matlab贝叶斯网络工具箱使用方法

How to use the Bayes Net Toolbox

This documentation was last updated on 29 October 2007.

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for a French version of this documentation (last updated in 2005).

Installation

Creating your first Bayes net

Creating a model by hand

Loading a model from a file

Creating a model using a GUI

Noisy-or nodes

Softmax (multinomial logit) nodes

Neural network nodes

Gaussian nodes

Classification/regression tree nodes

Hierarchical mixtures of experts

QMR

Conditional Gaussian models

Other hybrid models

Parameter learning

Loading data from a file

Maximum likelihood parameter estimation from complete data

Parameter priors

(Sequential) Bayesian parameter updating from complete data

Maximum likelihood parameter estimation with missing values (EM)

Active learning

Structural EM

Visualizing the learned graph structure

Inference engines

Junction tree

Quickscore

Creating your first Bayes net

To define a Bayes net, you must specify the graph structure and then the parameters. We look at each in turn, using a simple example (adapted

from Russell and Norvig, "Artificial Intelligence: a Modern Approach", Prentice Hall, 1995, p454).

Graph structure

Consider the following network.

To specify this directed acyclic graph (dag), we create an adjacency matrix:

N = 4;

dag = zeros(N,N);

C = 1; S = 2; R = 3; W = 4;

dag(C,[R S]) = 1;

around this below

dag = false(N,N);

dag(C,[R S]) = true;

some graph functions (eg acyclic) do not work on logical arrays

You can visualize the resulting graph structure using the methods discussed below

node_sizes = [4 2 3 5];

meaning that Cloudy has 4 possible values, Sprinkler has 2 possible values, etc. Note that these are cardinal values, not ordinal, i.e., they are not

ordered in any way, like 'low', 'medium', 'high'.

We are now ready to make the Bayes net:

bnet = mk_bnet(dag, node_sizes, 'discrete', discrete_nodes);

bnet = mk_bnet(dag, node_sizes);

You may also specify which nodes will be observed. If you don't know, or if this not fixed in advance, just use the empty list (the default).

onodes = [];

bnet = mk_bnet(dag, node_sizes, 'discrete', discrete_nodes, 'observed', onodes);

You can then refer to a node by its name:

C = bnet.names('cloudy'); % bnet.names is an associative array

bnet.CPD{C} = tabular_CPD(bnet, C, [0.5 0.5]);

This feature uses my own associative array class.

Parameters

Distribution), which define the probability distribution of a node given its parents. (We will use the terms "node" and "random variable"

interchangeably.) The simplest kind of CPD is a table (multi-dimensional array), which is suitable when all the nodes are discrete-valued. Note

that the discrete values are not assumed to be ordered in any way; that is, they represent categorical quantities, like male and female, rather than

ordinal quantities, like low, medium and high. (We will discuss CPDs in more detail below

CPT(1,1,1) = 1.0;

CPT(2,1,1) = 0.1;

Here is an easier way:

CPT = reshape([1 0.1 0.1 0.01 0 0.9 0.9 0.99], [2 2 2]);

In fact, we don't need to reshape the array, since the CPD constructor will do that for us. So we can just write

bnet.CPD{W} = tabular_CPD(bnet, W, 'CPT', [1 0.1 0.1 0.01 0 0.9 0.9 0.99]);

bnet.CPD{C} = tabular_CPD(bnet, C, [0.5 0.5]);

bnet.CPD{R} = tabular_CPD(bnet, R, [0.8 0.2 0.2 0.8]);

randn('state', seed);

encourages "deterministic" CPTs (one entry near 1, the rest near 0). If p = 1, each entry is drawn from U[0,1]. If p >> 1, the entries will all be

is the node_sizes.

k = ns(i);

ps = parents(dag, i);

psz = prod(ns(ps));

CPT = sample_dirichlet(p*ones(1,k), psz);

bnet.CPD{i} = tabular_CPD(bnet, i, 'CPT', CPT);