ _1"></span>一种</div><div class="t m0 x74 hd y83 ff1 fs7 fc2 sc2 ls7 ws0">符合这种关系的网络结构</div><div class="t m0 xd7 hd y82 ff1 fs7 fc2 sc2 ls0 ws0">；<span class="_ _8"> </span><span class="ff4">b</span>）</div><div class="t m0 xd8 hd y83 ff1 fs7 fc2 sc2 lsa ws0">基于评分搜索的方法</div><div class="t m0 xd9 hd y82 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xda hd y83 ff1 fs7 fc2 sc2 ls0 ws0">此<span class="_ _1"></span>种<span class="_ _1"></span>方<span class="_ _7"></span>法</div><div class="t m0 x74 hd y84 ff1 fs7 fc2 sc2 ls7 ws0">由评分函数和搜索算子两部分构成</div><div class="t m0 x81 hd y85 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xdb hd y84 ff1 fs7 fc2 sc2 ls7 ws0">评分算子评价网络结构与</div><div class="t m0 x74 hd yd6 ff1 fs7 fc2 sc2 ls7 ws0">实际网络结构的相似程度</div><div class="t m0 xd7 hd yd7 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xdc hd yd6 ff1 fs7 fc2 sc2 ls7 ws0">搜索算子决定对网络结构空间的搜</div><div class="t m0 x74 hd yd8 ff1 fs7 fc2 sc2 ls0 ws0">索步<span class="_ _1"></span>骤</div><div class="t m0 x7d hd yd9 ff1 fs7 fc2 sc2 ls0 ws0">；<span class="_ _8"> </span><span class="ff4">c</span>）</div><div class="t m0 x78 hd yd8 ff1 fs7 fc2 sc2 ls7 ws0">将上述两种方<span class="lsa">法结合的混合搜索算法</span></div><div class="t m0 xdd hd yd9 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xde hd yd8 ff1 fs7 fc2 sc2 ls0 ws0">通<span class="_ _1"></span>过<span class="_ _1"></span>统<span class="_ _7"></span>计<span class="_ _1"></span>分</div><div class="t m0 x74 hd yda ff1 fs7 fc2 sc2 ls7 ws0">析的方法缩小网络结构空间</div><div class="t m0 x89 hd ydb ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x8a hd yda ff1 fs7 fc2 sc2 ls7 ws0">然后通过对缩小后的网络结构空</div><div class="t m0 x74 hd ydc ff1 fs7 fc2 sc2 ls7 ws0">间进行评分搜索得出最优的网络结构</div><div class="t m0 xdf h14 ydd ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x74 h12 yde ff4 fs7 fc2 sc2 ls0 ws0">2.<span class="_ _4"> </span>1</div><div class="t m0 xe0 hd ydf ff2 fs7 fc2 sc2 ls7 ws0">基于依赖统计分析的方法</div><div class="t m0 x7a hd ye0 ff1 fs7 fc2 sc2 ls7 ws0">基于依赖统计分析<span class="lsa">的方法通常利用统计或信息论的方法</span></div><div class="t m0 x74 hd ye1 ff1 fs7 fc2 sc2 ls7 ws0">分析变量间的依赖关系</div><div class="t m0 xe1 hd ye2 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x17 hd ye1 ff1 fs7 fc2 sc2 ls7 ws0">从而获得最优的网络结构</div><div class="t m0 x98 h14 ye2 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 xe2 hd ye1 ff1 fs7 fc2 sc2 ls0 ws0">而节<span class="_ _1"></span>点之</div><div class="t m0 x74 hd ye3 ff1 fs7 fc2 sc2 ls7 ws0">间的依赖关系通常由两点的互信息或者条件互信息决定</div><div class="t m0 xe3 h14 ye4 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x7a hd ye5 ff2 fs7 fc2 sc2 ls0 ws0">定义</div><div class="t m0 xe4 h12 ye6 ff4 fs7 fc2 sc2 ls0 ws0">1</div><div class="t m0 xe5 hd ye5 ff1 fs7 fc2 sc2 ls0 ws0">设</div><div class="t m0 xe6 h19 ye6 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 xe7 h17 ye7 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x2d h14 ye6 ff7 fs7 fc2 sc2 ls0 ws0">、<span class="_ _16"></span><span class="ff8">X</span></div><div class="t m0 xe8 h17 ye7 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 xe9 hd ye5 ff1 fs7 fc2 sc2 ls0 ws0">为</div><div class="t m0 x26 h19 ye6 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 x89 hd ye5 ff1 fs7 fc2 sc2 ls0 ws0">上<span class="_ _7"></span>的<span class="_ _7"></span>两<span class="_ _7"></span>个<span class="_ _7"></span>变<span class="_ _7"></span>量</div><div class="t m0 xea hd ye6 ff1 fs7 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ff8">x</span></div><div class="t m0 xeb h17 ye7 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 xec h14 ye6 ff7 fs7 fc2 sc2 ls0 ws0">、<span class="_ _16"></span><span class="ff8">x</span></div><div class="t m0 x91 h17 ye7 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 x32 hd ye5 ff1 fs7 fc2 sc2 ls0 ws0">分<span class="_ _7"></span>别<span class="_ _7"></span>为<span class="_ _7"></span>变<span class="_ _17"></span>量</div><div class="t m0 x74 h19 ye8 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 xed h17 ye9 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x7e h14 ye8 ff7 fs7 fc2 sc2 ls0 ws0">、<span class="_ _1c"></span><span class="ff8">X</span></div><div class="t m0 x7a h17 ye9 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 xe0 hd yea ff1 fs7 fc2 sc2 ls0 ws0">的取<span class="_ _1"></span>值</div><div class="t m0 xee hd ye8 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x79 hd yea ff1 fs7 fc2 sc2 ls0 ws0">设</div><div class="t m0 xe6 h19 ye8 ff8 fs7 fc2 sc2 ls0 ws0">C</div><div class="t m0 x2d hd yea ff1 fs7 fc2 sc2 ls0 ws0">是</div><div class="t m0 xef h19 ye8 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 xf0 hd yea ff1 fs7 fc2 sc2 ls0 ws0">中<span class="_ _1"></span>非</div><div class="t m0 xd8 h19 ye8 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 xa h17 ye9 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 xf1 h14 ye8 ff7 fs7 fc2 sc2 ls0 ws0">、<span class="_ _1b"></span><span class="ff8">X</span></div><div class="t m0 x76 h17 ye9 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 x77 hd yea ff1 fs7 fc2 sc2 ls0 ws0">变<span class="_ _1"></span>量<span class="_ _1"></span>组<span class="_ _7"></span>成<span class="_ _7"></span>的<span class="_ _1"></span>集<span class="_ _7"></span>合</div><div class="t m0 xda hd ye8 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xf2 hd yea ff1 fs7 fc2 sc2 ls0 ws0">则</div><div class="t m0 xf3 h19 ye8 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 xf4 h17 ye9 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 xf5 h14 ye8 ff7 fs7 fc2 sc2 ls0 ws0">、<span class="_ _1b"></span><span class="ff8">X</span></div><div class="t m0 xf6 h17 ye9 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 x74 hd yeb ff1 fs7 fc2 sc2 ls0 ws0">关于</div><div class="t m0 xf7 h19 yec ff8 fs7 fc2 sc2 ls0 ws0">C</div><div class="t m0 xf8 hd yeb ff1 fs7 fc2 sc2 ls7 ws0">的条件互信息可以表示为</div><div class="t m0 x31 h4 yed ff8 fs1 fc2 sc2 ls0 ws0">I<span class="ff1">（<span class="_ _5"> </span></span>X</div><div class="t m0 xf9 h17 yee ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x2c h4 yed ff1 fs1 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ff8">X</span></div><div class="t m0 xfa h17 yee ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 x42 h4 yed ff4 fs1 fc2 sc2 ls0 ws0">|<span class="_ _1d"> </span><span class="ff8">C<span class="ff1">）<span class="_ _1a"> </span></span></span>=</div><div class="t m0 xfb h1b yef ffc fs1 fc2 sc2 ls0 ws0">∑</div><div class="t m0 xe8 h17 yf0 ff8 fsa fc2 sc2 ls0 ws0">x</div><div class="t m0 xfc h17 yf1 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 xfb h13 yf0 ff1 fsa fc2 sc2 ls0 ws0">，<span class="_ _19"></span><span class="ff8">x</span></div><div class="t m0 xf0 h17 yf1 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 x17 h13 yf0 ff1 fsa fc2 sc2 ls0 ws0">，<span class="_ _19"></span><span class="ff8">c</span></div><div class="t m0 xd7 h4 yed ff8 fs1 fc2 sc2 ls0 ws0">P<span class="ff1">（<span class="_ _12"> </span></span>x</div><div class="t m0 x8a h17 yee ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 xfd h4 yed ff1 fs1 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ff8">x</span></div><div class="t m0 xfe h17 yee ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 xff h4 yed ff1 fs1 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ff8">c<span class="ff1">）<span class="_ _5"> </span><span class="ff4">log</span></span></span></div><div class="t m0 x3f h4 yf2 ff8 fs1 fc2 sc2 ls0 ws0">P<span class="ff1">（<span class="_ _12"> </span></span>x</div><div class="t m0 x100 h17 yf3 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x101 h4 yf2 ff1 fs1 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ff8">x</span></div><div class="t m0 x102 h17 yf3 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 x8f h4 yf2 ff1 fs1 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ff8">c<span class="ff1">）<span class="_ _5"> </span></span>P<span class="_ _1"></span><span class="ff1">（<span class="_ _5"> </span></span>c<span class="ff1">）</span></span></div><div class="t m0 x3f h4 yf4 ff8 fs1 fc2 sc2 ls0 ws0">P<span class="ff1">（<span class="_ _12"> </span></span>x</div><div class="t m0 x100 h17 yf5 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x101 h4 yf4 ff1 fs1 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ff8">c<span class="ff1">）<span class="_ _5"> </span></span>P<span class="_ _1"></span><span class="ff1">（<span class="_ _5"> </span></span>x</span></div><div class="t m0 x18 h17 yf5 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 x32 h4 yf4 ff1 fs1 fc2 sc2 ls0 ws0">，<span class="_ _16"></span><span class="ff8">c<span class="ff1">）</span></span></div><div class="t m0 x103 h4 yf6 ff1 fs1 fc2 sc2 ls0 ws0">（<span class="_ _4"> </span><span class="ff4">3<span class="_ _7"></span></span>）</div><div class="t m0 x7a hd yf7 ff8 fs7 fc2 sc2 ls0 ws0">I<span class="ff1">（<span class="_ _a"> </span></span>X</div><div class="t m0 x104 h17 yf8 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x105 hd yf7 ff1 fs7 fc2 sc2 ls0 ws0">，<span class="_ _1c"></span><span class="ff8">X</span></div><div class="t m0 x106 h17 yf8 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 x107 hd yf7 ff4 fs7 fc2 sc2 ls0 ws0">|<span class="_ _1d"> </span><span class="ff8">C<span class="_ _1"></span><span class="ff1">）</span></span></div><div class="t m0 x16 hd yf9 ff1 fs7 fc2 sc2 ls0 ws0">的<span class="_ _1"></span>值越<span class="_ _1"></span>大</div><div class="t m0 x108 hd yf7 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xdc hd yf9 ff1 fs7 fc2 sc2 ls0 ws0">表<span class="_ _1"></span>示变<span class="_ _1"></span>量</div><div class="t m0 x3e h19 yf7 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 x3f h17 yf8 ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x109 h14 yf7 ff7 fs7 fc2 sc2 ls0 ws0">、<span class="_ _1b"></span><span class="ff8">X</span></div><div class="t m0 x10a h17 yf8 ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 xea hd yf9 ff1 fs7 fc2 sc2 ls0 ws0">关<span class="_ _1"></span>于</div><div class="t m0 x97 h19 yf7 ff8 fs7 fc2 sc2 ls0 ws0">C</div><div class="t m0 x98 hd yf9 ff1 fs7 fc2 sc2 ls0 ws0">的<span class="_ _1"></span>依赖<span class="_ _1"></span>关<span class="_ _1"></span>系</div><div class="t m0 x74 hd yfa ff1 fs7 fc2 sc2 ls0 ws0">越大</div><div class="t m0 x7a h14 yfb ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x7d hd yfa ff1 fs7 fc2 sc2 ls0 ws0">如果</div><div class="t m0 x107 hd yfb ff8 fs7 fc2 sc2 ls0 ws0">I<span class="ff1">（<span class="_ _a"> </span></span>X</div><div class="t m0 x16 h17 yfc ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 x42 hd yfb ff1 fs7 fc2 sc2 ls0 ws0">，<span class="_ _1c"></span><span class="ff8">X</span></div><div class="t m0 x10b h17 yfc ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 x44 hd yfb ff4 fs7 fc2 sc2 ls0 ws0">|<span class="_ _1d"> </span><span class="ff8">C<span class="_ _1"></span><span class="ff1">）</span></span></div><div class="t m0 x10c hd yfa ff1 fs7 fc2 sc2 ls11 ws0">小于设定的阈值<span class="_ _8"> </span><span class="ffa ls0">ξ</span></div><div class="t m0 x101 hd yfb ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x10d hd yfa ff1 fs7 fc2 sc2 ls0 ws0">则<span class="_ _1"></span>表<span class="_ _7"></span>示<span class="_ _7"></span>变<span class="_ _1"></span>量</div><div class="t m0 xf3 h19 yfb ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 xf4 h17 yfc ff8 fsa fc2 sc2 ls0 ws0">i</div><div class="t m0 xf5 h14 yfb ff7 fs7 fc2 sc2 ls0 ws0">、<span class="_ _1b"></span><span class="ff8">X</span></div><div class="t m0 xf6 h17 yfc ff8 fsa fc2 sc2 ls0 ws0">j</div><div class="t m0 x74 hd yfd ff1 fs7 fc2 sc2 ls0 ws0">关于</div><div class="t m0 xf7 h19 yfe ff8 fs7 fc2 sc2 ls0 ws0">C</div><div class="t m0 xf8 hd yfd ff1 fs7 fc2 sc2 ls0 ws0">条件<span class="_ _1"></span>独立</div><div class="t m0 xe6 hd yfe ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x10e hd yfd ff1 fs7 fc2 sc2 ls0 ws0">故式</div><div class="t m0 xfc hd yfe ff1 fs7 fc2 sc2 ls0 ws0">（<span class="_ _8"> </span><span class="ff4">3<span class="_ _7"></span></span>）</div><div class="t m0 x10f hd yfd ff1 fs7 fc2 sc2 ls7 ws0">也表示节点间的条件独立性测试</div><div class="t m0 x110 h14 yfe ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x7a h12 yff ff4 fs7 fc2 sc2 ls0 ws0">SGS</div><div class="t m0 x105 hd y100 ff1 fs7 fc2 sc2 ls0 ws0">算法<span class="_ _1"></span>是由</div><div class="t m0 x2d h12 yff ff4 fs7 fc2 sc2 ls0 ws0">Spirtes</div><div class="t m0 xd7 hd y100 ff1 fs7 fc2 sc2 lsa ws0">等人提出的一种典型的利用节点间</div><div class="t m0 x74 hd y101 ff1 fs7 fc2 sc2 ls7 ws0">条件独立性来确定网络结构的方法</div><div class="t m0 x81 hd y102 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xdb hd y101 ff1 fs7 fc2 sc2 ls7 ws0">算法利用特定的因果模型</div><div class="t m0 x74 hd y103 ff1 fs7 fc2 sc2 ls7 ws0">解决了统计意义的独立<span class="lsa">性不能适用于非测量性变量关系的问</span></div><div class="t m0 x74 hd y104 ff1 fs7 fc2 sc2 ls0 ws0">题</div><div class="t m0 x75 hd y105 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x24 hd y104 ff1 fs7 fc2 sc2 ls7 ws0">最终得出整个网络结构</div><div class="t m0 xdc h12 y105 ff7 fs7 fc2 sc2 ls0 ws0">。<span class="_ _1"></span><span class="ff4">PC</span></div><div class="t m0 x111 hd y104 ff1 fs7 fc2 sc2 ls0 ws0">算<span class="_ _1"></span>法</div><div class="t m0 x3e h13 y106 ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">9<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 x112 hd y104 ff1 fs7 fc2 sc2 ls0 ws0">是<span class="_ _1"></span>在</div><div class="t m0 xeb h12 y105 ff4 fs7 fc2 sc2 ls0 ws0">SGS</div><div class="t m0 xde hd y104 ff1 fs7 fc2 sc2 ls0 ws0">算<span class="_ _1"></span>法<span class="_ _1"></span>的<span class="_ _7"></span>基<span class="_ _1"></span>础</div><div class="t m0 x74 hd y107 ff1 fs7 fc2 sc2 ls0 ws0">上</div><div class="t m0 x75 hd y108 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x24 hd y107 ff1 fs7 fc2 sc2 ls7 ws0">利用稀疏网络中节<span class="lsa">点不需要高阶独立性检验的特点</span></div><div class="t m0 x113 hd y108 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x7c hd y107 ff1 fs7 fc2 sc2 ls0 ws0">提<span class="_ _1"></span>出</div><div class="t m0 x74 hd y109 ff1 fs7 fc2 sc2 ls0 ws0">了一<span class="_ _1"></span>种削<span class="_ _1"></span>减策<span class="_ _1"></span>略</div><div class="t m0 x42 hd y10a ff1 fs7 fc2 sc2 ls0 ws0">：</div><div class="t m0 x114 hd y109 ff1 fs7 fc2 sc2 ls0 ws0">依次<span class="_ _1"></span>由</div><div class="t m0 x115 h12 y10a ff4 fs7 fc2 sc2 ls0 ws0">0</div><div class="t m0 xdc hd y109 ff1 fs7 fc2 sc2 ls7 ws0">阶独立性检验开始到高阶独立性检</div><div class="t m0 x74 hd y10b ff1 fs7 fc2 sc2 ls0 ws0">验</div><div class="t m0 x75 hd y10c ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x24 hd y10d ff1 fs7 fc2 sc2 ls7 ws0">对初始网络中节点之间的连接进行削减</div><div class="t m0 x87 h14 y10c ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x116 hd y10d ff1 fs7 fc2 sc2 ls7 ws0">此种策略有效地</div><div class="t m0 x74 hd y10e ff1 fs7 fc2 sc2 ls7 ws0">从稀疏模型中建立<span class="_ _1"></span>贝<span class="_ _1"></span>叶<span class="_ _1"></span>斯<span class="_ _7"></span>网<span class="_ _1"></span>络</div><div class="t m0 xa hd y10f ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xff hd y110 ff1 fs7 fc2 sc2 ls0 ws0">解<span class="_ _7"></span>决<span class="_ _7"></span>了</div><div class="t m0 x85 h12 y10f ff4 fs7 fc2 sc2 ls0 ws0">SGS</div><div class="t m0 x8f hd y110 ff1 fs7 fc2 sc2 ls9 ws0">算法随着网络中</div><div class="t m0 x74 hd y111 ff1 fs7 fc2 sc2 ls7 ws0">节点数的增长复杂<span class="lsa">度呈指数倍增长的问题</span></div><div class="t m0 xea h14 y112 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x117 hd y111 ff1 fs7 fc2 sc2 lsa ws0">为了进一步减少</div><div class="t m0 x74 hd y113 ff1 fs7 fc2 sc2 ls0 ws0">计算<span class="_ _1"></span>的复<span class="_ _1"></span>杂度</div><div class="t m0 x79 hd y114 ff1 fs7 fc2 sc2 ls0 ws0">，<span class="_ _1c"></span><span class="ff4">Cheng</span></div><div class="t m0 x118 hd y113 ff1 fs7 fc2 sc2 ls0 ws0">等人</div><div class="t m0 xd7 h13 y115 ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">10<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 x8a hd y113 ff1 fs7 fc2 sc2 ls0 ws0">提出<span class="_ _1"></span>的</div><div class="t m0 x3e h12 y114 ff4 fs7 fc2 sc2 ls0 ws0">TPDA</div><div class="t m0 x119 hd y113 ff1 fs7 fc2 sc2 ls0 ws0">算法<span class="_ _1"></span>把结<span class="_ _1"></span>构<span class="_ _1"></span>学<span class="_ _1"></span>习<span class="_ _1"></span>过</div><div class="t m0 x74 hd y116 ff1 fs7 fc2 sc2 ls7 ws0">程分三个阶段进行</div><div class="t m0 x88 hd y117 ff1 fs7 fc2 sc2 ls0 ws0">：<span class="_ _8"> </span><span class="ff4">a</span>）</div><div class="t m0 xfc hd y118 ff1 fs7 fc2 sc2 ls0 ws0">起草</div><div class="t m0 xdc hd y117 ff1 fs7 fc2 sc2 ls0 ws0">（<span class="_ _12"> </span><span class="ff4">drafting<span class="_ _1"></span></span>）</div><div class="t m0 x3e hd y118 ff1 fs7 fc2 sc2 ls0 ws0">网<span class="_ _1"></span>络<span class="_ _1"></span>结<span class="_ _1"></span>构</div><div class="t m0 x11a hd y117 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x11b hd y118 ff1 fs7 fc2 sc2 ls0 ws0">利<span class="_ _1"></span>用<span class="_ _1"></span>节<span class="_ _1"></span>点<span class="_ _1"></span>之<span class="_ _7"></span>间</div><div class="t m0 x74 hd y119 ff1 fs7 fc2 sc2 ls7 ws0">的互信息得到一个<span class="ls11">初始的网络结构</span></div><div class="t m0 x11c hd y11a ff1 fs7 fc2 sc2 ls0 ws0">；<span class="_ _5"> </span><span class="ff4">b<span class="_ _7"></span></span>）</div><div class="t m0 x11d hd y119 ff1 fs7 fc2 sc2 ls0 ws0">增<span class="_ _1"></span>厚</div><div class="t m0 x11e hd y11a ff1 fs7 fc2 sc2 ls0 ws0">（<span class="_ _a"> </span><span class="ff4">thickening<span class="_ _1"></span></span>）</div><div class="t m0 x7c hd y119 ff1 fs7 fc2 sc2 ls0 ws0">网<span class="_ _1"></span>络</div><div class="t m0 x74 hd y11b ff1 fs7 fc2 sc2 ls0 ws0">结构</div><div class="t m0 x7a hd y11c ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 xe0 hd y11b ff1 fs7 fc2 sc2 ls0 ws0">在步<span class="_ _1"></span>骤</div><div class="t m0 x2c hd y11c ff4 fs7 fc2 sc2 ls0 ws0">a<span class="ff1">）</span></div><div class="t m0 x16 hd y11b ff1 fs7 fc2 sc2 ls11 ws0">网<span class="_ _6"></span>络结<span class="_ _6"></span>构的基础上计算网络中不存在连接节</div><div class="t m0 x74 hd y11d ff1 fs7 fc2 sc2 ls7 ws0">点间的条件互信息</div><div class="t m0 x88 hd y11e ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x11f hd y11d ff1 fs7 fc2 sc2 lsa ws0">对<span class="_ _6"></span>满足<span class="_ _6"></span>条件的两节点之间添加边</div><div class="t m0 x19 hd y11e ff1 fs7 fc2 sc2 ls0 ws0">；<span class="_ _5"> </span><span class="ff4">c<span class="_ _1"></span></span>）</div><div class="t m0 x7c hd y11d ff1 fs7 fc2 sc2 ls0 ws0">削<span class="_ _1"></span>减</div><div class="t m0 x74 hd y11f ff1 fs7 fc2 sc2 ls0 ws0">（<span class="_ _12"> </span><span class="ff4">thinning</span>）</div><div class="t m0 x120 hd y120 ff1 fs7 fc2 sc2 ls0 ws0">网<span class="_ _1"></span>络<span class="_ _7"></span>结<span class="_ _7"></span>构</div><div class="t m0 x11f hd y11f ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x45 hd y120 ff1 fs7 fc2 sc2 ls0 ws0">计<span class="_ _7"></span>算<span class="_ _7"></span>步<span class="_ _7"></span>骤</div><div class="t m0 xfe hd y11f ff4 fs7 fc2 sc2 ls0 ws0">b<span class="_ _1"></span><span class="ff1">）</span></div><div class="t m0 x121 hd y120 ff1 fs7 fc2 sc2 ls8 ws0">网络结构中边的条件互<span class="_ _1"></span>信</div><div class="t m0 x74 hd y121 ff1 fs7 fc2 sc2 ls0 ws0">息</div><div class="t m0 x75 hd y122 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x24 hd y121 ff1 fs7 fc2 sc2 ls7 ws0">删除不满足条件的边</div><div class="t m0 x17 h14 y122 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 xdc hd y121 ff1 fs7 fc2 sc2 ls7 ws0">现阶段对于基于依赖统计的方法的</div><div class="t m0 x74 hd y123 ff1 fs7 fc2 sc2 ls7 ws0">研究可分为基于分解的<span class="_ _1"></span>方<span class="_ _1"></span>法</div><div class="t m0 x122 h14 y124 ff7 fs7 fc2 sc2 ls0 ws0">、</div><div class="t m0 xd8 hd y123 ff1 fs7 fc2 sc2 ls0 ws0">基<span class="_ _1"></span>于</div><div class="t m0 x123 h12 y124 ff4 fs7 fc2 sc2 ls0 ws0">Markov<span class="_ _14"> </span>blanket</div><div class="t m0 xde hd y123 ff1 fs7 fc2 sc2 ls0 ws0">的<span class="_ _1"></span>方<span class="_ _1"></span>法<span class="_ _7"></span>和<span class="_ _1"></span>基</div><div class="t m0 x74 hd y125 ff1 fs7 fc2 sc2 ls7 ws0">于结构空间限制的方法三种</div><div class="t m0 x89 h14 y126 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x74 h12 y127 ff4 fs7 fc2 sc2 ls0 ws0">2.<span class="_ _4"> </span>1.<span class="_ _8"> </span>1</div><div class="t m0 x30 hd y128 ff6 fs7 fc2 sc2 ls7 ws0">基于分解的方法</div><div class="t m0 x7a hd y129 ff2 fs7 fc2 sc2 ls0 ws0">定义</div><div class="t m0 xe4 h12 y12a ff4 fs7 fc2 sc2 ls0 ws0">2</div><div class="t m0 x2c hd y129 ff1 fs7 fc2 sc2 ls0 ws0">路径</div><div class="t m0 x88 h19 y12a ff8 fs7 fc2 sc2 ls0 ws0">l</div><div class="t m0 x11f hd y129 ff1 fs7 fc2 sc2 ls0 ws0">被节<span class="_ _1"></span>点集<span class="_ _1"></span>合</div><div class="t m0 xff h14 y12a ff8 fs7 fc2 sc2 ls0 ws0">Z<span class="_ _f"></span><span class="ff7">“<span class="_ _0"></span><span class="ff8">d</span></span></div><div class="t m0 x124 hd y129 ff1 fs7 fc2 sc2 ls0 ws0">分割</div><div class="t m0 x125 h14 y12a ff7 fs7 fc2 sc2 ls0 ws0">”</div><div class="t m0 xea hd y129 ff1 fs7 fc2 sc2 ls0 ws0">当且<span class="_ _1"></span>仅当</div><div class="t m0 x126 hd y12a ff1 fs7 fc2 sc2 ls0 ws0">：<span class="_ _5"> </span><span class="ff4">a<span class="_ _1"></span></span>）<span class="_ _a"> </span><span class="ff8">l</span></div><div class="t m0 x7c hd y129 ff1 fs7 fc2 sc2 ls0 ws0">包<span class="_ _1"></span>含</div><div class="t m0 x74 hd y12b ff1 fs7 fc2 sc2 ls0 ws0">一个<span class="_ _1"></span>链模<span class="_ _1"></span>型</div><div class="t m0 x107 h19 y12c ff8 fs7 fc2 sc2 ls0 ws0">u</div><div class="t m0 x2c h18 y12d ffc fs7 fc2 sc2 ls0 ws0">→</div><div class="t m0 x127 h19 y12c ff8 fs7 fc2 sc2 ls0 ws0">v</div><div class="t m0 xe6 h18 y12d ffc fs7 fc2 sc2 ls0 ws0">→</div><div class="t m0 x2d h19 y12c ff8 fs7 fc2 sc2 ls0 ws0">w</div><div class="t m0 x8b hd y12b ff1 fs7 fc2 sc2 ls7 ws0">或者包含一个分叉模<span class="_ _1"></span>型</div><div class="t m0 x117 h19 y12c ff8 fs7 fc2 sc2 ls0 ws0">u</div><div class="t m0 x11a h18 y12d ffc fs7 fc2 sc2 ls0 ws0">←</div><div class="t m0 xdd h19 y12c ff8 fs7 fc2 sc2 ls0 ws0">v</div><div class="t m0 xde h18 y12d ffc fs7 fc2 sc2 ls0 ws0">→</div><div class="t m0 x126 hd y12c ff8 fs7 fc2 sc2 ls0 ws0">w<span class="ff1">，</span></div><div class="t m0 x128 hd y12b ff1 fs7 fc2 sc2 ls0 ws0">中<span class="_ _1"></span>间<span class="_ _1"></span>节</div><div class="t m0 x74 hd y12e ff1 fs7 fc2 sc2 ls0 ws0">点</div><div class="t m0 x129 h19 y12f ff8 fs7 fc2 sc2 ls0 ws0">v</div><div class="t m0 x12a hd y12e ff1 fs7 fc2 sc2 ls0 ws0">属于<span class="_ _1"></span>节点<span class="_ _1"></span>集合</div><div class="t m0 x2d hd y12f ff8 fs7 fc2 sc2 ls0 ws0">Z<span class="ff1">；<span class="_ _8"> </span><span class="ff4">b<span class="_ _1"></span></span>）<span class="_ _12"> </span></span>l</div><div class="t m0 x108 hd y12e ff1 fs7 fc2 sc2 ls0 ws0">包含<span class="_ _1"></span>一<span class="_ _1"></span>个<span class="_ _1"></span>冲<span class="_ _1"></span>突<span class="_ _1"></span>模<span class="_ _1"></span>型</div><div class="t m0 x117 h19 y12f ff8 fs7 fc2 sc2 ls0 ws0">u</div><div class="t m0 x11a h18 y130 ffc fs7 fc2 sc2 ls0 ws0">→</div><div class="t m0 xdd h19 y12f ff8 fs7 fc2 sc2 ls0 ws0">v</div><div class="t m0 x12b h18 y130 ffc fs7 fc2 sc2 ls0 ws0">←</div><div class="t m0 x126 hd y12f ff8 fs7 fc2 sc2 ls0 ws0">w<span class="ff1">，</span></div><div class="t m0 x128 hd y12e ff1 fs7 fc2 sc2 ls0 ws0">中<span class="_ _1"></span>间<span class="_ _1"></span>节</div><div class="t m0 x74 hd y131 ff1 fs7 fc2 sc2 ls0 ws0">点</div><div class="t m0 x129 h19 y132 ff8 fs7 fc2 sc2 ls0 ws0">v</div><div class="t m0 x12a hd y131 ff1 fs7 fc2 sc2 ls11 ws0">和<span class="_ _6"></span>其<span class="_ _6"></span>子<span class="_ _6"></span>节<span class="_ _6"></span>点都不属于节点集合</div><div class="t m0 xdb h14 y132 ff8 fs7 fc2 sc2 ls0 ws0">Z<span class="ff7">。</span></div><div class="t m0 x112 hd y131 ff1 fs7 fc2 sc2 ls11 ws0">包含不同节点的集合</div><div class="t m0 x74 h14 y133 ff8 fs7 fc2 sc2 ls0 ws0">X<span class="ff7">、<span class="_ _1c"></span><span class="ff8">Y</span></span></div><div class="t m0 x12a hd y134 ff1 fs7 fc2 sc2 ls0 ws0">被节<span class="_ _1"></span>点集<span class="_ _1"></span>合</div><div class="t m0 xe6 h14 y133 ff8 fs7 fc2 sc2 ls0 ws0">Z<span class="_ _f"></span><span class="ff7">“<span class="_ _0"></span><span class="ff8">d</span></span></div><div class="t m0 x45 hd y134 ff1 fs7 fc2 sc2 ls0 ws0">分割</div><div class="t m0 x26 h14 y133 ff7 fs7 fc2 sc2 ls0 ws0">”</div><div class="t m0 x12c hd y134 ff1 fs7 fc2 sc2 ls7 ws0">当且仅当节点集合</div><div class="t m0 x90 h14 y133 ff8 fs7 fc2 sc2 ls0 ws0">Z<span class="_ _f"></span><span class="ff7">“<span class="_ _0"></span><span class="ff8">d</span></span></div><div class="t m0 xd9 hd y134 ff1 fs7 fc2 sc2 ls0 ws0">分割</div><div class="t m0 x113 h14 y133 ff7 fs7 fc2 sc2 ls0 ws0">”</div><div class="t m0 x7c hd y134 ff1 fs7 fc2 sc2 ls0 ws0">所有</div><div class="t m0 x74 h19 y135 ff8 fs7 fc2 sc2 ls0 ws0">X</div><div class="t m0 x7e hd y136 ff1 fs7 fc2 sc2 ls0 ws0">中节<span class="_ _1"></span>点到</div><div class="t m0 x12d h19 y135 ff8 fs7 fc2 sc2 ls0 ws0">Y</div><div class="t m0 xe5 hd y136 ff1 fs7 fc2 sc2 ls0 ws0">中节<span class="_ _1"></span>点的<span class="_ _1"></span>路径</div><div class="t m0 x12e h14 y135 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x12f hd y136 ff1 fs7 fc2 sc2 ls0 ws0">当节<span class="_ _1"></span>点</div><div class="t m0 x84 h14 y135 ff8 fs7 fc2 sc2 ls0 ws0">u<span class="ff7">、<span class="_ _1b"></span><span class="ff8">v</span></span></div><div class="t m0 x10a hd y136 ff1 fs7 fc2 sc2 ls0 ws0">之<span class="_ _1"></span>间<span class="_ _1"></span>没<span class="_ _1"></span>有<span class="_ _1"></span>连<span class="_ _1"></span>接</div><div class="t m0 x113 hd y135 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x7c hd y136 ff1 fs7 fc2 sc2 ls0 ws0">冲<span class="_ _1"></span>突</div><div class="t m0 x74 hd y137 ff1 fs7 fc2 sc2 ls0 ws0">模型</div><div class="t m0 xf7 h19 y138 ff8 fs7 fc2 sc2 ls0 ws0">u</div><div class="t m0 x130 h18 y139 ffc fs7 fc2 sc2 ls0 ws0">→</div><div class="t m0 x80 h19 y138 ff8 fs7 fc2 sc2 ls0 ws0">v</div><div class="t m0 xe4 h18 y139 ffc fs7 fc2 sc2 ls0 ws0">←</div><div class="t m0 x12d h19 y138 ff8 fs7 fc2 sc2 ls0 ws0">w</div><div class="t m0 x79 hd y137 ff1 fs7 fc2 sc2 ls0 ws0">被称<span class="_ _1"></span>为</div><div class="t m0 xe8 h19 y138 ff8 fs7 fc2 sc2 ls0 ws0">V</div><div class="t m0 xe1 hd y137 ff1 fs7 fc2 sc2 ls0 ws0">结构</div><div class="t m0 x12e h13 y13a ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">11<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 xf1 h14 y138 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x7a hd y13b ff1 fs7 fc2 sc2 ls0 ws0">文献</div><div class="t m0 x105 hd y13c ff1 fs7 fc2 sc2 ls0 ws0">［<span class="_ _19"></span><span class="ff4">11<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 x131 hd y13b ff1 fs7 fc2 sc2 ls11 ws0">提<span class="_ _6"></span>出了一种贝叶斯网络的分<span class="_ _1"></span>解方法</div><div class="t m0 x33 hd y13c ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x126 hd y13b ff1 fs7 fc2 sc2 ls0 ws0">将<span class="_ _7"></span>庞<span class="_ _7"></span>大<span class="_ _1"></span>的</div><div class="t m0 x74 hd y13d ff1 fs7 fc2 sc2 ls7 ws0">贝叶斯网络分解为多个</div><div class="t m0 xf0 h19 y13e ff8 fs7 fc2 sc2 ls0 ws0">V</div><div class="t m0 x26 hd y13d ff1 fs7 fc2 sc2 ls0 ws0">结<span class="_ _1"></span>构</div><div class="t m0 x132 h14 y13e ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x133 hd y13d ff1 fs7 fc2 sc2 lsa ws0">通过节点间条件独立性检验</div><div class="t m0 x74 hd y13f ff1 fs7 fc2 sc2 ls7 ws0">得出一个初始网络结构</div><div class="t m0 xe1 hd y140 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x17 hd y141 ff1 fs7 fc2 sc2 ls7 ws0">然后找出网络中</div><div class="t m0 x85 h14 y140 ff7 fs7 fc2 sc2 ls0 ws0">“<span class="_ _0"></span><span class="ff8">d</span></div><div class="t m0 x134 hd y141 ff1 fs7 fc2 sc2 ls0 ws0">分割</div><div class="t m0 xdd h14 y140 ff7 fs7 fc2 sc2 ls0 ws0">”</div><div class="t m0 xde hd y141 ff1 fs7 fc2 sc2 ls0 ws0">集合<span class="_ _1"></span>并<span class="_ _1"></span>分<span class="_ _1"></span>割</div><div class="t m0 x74 hd y142 ff1 fs7 fc2 sc2 ls0 ws0">初始<span class="_ _1"></span>网络<span class="_ _1"></span>结构</div><div class="t m0 x79 hd y143 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x41 hd y142 ff1 fs7 fc2 sc2 ls0 ws0">得出<span class="_ _1"></span>多个</div><div class="t m0 x10c h14 y143 ff7 fs7 fc2 sc2 ls0 ws0">“<span class="_ _0"></span><span class="ff8">d</span></div><div class="t m0 x135 hd y142 ff1 fs7 fc2 sc2 ls0 ws0">分<span class="_ _1"></span>割</div><div class="t m0 x111 h14 y143 ff7 fs7 fc2 sc2 ls0 ws0">”</div><div class="t m0 x8d hd y142 ff1 fs7 fc2 sc2 ls0 ws0">的<span class="_ _1"></span>网<span class="_ _1"></span>络<span class="_ _7"></span>结<span class="_ _1"></span>构</div><div class="t m0 xec hd y143 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x136 hd y142 ff1 fs7 fc2 sc2 ls0 ws0">最<span class="_ _1"></span>后<span class="_ _1"></span>搜<span class="_ _7"></span>索<span class="_ _1"></span>出</div><div class="t m0 xf5 h14 y143 ff7 fs7 fc2 sc2 ls0 ws0">“<span class="_ _0"></span><span class="ff8">d</span></div><div class="t m0 x74 hd y144 ff1 fs7 fc2 sc2 ls0 ws0">分割</div><div class="t m0 x7a h14 y145 ff7 fs7 fc2 sc2 ls0 ws0">”</div><div class="t m0 x137 hd y144 ff1 fs7 fc2 sc2 ls0 ws0">网络<span class="_ _1"></span>结构<span class="_ _1"></span>中<span class="_ _1"></span>的</div><div class="t m0 x138 h19 y145 ff8 fs7 fc2 sc2 ls0 ws0">V</div><div class="t m0 xe9 hd y144 ff1 fs7 fc2 sc2 ls0 ws0">结<span class="_ _7"></span>构</div><div class="t m0 x135 h12 y145 ff7 fs7 fc2 sc2 ls0 ws0">。<span class="_ _1"></span><span class="ff4">Xie</span></div><div class="t m0 x8d hd y144 ff1 fs7 fc2 sc2 ls0 ws0">等<span class="_ _1"></span>人</div><div class="t m0 x139 h13 y146 ff1 fsa fc2 sc2 ls0 ws0">［<span class="_ _0"></span><span class="ff4">12<span class="_ _0"></span><span class="ff1">］</span></span></div><div class="t m0 x86 hd y144 ff1 fs7 fc2 sc2 ls0 ws0">将<span class="_ _1"></span>文<span class="_ _7"></span>献</div><div class="t m0 x18 hd y145 ff1 fs7 fc2 sc2 ls0 ws0">［<span class="_ _f"></span><span class="ff4">11<span class="_ _3"></span><span class="ff1">］</span></span></div><div class="t m0 x128 hd y144 ff1 fs7 fc2 sc2 ls0 ws0">贝<span class="_ _1"></span>叶<span class="_ _7"></span>斯</div><div class="t m0 x74 hd y147 ff1 fs7 fc2 sc2 ls7 ws0">网络的分解方法运用于贝叶斯网络结构学习</div><div class="t m0 x102 hd y148 ff1 fs7 fc2 sc2 ls0 ws0">，</div><div class="t m0 x116 hd y147 ff1 fs7 fc2 sc2 ls7 ws0">并提出了基于分</div><div class="t m0 x74 hd y149 ff1 fs7 fc2 sc2 ls7 ws0">解的贝叶斯网络结构<span class="_ _1"></span>学<span class="_ _1"></span>习<span class="_ _1"></span>的<span class="_ _1"></span>方<span class="_ _1"></span>法</div><div class="t m0 x13a h14 yd4 ff7 fs7 fc2 sc2 ls0 ws0">。</div><div class="t m0 x11c hd yd3 ff1 fs7 fc2 sc2 ls11 ws0">通过搜索网络结构中的</div><div class="t m0 x83 h19 yd4 ff8 fs7 fc2 sc2 ls0 ws0">V</div><div class="t m0 x5b h10 y14a ff7 fs9 fc2 sc2 ls0 ws0">·<span class="_ _21"></span><span class="ff4">2<span class="_ _22"></span>4<span class="_ _22"></span>6<span class="_ _21"></span><span class="ff7">·</span></span></div><div class="t m0 x14 ha y14b ff6 fs5 fc2 sc2 lse ws0">计算机应用研究<span class="_ _23"> </span>第</div><div class="t m0 x13b h16 y14c ff4 fs5 fc2 sc2 ls0 ws0">32</div><div class="t m0 xf4 ha y14b ff6 fs5 fc2 sc2 ls0 ws0">卷</div></div><div class="pi" data-data='{"ctm":[1.612022,0.000000,0.000000,1.612022,0.000000,0.000000]}'></div></div>
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