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297 lines
12 KiB
C++
297 lines
12 KiB
C++
// The contents of this file are in the public domain. See LICENSE_FOR_EXAMPLE_PROGRAMS.txt
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/*
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This is an example illustrating the use of the Bayesian Network
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inference utilities found in the dlib C++ library.
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In this example all the nodes in the Bayesian network are
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boolean variables. That is, they take on either the value
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0 or the value 1.
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The network contains 4 nodes and looks as follows:
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B C
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\\ //
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\/ \/
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A
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||
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\/
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D
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The probabilities of each node are summarized below. (The probability
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of each node being 0 is not listed since it is just P(X=0) = 1-p(X=1) )
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p(B=1) = 0.01
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p(C=1) = 0.001
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p(A=1 | B=0, C=0) = 0.01
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p(A=1 | B=0, C=1) = 0.5
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p(A=1 | B=1, C=0) = 0.9
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p(A=1 | B=1, C=1) = 0.99
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p(D=1 | A=0) = 0.2
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p(D=1 | A=1) = 0.5
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*/
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#include "dlib/bayes_utils.h"
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#include "dlib/graph_utils.h"
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#include "dlib/graph.h"
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#include "dlib/directed_graph.h"
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#include <iostream>
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using namespace dlib;
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using namespace std;
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// ----------------------------------------------------------------------------------------
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int main()
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{
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// There are many useful convenience functions in this namespace. They all
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// perform simple access or modify operations on the nodes of a bayesian network.
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// You don't have to use them but they are convenient and they also will check for
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// various errors in your bayesian network when your application is built with
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// the DEBUG or ENABLE_ASSERTS preprocessor definitions defined. So their use
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// is recommended. In fact, most of the global functions used in this example
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// program are from this namespace.
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using namespace bayes_node_utils;
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// This statement declares a bayesian network called bn. Note that a bayesian network
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// in the dlib world is just a directed_graph object that contains a special kind
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// of node called a bayes_node.
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directed_graph<bayes_node>::kernel_1a_c bn;
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// Use an enum to make some more readable names for our nodes.
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enum nodes
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{
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A = 0,
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B = 1,
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C = 2,
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D = 3
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};
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// The next few blocks of code setup our bayesian network.
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// The first thing we do is tell the bn object how many nodes it has
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// and also add the three edges. Again, we are using the network
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// shown in ASCII art at the top of this file.
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bn.set_number_of_nodes(4);
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bn.add_edge(A, D);
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bn.add_edge(B, A);
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bn.add_edge(C, A);
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// Now we inform all the nodes in the network that they are binary
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// nodes. That is, they only have two possible values.
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set_node_num_values(bn, A, 2);
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set_node_num_values(bn, B, 2);
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set_node_num_values(bn, C, 2);
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set_node_num_values(bn, D, 2);
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assignment parent_state;
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// Now we will enter all the conditional probability information for each node.
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// Each node's conditional probability is dependent on the state of its parents.
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// To specify this state we need to use the assignment object. This assignment
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// object allows us to specify the state of each nodes parents.
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// Here we specify that p(B=1) = 0.01
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// parent_state is empty in this case since B is a root node.
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set_node_probability(bn, B, 1, parent_state, 0.01);
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// Here we specify that p(B=0) = 1-0.01
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set_node_probability(bn, B, 0, parent_state, 1-0.01);
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// Here we specify that p(C=1) = 0.001
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// parent_state is empty in this case since B is a root node.
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set_node_probability(bn, C, 1, parent_state, 0.001);
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// Here we specify that p(C=0) = 1-0.001
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set_node_probability(bn, C, 0, parent_state, 1-0.001);
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// This is our first node that has parents. So we set the parent_state
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// object to reflect that A has both B and C as parents.
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parent_state.add(B, 1);
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parent_state.add(C, 1);
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// Here we specify that p(A=1 | B=1, C=1) = 0.99
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set_node_probability(bn, A, 1, parent_state, 0.99);
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// Here we specify that p(A=0 | B=1, C=1) = 1-0.99
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set_node_probability(bn, A, 0, parent_state, 1-0.99);
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// Here we use the [] notation because B and C have already
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// been added into parent state.
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parent_state[B] = 1;
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parent_state[C] = 0;
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// Here we specify that p(A=1 | B=1, C=0) = 0.9
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set_node_probability(bn, A, 1, parent_state, 0.9);
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set_node_probability(bn, A, 0, parent_state, 1-0.9);
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parent_state[B] = 0;
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parent_state[C] = 1;
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// Here we specify that p(A=1 | B=0, C=1) = 0.5
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set_node_probability(bn, A, 1, parent_state, 0.5);
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set_node_probability(bn, A, 0, parent_state, 1-0.5);
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parent_state[B] = 0;
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parent_state[C] = 0;
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// Here we specify that p(A=1 | B=0, C=0) = 0.01
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set_node_probability(bn, A, 1, parent_state, 0.01);
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set_node_probability(bn, A, 0, parent_state, 1-0.01);
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// Here we set probabilities for node D.
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// First we clear out parent state so that it doesn't have any of
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// the assignments for the B and C nodes used above.
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parent_state.clear();
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parent_state.add(A,1);
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// Here we specify that p(D=1 | A=1) = 0.5
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set_node_probability(bn, D, 1, parent_state, 0.5);
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set_node_probability(bn, D, 0, parent_state, 1-0.5);
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parent_state[A] = 0;
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// Here we specify that p(D=1 | A=0) = 0.2
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set_node_probability(bn, D, 1, parent_state, 0.2);
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set_node_probability(bn, D, 0, parent_state, 1-0.2);
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// We have now finished setting up our bayesian network. So lets compute some
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// probability values. The first thing we will do is compute the prior probability
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// of each node in the network. To do this we will use the join tree algorithm which
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// is an algorithm for performing exact inference in a bayesian network.
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// First we need to create an undirected graph which contains set objects at each node and
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// edge. This long declaration does the trick.
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typedef set<unsigned long>::compare_1b_c set_type;
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typedef graph<set_type, set_type>::kernel_1a_c join_tree_type;
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join_tree_type join_tree;
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// Now we need to populate the join_tree with data from our bayesian network. The next
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// function calls do this. Explaining exactly what they do is outside the scope of this
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// example. Just think of them as filling join_tree with information that is useful
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// later on for dealing with our bayesian network.
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create_moral_graph(bn, join_tree);
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create_join_tree(join_tree, join_tree);
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// Now that we have a proper join_tree we can use it to obtain a solution to our
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// bayesian network. Doing this is as simple as declaring an instance of
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// the bayesian_network_join_tree object as follows:
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bayesian_network_join_tree solution(bn, join_tree);
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// now print out the probabilities for each node
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cout << "Using the join tree algorithm:\n";
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cout << "p(A=1) = " << solution.probability(A)(1) << endl;
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cout << "p(A=0) = " << solution.probability(A)(0) << endl;
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cout << "p(B=1) = " << solution.probability(B)(1) << endl;
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cout << "p(B=0) = " << solution.probability(B)(0) << endl;
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cout << "p(C=1) = " << solution.probability(C)(1) << endl;
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cout << "p(C=0) = " << solution.probability(C)(0) << endl;
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cout << "p(D=1) = " << solution.probability(D)(1) << endl;
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cout << "p(D=0) = " << solution.probability(D)(0) << endl;
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cout << "\n\n\n";
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// Now to make things more interesting lets say that we have discovered that the C
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// node really has a value of 1. That is to say, we now have evidence that
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// C is 1. We can represent this in the network using the following two function
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// calls.
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set_node_value(bn, C, 1);
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set_node_as_evidence(bn, C);
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// Now we want to compute the probabilities of all the nodes in the network again
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// given that we now know that C is 1. We can do this as follows:
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bayesian_network_join_tree solution_with_evidence(bn, join_tree);
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// now print out the probabilities for each node
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cout << "Using the join tree algorithm:\n";
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cout << "p(A=1 | C=1) = " << solution_with_evidence.probability(A)(1) << endl;
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cout << "p(A=0 | C=1) = " << solution_with_evidence.probability(A)(0) << endl;
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cout << "p(B=1 | C=1) = " << solution_with_evidence.probability(B)(1) << endl;
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cout << "p(B=0 | C=1) = " << solution_with_evidence.probability(B)(0) << endl;
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cout << "p(C=1 | C=1) = " << solution_with_evidence.probability(C)(1) << endl;
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cout << "p(C=0 | C=1) = " << solution_with_evidence.probability(C)(0) << endl;
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cout << "p(D=1 | C=1) = " << solution_with_evidence.probability(D)(1) << endl;
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cout << "p(D=0 | C=1) = " << solution_with_evidence.probability(D)(0) << endl;
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cout << "\n\n\n";
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// Note that when we made our solution_with_evidence object we reused our join_tree object.
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// This saves us the time it takes to calculate the join_tree object from scratch. But
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// it is important to note that we can only reuse the join_tree object if we haven't changed
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// the structure of our bayesian network. That is, if we have added or removed nodes or
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// edges from our bayesian network then we must recompute our join_tree. But in this example
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// all we did was change the value of a bayes_node object (we made node C be evidence)
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// so we are ok.
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// Next this example will show you how to use the bayesian_network_gibbs_sampler object
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// to perform approximate inference in a bayesian network. This is an algorithm
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// that doesn't give you an exact solution but it may be necessary to use in some
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// instances. For example, the join tree algorithm used above, while fast in many
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// instances, has exponential runtime in some cases. Moreover, inference in bayesian
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// networks is NP-Hard for general networks so sometimes the best you can do is
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// find an approximation.
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// However, it should be noted that the gibbs sampler does not compute the correct
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// probabilities if the network contains a deterministic node. That is, if any
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// of the conditional probability tables in the bayesian network have a probability
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// of 1.0 for something the gibbs sampler should not be used.
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// This Gibbs sampler algorithm works by randomly sampling possibles values of the
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// network. So to use it we should set the network to some initial state.
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set_node_value(bn, A, 0);
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set_node_value(bn, B, 0);
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set_node_value(bn, D, 0);
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// We will leave the C node with a value of 1 and keep it as an evidence node.
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// First create an instance of the gibbs sampler object
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bayesian_network_gibbs_sampler sampler;
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// To use this algorithm all we do is go into a loop for a certain number of times
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// and each time through we sample the bayesian network. Then we count how
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// many times a node has a certain state. Then the probability of that node
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// having that state is just its count/total times through the loop.
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// The following code illustrates the general procedure.
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unsigned long A_count = 0;
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unsigned long B_count = 0;
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unsigned long C_count = 0;
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unsigned long D_count = 0;
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// The more times you let the loop run the more accurate the result will be. Here we loop
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// 2000 times.
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const long rounds = 2000;
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for (long i = 0; i < rounds; ++i)
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{
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sampler.sample_graph(bn);
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if (node_value(bn, A) == 1)
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++A_count;
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if (node_value(bn, B) == 1)
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++B_count;
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if (node_value(bn, C) == 1)
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++C_count;
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if (node_value(bn, D) == 1)
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++D_count;
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}
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cout << "Using the approximate Gibbs Sampler algorithm:\n";
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cout << "p(A=1 | C=1) = " << (double)A_count/(double)rounds << endl;
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cout << "p(B=1 | C=1) = " << (double)B_count/(double)rounds << endl;
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cout << "p(C=1 | C=1) = " << (double)C_count/(double)rounds << endl;
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cout << "p(D=1 | C=1) = " << (double)D_count/(double)rounds << endl;
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}
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