Question

我正在尝试使用BNT和MATLAB实现朴素贝叶斯分类器。到目前为止，我一直坚持使用简单的tabular_CPD变量和变量的“猜测”概率。到目前为止，我的原型网包含以下内容：

DAG = false(5);
DAG(1, 2:5) = true;
bnet = mk_bnet(DAG, [2 3 4 3 3]);
bnet.CPD{1} = tabular_CPD(bnet, 1, [.5  .5]);
bnet.CPD{2} = tabular_CPD(bnet, 2, [.1  .345   .45 .355   .45 .3]);
bnet.CPD{3} = tabular_CPD(bnet, 3, [.2  .02    .59 .2     .2  .39    .01 .39]);
bnet.CPD{4} = tabular_CPD(bnet, 4, [.4  .33333 .5  .33333 .1  .33333]);
bnet.CPD{5} = tabular_CPD(bnet, 5, [.5  .33333 .4  .33333 .1  .33333]);
engine = jtree_inf_engine(bnet);

这里变量1是我想要的输出变量，设置为最初为输出类分配0.5概率。

变量2-5定义我测量的特征的CPD：

2是簇大小，范围从1到12或更多
3是将是实际值＆gt; = 1
4和5是标准偏差（实际）值（X和Y散射）

为了对候选聚类进行分类，我将所有特征测量分解为3-4个范围括号，如下所示：

...
    evidence = cell(1, 5);
    evidence{2} = sum(M > [0 2 6]);
    evidence{3} = sum(O > [0 1.57 2 3]);
    evidence{4} = sum(S(1) > [-Inf 1 2]);
    evidence{5} = sum(S(2) > [-Inf 0.4 0.8]);
    eng = enter_evidence(engine, evidence);
    marginals = marginal_nodes(eng, 1);
    e = marginals.T(1);
...

考虑到我只是猜测范围括号和概率值，这实际上效果很好。但我相信我应该在这里使用的是gaussian_CPD。我认为 gaussian_CPD可以学习最优括号和概率（作为均值和协方差矩阵和权重）。

我的问题是，我没有找到任何关于如何使用BNT gaussian_CPD类的简单示例。例如，我是如何将gaussian_CPD初始化为与上述某个tabular_CPD变量大致相同的行为？

Answer 1

我最终通过在MATLAB命令提示符下试验BNT来解决这个问题。以下是我使用gaussian_CPD节点定义分类器网络的方法：

DAG = false(5); DAG(1, 2:5) = true
bnet = mk_bnet(DAG, [2 1 1 2 1], 'discrete', 1);
bnet.CPD{1} = tabular_CPD(bnet, 1, 'prior_type', 'dirichlet');
for node = 2:5
   bnet.CPD{node} = gaussian_CPD(bnet, node);
end
bnet

DAG =

     0     1     1     1     1
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0
     0     0     0     0     0

bnet = 

               equiv_class: [1 2 3 4 5]
                    dnodes: 1
                  observed: []
                     names: {}
                    hidden: [1 2 3 4 5]
               hidden_bitv: [1 1 1 1 1]
                       dag: [5x5 logical]
                node_sizes: [2 1 1 2 1]
                    cnodes: [2 3 4 5]
                   parents: {[1x0 double]  [1]  [1]  [1]  [1]}
    members_of_equiv_class: {[1]  [2]  [3]  [4]  [5]}
                       CPD: {[1x1 tabular_CPD]  [1x1 gaussian_CPD]  [1x1 gaussian_CPD]  [1x1 gaussian_CPD]  [1x1 gaussian_CPD]}
             rep_of_eclass: [1 2 3 4 5]
                     order: [1 5 4 3 2]

要训练它，我用我原来的分类，帮我标注一组300个样本，后来干脆跑到他们的2 /三分之二通过训练算法。

bnet = learn_params(bnet, lsamples);
CPD = struct(bnet.CPD{1}); % Peek inside CPD{1}
dispcpt(CPD.CPT);

1 : 0.6045 
2 : 0.3955

dispcpt的输出粗略地概述了训练集中标记样本中的类别分配。

为了测试新的分类器，我通过原始和新的贝叶斯网络运行了最后1/3的结果。这是我用于新网的代码：

engine = jtree_inf_engine(bnet);
evidence = cell(1, 5);
tresults = cell(3, length(tsamples));
tresults(3, :) = tsamples(1, :);
for i = 1:length(tsamples)
    evidence(2:5) = tsamples(2:5, i);
    marginal = marginal_nodes(enter_evidence(engine, evidence), 1);
    tresults{1, i} = find(marginal.T == max(marginal.T)); % Generic decision point
    tresults{2, i} = marginal.T(1);
end
tresults(:, 1:8)

ans = 

    [         2]    [     1]    [         2]    [         2]    [         2]    [     1]    [     1]    [     1]
    [1.8437e-10]    [0.9982]    [3.3710e-05]    [3.8349e-04]    [2.2995e-11]    [0.9997]    [0.9987]    [0.5116]
    [         2]    [     1]    [         2]    [         2]    [         2]    [     1]    [     1]    [     2]

然后，为了弄清楚是否有任何改进，我绘制了重叠的ROC图。事实证明，我的原始网络做得很好，很难确定使用高斯CPD的训练网是否做得更好。在ROC曲线下打印区域澄清了新网确实表现稍好一些。（base area是原始网络，area是新网络。）

conf = cell2mat(tresults(2,:));
hit = cell2mat(tresults(3,:)) == 1;
[~, ~, basearea] = plotROC(baseconf, basehit, 'r')
hold all;
[~, ~, area] = plotROC(conf, hit, 'b')
hold off;

basearea =

    0.9371

area =

    0.9555

ROC Diagram

我在这里张贴这一点，以便下一次我要做到这一点，我就可以找到答案...希望别人会发现它也是有用的。

Answer 2

我在下面给出一个完整的例子，说明如何使用BNT工具箱构建一个朴素的贝叶斯网络。我正在使用cars dataset的子集。它包含离散和连续属性。

为方便起见，我使用了一些需要统计工具箱的函数。

我们首先准备数据集：

%# load dataset
D = load('carsmall');

%# keep only features of interest
D = rmfield(D, {'Mfg','Horsepower','Displacement','Model'});

%# filter the rows to keep only two classes
idx = ismember(D.Origin, {'USA' 'Japan'});
D = structfun(@(x)x(idx,:), D, 'UniformOutput',false);
numInst = sum(idx);

%# replace missing values with mean
D.MPG(isnan(D.MPG)) = nanmean(D.MPG);

%# convert discrete attributes to numeric indices 1:mx
[D.Origin,~,gnOrigin] = grp2idx( cellstr(D.Origin) );
[D.Cylinders,~,gnCylinders] = grp2idx( D.Cylinders );
[D.Model_Year,~,gnModel_Year] = grp2idx( D.Model_Year );

接下来我们构建我们的图形模型：

%# info about the nodes
nodeNames = fieldnames(D);
numNodes = numel(nodeNames);
node = [nodeNames num2cell((1:numNodes)')]';
node = struct(node{:});
dNodes = [node.Origin node.Cylinders node.Model_Year];
cNodes = [node.MPG node.Weight node.Acceleration];
depNodes = [node.MPG node.Cylinders node.Weight ...
            node.Acceleration node.Model_Year];

vals = cell(1,numNodes);
vals(dNodes) = cellfun(@(f) unique(D.(f)), nodeNames(dNodes), 'Uniform',false);
nodeSize = ones(1,numNodes);
nodeSize(dNodes) = cellfun(@numel, vals(dNodes));

%# DAG
dag = false(numNodes);
dag(node.Origin, depNodes) = true;

%# create naive bayes net
bnet = mk_bnet(dag, nodeSize, 'discrete',dNodes, 'names',nodeNames, ...
    'observed',depNodes);
for i=1:numel(dNodes)
    name = nodeNames{dNodes(i)};
    bnet.CPD{dNodes(i)} = tabular_CPD(bnet, node.(name), ...
        'prior_type','dirichlet');
end
for i=1:numel(cNodes)
    name = nodeNames{cNodes(i)};
    bnet.CPD{cNodes(i)} = gaussian_CPD(bnet, node.(name));
end

%# visualize the graph
[~,~,h] = draw_graph(bnet.dag, nodeNames);
hTxt = h(:,1); hNodes = h(:,2);
set(hTxt(node.Origin), 'FontWeight','bold', 'Interpreter','none')
set(hNodes(node.Origin), 'FaceColor','g')
set(hTxt(depNodes), 'Color','k', 'Interpreter','none')
set(hNodes(depNodes), 'FaceColor','y')

现在我们将数据分成训练/测试：

%# build samples as cellarray
data = num2cell(cell2mat(struct2cell(D)')');

%# split train/test: 1/3 for testing, 2/3 for training
cv = cvpartition(D.Origin, 'HoldOut',1/3);
trainData = data(:,cv.training);
testData = data(:,cv.test);
testData(1,:) = {[]};    %# remove class

最后，我们从训练集中学习参数，并预测测试数据的类别：

%# training
bnet = learn_params(bnet, trainData);

%# testing
prob = zeros(nodeSize(node.Origin), sum(cv.test));
engine = jtree_inf_engine(bnet);         %# Inference engine
for i=1:size(testData,2)
    [engine,loglik] = enter_evidence(engine, testData(:,i));
    marg = marginal_nodes(engine, node.Origin);
    prob(:,i) = marg.T;

end
[~,pred] = max(prob);
actual = D.Origin(cv.test)';

%# confusion matrix
predInd = full(sparse(1:numel(pred),pred,1));
actualInd = full(sparse(1:numel(actual),actual,1));
conffig(predInd, actualInd);             %# confmat

%# ROC plot and AUC
figure
[~,~,auc] = plotROC(max(prob), pred==actual, 'b')
title(sprintf('Area Under the Curve = %g',auc))
set(findobj(gca, 'type','line'), 'LineWidth',2)

结果：

naive bayes net confusion matrix ROC plot

我们可以在每个节点提取CPT和均值/西格玛：

cellfun(@(x)dispcpt(struct(x).CPT), bnet.CPD(dNodes), 'Uniform',false)
celldisp(cellfun(@(x)struct(x).mean, bnet.CPD(cNodes), 'Uniform',false))
celldisp(cellfun(@(x)struct(x).cov, bnet.CPD(cNodes), 'Uniform',false))

BNT gaussian_CPD的简单示例/用例？

2 个答案: