FullBNT学习笔记之一(matlab)

</pre>      <span style="font-size:18px;">首先来看一个草地湿润模型，Cloudy表示天气是否多云C=1(F)表示False，C=2(T)表示True,一下表示均相同，Sprinklet表示洒水车是否出动，Rain表示是否下雨，WetGrass表示草地是否是湿的。旁边的表格表示各种条件概率。</span></div><div style="text-align: center;"><span style="font-size:18px;"><img 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" alt="" /></span></div><div style="text-align: left;"><span style="font-size:18px;"></span></div><div style="text-align: left;"><span style="font-size:18px;"></span><pre name="code" class="plain">clear;clc;

N = 4;                        %四个节点 分别是cloudy，sprinkler，rain，wetgrass
dag = zeros(N,N);
C = 1; S = 2; R = 3; W = 4;
dag(C,[R S]) = 1;             %节点之间的连接关系
dag(R,W) = 1;
dag(S,W) = 1;
discrete_nodes = 1:N;         %离散节点
node_sizes = 2*ones(1,N);     %节点状态数
bnet =mk_bnet(dag,node_sizes,'names',{'cloudy',...
    'sprinkler','rain','wetgrass'},'discrete',discrete_nodes);
bnet.CPD{C} = tabular_CPD(bnet,C,[0.5 0.5]);        %手动输入条件概率
bnet.CPD{R} = tabular_CPD(bnet,R,[0.8 0.2 0.2 0.8]);
bnet.CPD{S} = tabular_CPD(bnet,S,[0.5 0.9 0.5 0.1]);
bnet.CPD{W} = tabular_CPD(bnet,W,[1 0.1 0.1 0.01 0 0.9 0.9 0.99]);

%画出建立好的贝叶斯网络
figure
draw_graph(dag);

<p style="margin-top: 0px; margin-bottom: 5px; padding-top: 0px; padding-bottom: 0px; border: 0px; list-style: none; word-wrap: normal; word-break: normal; line-height: 21px; color: rgb(50, 62, 50); font-family: simsun; font-size: 14px; background-color: rgb(216, 204, 224);"></p>

</pre><span style="color: rgb(50, 62, 50); font-family: simsun; font-size: 14px; line-height: 21px; background-color: rgb(216, 204, 224);"></span><pre name="code" class="plain">

      接下来比如我们想计算洒水器导致草地是湿润的概率。证据的构成是W=2，enter_evidenc 执行一个双通道的信息传递模式。第一次返回的变量包括修正的结合着证据的引擎，第二次返回的变量包括证据的对数似然。

按如下方式计算p=P(S=2|W=2):

</pre></p></div><div style="text-align: left;"><span style="font-size:18px;"></span><pre name="code" class="plain">

</pre><pre name="code" class="plain" style="font-size: 18px;">engine = jtree_inf_engine(bnet);

evidence = cell(1,N);
evidence{W} = 2;
[engine, loglik] = enter_evidence(engine, evidence);
marg = marginal_nodes(engine, S);
p = marg.T(2);

</pre><pre name="code" class="plain" style="font-size: 18px;">evidence = cell(1,N);
[engine, ll] = enter_evidence(engine, evidence);
m = marginal_nodes(engine, [W]);
m.T

<p>evidence = cell(1,N);</p><p>[engine, ll] = enter_evidence(engine,evidence);</p><p>m = marginal_nodes(engine, [S R W]);</p>