// 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; // ----------------------------------------------------------------------------------------intmain(){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. enumnodes{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<unsignedlong>::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.unsignedlongA_count = 0;unsignedlongB_count = 0;unsignedlongC_count = 0;unsignedlongD_count = 0; // The more times you let the loop run the more accurate the result will be. Here we loop // 2000 times. constlongrounds = 2000; for (longi = 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();}}