test9.cpp

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#include "indii/ml/aux/GaussianMixturePdf.hpp"
#include "indii/ml/aux/GaussianPdf.hpp"
#include "indii/ml/aux/DensityTreePdf.hpp"
#include "indii/ml/aux/DiracMixturePdf.hpp"
#include "indii/ml/aux/vector.hpp"
#include "indii/ml/aux/matrix.hpp"
#include "indii/ml/aux/Random.hpp"

#include <gsl/gsl_statistics_double.h>

#include <iostream>
#include <fstream>

using namespace std;

namespace aux = indii::ml::aux;

/**
 * @file test9.cpp
 *
 * Test of DensityTreePdf.
 *
 * This test:
 *
 * @li creates a random multivariate Gaussian mixture,
 * @li samples from this mixture and constructs a density tree,
 * @li compares the mean and covariance of the density tree with that of
 * the original mixture.
 * @li directly samples from the density tree and compares the mean and
 * covariance of this sample set with that of the original mixture.
 * @li importance samples from the density tree using a single Gaussian fit
 * to the original mixture and compares the mean and covariance of this
 * sample set with that of the original mixture.
 *
 * Results are as follows:
 *
 * @include test9.out
 *
 * \image html test9_mixture.png "Original Gaussian mixture"
 * \image latex test9_mixture.eps "Original Gaussian mixture"
 * \image html test9_tree.png "Density tree approximation"
 * \image latex test9_tree.eps "Density tree approximation"
 */

/**
 * Dimensionality of the distribution.
 */
unsigned int M = 2;

/**
 * Number of components in the Gaussian mixture.
 */
unsigned int COMPONENTS = 4;

/**
 * Number of samples to take.
 */
unsigned int P = 1000000;

/**
 * Resolution of plots.
 */
unsigned int RES = 200;

/**
 * Create random Gaussian distribution.
 *
 * @param M Dimensionality of the Gaussian.
 * @param minMean Minimum value of any component of the mean.
 * @param maxMean Maximum value of any component of the mean.
 * @param minCov Minimum value of any component of the covariance.
 * @param maxCov Maximum value of any component of the covariance.
 *
 * @return Gaussian with given dimensionality, with mean and
 * covariance randomly generated uniformly from within the given
 * bounds.
 */
aux::GaussianPdf createRandomGaussian(const unsigned int M,
    const double minMean = -1.0, const double maxMean = 1.0,
    const double minCov = -1.0, const double maxCov = 1.0) {
  aux::vector mu(M);
  aux::symmetric_matrix sigma(M);
  aux::lower_triangular_matrix L(M,M);

  unsigned int i, j;

  /* mean */
  for (i = 0; i < M; i++) {
    mu(i) = aux::Random::uniform(minMean, maxMean);
  }

  /* covariance */
  for (i = 0; i < M; i++) {
    for (j = 0; j <= i; j++) {
      L(i,j) = aux::Random::uniform(minCov, maxCov);
    }
  }
  sigma = prod(L, trans(L)); // ensures cholesky decomposable

  return aux::GaussianPdf(mu, sigma);
}

/**
 * Run tests.
 */
int main(int argc, const char* argv[]) {
  unsigned int i, j;

  /* create distribution */
  aux::GaussianMixturePdf mixture(M);
  for (i = 0; i < COMPONENTS; i++) {
    mixture.addComponent(createRandomGaussian(M),
        aux::Random::uniform(0.5,1.0));
  }

  /* sample from distribution */
  aux::DiracMixturePdf mixtureSamples(mixture, P);

  /* construct density tree */
  aux::DensityTreeFactory factory(sqrt(P), 0.5*log(P)/log(2), 0.0,
      aux::DensityTreeFactory::SPLIT_VARIANCE);
  aux::DensityTreePdf tree(mixtureSamples, factory);

  /* sample from density tree */
  aux::DiracMixturePdf treeSamples(tree, P);

  /* importance sample from density tree */
  aux::GaussianPdf importance(mixture.getExpectation(),
      mixture.getCovariance());
  aux::DiracMixturePdf treeImportanceSamples(M);
  double treeDensity, importanceDensity;
  aux::vector sample(M);
  for (i = 0; i < P; i++) {
    sample = importance.sample();
    importanceDensity = importance.densityAt(sample);
    treeDensity = tree.densityAt(sample);
    treeImportanceSamples.addComponent(sample, treeDensity/importanceDensity);
  }

  cout << "Mixture mean" << endl <<
      mixture.getExpectation() << endl;
  cout << "Mixture covariance" << endl <<
      mixture.getCovariance() << endl;
  cout << "Sample mean" << endl <<
      mixtureSamples.getExpectation() << endl;
  cout << "Sample covariance" << endl <<
      mixtureSamples.getCovariance() << endl;
  cout << "Density tree mean" << endl <<
      tree.getExpectation() << endl;
  cout << "Density tree covariance" << endl <<
      tree.getCovariance() << endl;
  cout << "Density tree sample mean" << endl <<
      treeSamples.getExpectation() << endl;
  cout << "Density tree sample covariance" << endl <<
      treeSamples.getCovariance() << endl;
  cout << "Density tree importance sample mean" << endl <<
      treeImportanceSamples.getExpectation() << endl;
  cout << "Density tree importance sample covariance" << endl <<
      treeImportanceSamples.getCovariance() << endl;
      
  /* output for plots */
  ofstream fMixture("results/test9_mixture.out");
  ofstream fTree("results/test9_tree.out");
  const aux::vector& lower = tree.getLower();
  const aux::vector& upper = tree.getUpper();
  aux::vector coord(M);
  double x, y, density;
  
  for (i = 0; i < RES; i++) {
    x = lower(0) + (upper(0) - lower(0)) * i / RES;
    coord(0) = x;
    for (j = 0; j < RES; j++) {
      y = lower(1) + (upper(1) - lower(1)) * j / RES;
      coord(1) = y;
      
      density = mixture.densityAt(coord);
      fMixture << x << '\t' << y << '\t' << density << endl;
      
      density = tree.densityAt(coord);
      fTree << x << '\t' << y << '\t' << density << endl;
    }
    
    /* end isolines */
    fMixture << endl;
    fTree << endl;
  }
 
  return 0; 
}

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