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如何使用贝叶斯网络工具箱

  如何使用贝叶斯网络工具箱

  贝叶斯网络是一种概率网络，它是基于概率推理的图形化网络，而贝叶斯公式则是这个概率网络的基础。

  贝叶斯网络的拓扑结构是一个具有概率分布的有向弧段（DAG）。它是由节点和有向弧段组成的。节点代表事件或变量，弧段代表节点之间的因果关系或概率关系，而弧段是有向的，不构成回路。

  贝叶斯网络工具箱采用MATLAB语言编制的贝叶斯网络工具箱(Bayesian Networks Toolbox,BNT)可实现贝叶斯网络结构学习、参数学习、推理和构建贝叶斯分类器,此工具箱在贝叶斯学习编程方面非常灵活。利用贝叶斯网络工具箱可以解决贝叶斯学习和推理问题，下面以运行官方模板为例。

  详细信息：http://www.media.mit.edu/wearables/mithril/BNT/mixtureBNT.txt

  下载mixtureBNT
  http://www.media.mit.edu/wearables/mithril/BNT/mixtureBNT.zip
  http://www.media.mit.edu/wearables/mithril/BNT/mixtureBNT.tar.gz

  >> cd d:\我的文档\桌面\mixtureBNT
  >> dir

  .               mixtureBNT.m    mixtureBNT.txt 
  ..              mixtureBNT.mat

  >> mixtureBNT

  ans =

     570    31

  
  ans =

     120    31

  EM iteration 1, ll = -20167.3701
  EM iteration 2, ll = 6959.8468
  EM iteration 3, ll = 6959.8468
  EM iteration 4, ll = 6959.8469
  EM iteration 5, ll = 6959.8471
  EM iteration 6, ll = 6959.8482
  EM iteration 7, ll = 6959.8519
  EM iteration 8, ll = 6959.8640
  EM iteration 9, ll = 6959.8963
  EM iteration 10, ll = 6959.9513

  Current plot held
  Current plot held
  >>

  附：mixtureBNT.m 内容

  load 'mixtureBNT.mat'
  size(walkingX)
  size(runningX)
  dag = [ 0 1 1 ; 0 0 1 ; 0 0 0 ];
  discrete_nodes = [1 2];
  nodes = [1 : 3];
  node_sizes=[ 2 2 31];
  bnet = mk_bnet(dag, node_sizes, 'discrete', discrete_nodes);
  bnet.CPD{1} = tabular_CPD(bnet,1);
  bnet.CPD{2} = tabular_CPD(bnet,2);
  bnet.CPD{3} = gaussian_CPD(bnet, 3);
  %bnet.CPD{3} = gaussian_CPD(bnet, 3,'cov_type','diag');
  trainingX = walkingX(1:100,:);
  trainingX(101:200,:)=runningX(1:100,:);
  trainingC(1:100) = 1;   %% Class 1 is walking
  trainingC(101:200) = 2; %% Class 2 is running
  testX(1:20,:) = walkingX(101:120,:);   %% The first 20 are walking
  testX(21:40,:) = runningX(101:120,:); %% The next 20 are running
  training= cell(3,length(trainingX));
  training(3,:) = num2cell(trainingX',1);
  training(1,:) = num2cell(trainingC,1);
  engine = jtree_inf_engine(bnet);
  maxiter=10;     %% The number of iterations of EM (max)
  epsilon=1e-100; %% A very small stopping criterion
  [bnet2, ll, engine2] = learn_params_em(engine,training,maxiter,epsilon);
  class0= cell(3,1); %% Create an empty cell array for observations
  class1 = class0;
  class2 = class0;
  class1{1} = 1;     %% The class node is observed to be walking
  class2{1} = 2;     %% The class node is observed to be running
  for i=1:100
     sample1=sample_bnet(bnet2,'evidence',class1);
     sample2=sample_bnet(bnet2,'evidence',class2);
     modelX(i,:)=sample1{3}';
     modelX(i+100,:)=sample2{3}';
  end
  figure
  subplot(2,1,1);
  plot(trainingX);
  subplot(2,1,2);
  plot(modelX);
  evidence=class0;   %% Start out with nothing observed
  for i=1:40
     evidence{3}=testX(i,:)';
     [engine3, ll] = enter_evidence(engine2,evidence);
     marg = marginal_nodes(engine3,1);
     p(i,:)=marg.T';
  end
  figure;
  subplot(2,1,1);
  plot(testX);
  hold
  plot(p(:,1)); %% Plot the output of the walking classifier
  subplot(2,1,2);
  plot(testX);
  hold
  plot(p(:,2)); %% Plot the output of the running classifier