DiscreteBayesNet_FG.cpp

/* ----------------------------------------------------------------------------

 * 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 <gtsam/discrete/DiscreteFactorGraph.h>
#include <gtsam/discrete/DiscreteSequentialSolver.h>
#include <iomanip>

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;
}