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