/* ---------------------------------------------------------------------------- * GTSAM Copyright 2010, Georgia Tech Research Corporation, * Atlanta, Georgia 30332-0415 * All Rights Reserved * Authors: Frank Dellaert, et al. (see THANKS for the full author list) * See LICENSE for the license information * -------------------------------------------------------------------------- */ /** * @file DiscreteBayesNet_FG.cpp * @brief Discrete Bayes Net example using Factor Graphs * @author Abhijit * @date Jun 4, 2012 * * We use the famous Rain/Cloudy/Sprinkler Example of [Russell & Norvig, 2009, p529] * You may be familiar with other graphical model packages like BNT (available * at http://bnt.googlecode.com/svn/trunk/docs/usage.html) where this is used as an * example. The following demo is same as that in the above link, except that * everything is using GTSAM. */ #include #include #include using namespace std; using namespace gtsam; int main(int argc, char **argv) { // We assume binary state variables // we have 0 == "False" and 1 == "True" const size_t nrStates = 2; // define variables DiscreteKey Cloudy(1, nrStates), Sprinkler(2, nrStates), Rain(3, nrStates), WetGrass(4, nrStates); // create Factor Graph of the bayes net DiscreteFactorGraph graph; // add factors graph.add(Cloudy, "0.5 0.5"); //P(Cloudy) graph.add(Cloudy & Sprinkler, "0.5 0.5 0.9 0.1"); //P(Sprinkler | Cloudy) graph.add(Cloudy & Rain, "0.8 0.2 0.2 0.8"); //P(Rain | Cloudy) graph.add(Sprinkler & Rain & WetGrass, "1 0 0.1 0.9 0.1 0.9 0.001 0.99"); //P(WetGrass | Sprinkler, Rain) // Alternatively we can also create a DiscreteBayesNet, add DiscreteConditional // factors and create a FactorGraph from it. (See testDiscreteBayesNet.cpp) // Since this is a relatively small distribution, we can as well print // the whole distribution.. cout << "Distribution of Example: " << endl; cout << setw(11) << "Cloudy(C)" << setw(14) << "Sprinkler(S)" << setw(10) << "Rain(R)" << setw(14) << "WetGrass(W)" << setw(15) << "P(C,S,R,W)" << endl; for (size_t a = 0; a < nrStates; a++) for (size_t m = 0; m < nrStates; m++) for (size_t h = 0; h < nrStates; h++) for (size_t c = 0; c < nrStates; c++) { DiscreteFactor::Values values; values[Cloudy.first] = c; values[Sprinkler.first] = h; values[Rain.first] = m; values[WetGrass.first] = a; double prodPot = graph(values); cout << boolalpha << setw(8) << (bool) c << setw(14) << (bool) h << setw(12) << (bool) m << setw(13) << (bool) a << setw(16) << prodPot << endl; } // "Most Probable Explanation", i.e., configuration with largest value DiscreteSequentialSolver solver(graph); DiscreteFactor::sharedValues optimalDecoding = solver.optimize(); cout <<"\nMost Probable Explanation (MPE):" << endl; cout << boolalpha << "Cloudy = " << (bool)(*optimalDecoding)[Cloudy.first] << " Sprinkler = " << (bool)(*optimalDecoding)[Sprinkler.first] << " Rain = " << boolalpha << (bool)(*optimalDecoding)[Rain.first] << " WetGrass = " << (bool)(*optimalDecoding)[WetGrass.first]<< endl; // "Inference" We show an inference query like: probability that the Sprinkler was on; // given that the grass is wet i.e. P( S | W=1) =? cout << "\nInference Query: Probability of Sprinkler being on given Grass is Wet" << endl; // Method 1: we can compute the joint marginal P(S,W) and from that we can compute // P(S | W=1) = P(S,W=1)/P(W=1) We do this in following three steps.. //Step1: Compute P(S,W) DiscreteFactorGraph jointFG; jointFG = *solver.jointFactorGraph(DiscreteKeys(Sprinkler & WetGrass).indices()); DecisionTreeFactor probSW = jointFG.product(); //Step2: Compute P(W) DiscreteFactor::shared_ptr probW = solver.marginalFactor(WetGrass.first); //Step3: Computer P(S | W=1) = P(S,W=1)/P(W=1) DiscreteFactor::Values values; values[WetGrass.first] = 1; //print P(S=0|W=1) values[Sprinkler.first] = 0; cout << "P(S=0|W=1) = " << probSW(values)/(*probW)(values) << endl; //print P(S=1|W=1) values[Sprinkler.first] = 1; cout << "P(S=1|W=1) = " << probSW(values)/(*probW)(values) << endl; // TODO: Method 2 : One way is to modify the factor graph to // incorporate the evidence node and compute the marginal // TODO: graph.addEvidence(Cloudy,0); return 0; }