dlib C++ Library - bayes_net_ex.cpp

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