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/*
* File: DirichletProcessMixtureModel.java
* Authors: Kevin R. Dixon
* Company: Sandia National Laboratories
* Project: Cognitive Foundry
*
* Copyright Apr 26, 2010, Sandia Corporation.
* Under the terms of Contract DE-AC04-94AL85000, there is a non-exclusive
* license for use of this work by or on behalf of the U.S. Government.
* Export of this program may require a license from the United States
* Government. See CopyrightHistory.txt for complete details.
*
*/
package gov.sandia.cognition.statistics.bayesian;
import gov.sandia.cognition.annotation.PublicationReference;
import gov.sandia.cognition.annotation.PublicationReferences;
import gov.sandia.cognition.annotation.PublicationType;
import gov.sandia.cognition.collection.CollectionUtil;
import gov.sandia.cognition.learning.algorithm.clustering.cluster.DefaultCluster;
import gov.sandia.cognition.math.matrix.Matrix;
import gov.sandia.cognition.math.matrix.Vector;
import gov.sandia.cognition.math.matrix.VectorFactory;
import gov.sandia.cognition.statistics.ProbabilityFunction;
import gov.sandia.cognition.statistics.bayesian.conjugate.MultivariateGaussianMeanBayesianEstimator;
import gov.sandia.cognition.statistics.bayesian.conjugate.MultivariateGaussianMeanCovarianceBayesianEstimator;
import gov.sandia.cognition.statistics.distribution.BetaDistribution;
import gov.sandia.cognition.statistics.distribution.ChineseRestaurantProcess;
import gov.sandia.cognition.statistics.distribution.GammaDistribution;
import gov.sandia.cognition.statistics.distribution.MultivariateGaussian;
import gov.sandia.cognition.statistics.distribution.MultivariateStudentTDistribution;
import gov.sandia.cognition.statistics.distribution.NormalInverseWishartDistribution;
import gov.sandia.cognition.util.AbstractCloneableSerializable;
import gov.sandia.cognition.util.CloneableSerializable;
import gov.sandia.cognition.util.ObjectUtil;
import java.util.ArrayList;
import java.util.Collection;
import java.util.LinkedList;
import java.util.Random;
/**
* An implementation of Dirichlet Process clustering, which estimates the
* number of clusters and the centroids of the clusters from a set of
* data.
* @param
* Type of observations handled by the mixture model
* @author Kevin R. Dixon
* @since 3.0
*/
@PublicationReferences(
references={
@PublicationReference(
author="Radform M. Neal",
title="Markov Chain Sampling Methods for Dirichlet Process Mixture Models",
type=PublicationType.Journal,
year=2000,
publication="Journal of Computational and Graphical Statistics, Vol. 9, No. 2",
pages={249,265},
notes="Based in part on Algorithm 2 from Neal"
)
,
@PublicationReference(
author={
"Michael D. Escobar",
"Mike West"
},
title="Bayesian Density Estimation and Inference Using Mixtures",
type=PublicationType.Journal,
publication="Journal of the American Statistical Association",
year=1995
)
}
)
public class DirichletProcessMixtureModel
extends AbstractMarkovChainMonteCarlo>
{
/**
* Default concentration parameter of the Dirichlet Process, {@value}.
*/
public static final double DEFAULT_ALPHA = 1.0;
/**
* Default number of initial clusters
*/
public static final int DEFAULT_NUM_INITIAL_CLUSTERS = 2;
/**
* The default value for re-estimating alpha is {@value}.
*/
public static final boolean DEFAULT_REESTIMATE_ALPHA = true;
/**
* Creates the clusters and predictive prior distributions
*/
protected Updater updater;
/**
* Number of clusters to initialize
*/
private int numInitialClusters;
/**
* Flag to automatically re-estimate the alpha parameter
*/
protected boolean reestimateAlpha;
/**
* Initial value of alpha, the concentration parameter of the
* Dirichlet Process
*/
protected double initialAlpha;
/**
* Creates a new instance of DirichletProcessMixtureModel
*/
public DirichletProcessMixtureModel()
{
this.setReestimateAlpha(DEFAULT_REESTIMATE_ALPHA);
this.setInitialAlpha(DEFAULT_ALPHA);
this.setNumInitialClusters( DEFAULT_NUM_INITIAL_CLUSTERS );
}
@Override
public DirichletProcessMixtureModel clone()
{
@SuppressWarnings("unchecked")
DirichletProcessMixtureModel clone =
(DirichletProcessMixtureModel) super.clone();
clone.setUpdater( ObjectUtil.cloneSafe( this.getUpdater() ) );
return clone;
}
/**
* Base predictive distribution that determines the value of the
* new cluster weighting during the Gibbs sampling.
*/
transient protected ProbabilityFunction conditionalPriorPredictive;
/**
* Holds the cluster weights so that we don't have to re-allocate them
* each mcmcUpdate step.
*/
transient protected double[] clusterWeights;
@Override
protected void mcmcUpdate()
{
// This is the "mother" or the "none of the above" distribution...
// The omnipresent distribution hiding in the background that we
// we will compute the weight of creating a new cluster.
if( this.conditionalPriorPredictive == null )
{
this.conditionalPriorPredictive =
this.updater.createPriorPredictive(this.data);
}
// This assigns observations to each of the K clusters, plus the
// as-yet-uncreated new cluster
final int K = this.currentParameter.getNumClusters();
DPMMLogConditional logConditional = new DPMMLogConditional();
ArrayList> clusterAssignments =
this.assignObservationsToClusters( K, logConditional );
final int numObservations = CollectionUtil.size(this.data);
// Through a bizarre quirk of the math, the log conditional is for
// the sample we previously generated...
if( (this.previousParameter != null) &&
(this.previousParameter.posteriorLogLikelihood == null) )
{
this.previousParameter.posteriorLogLikelihood =
this.previousParameter.computePosteriorLogLikelihood(
numObservations, logConditional.logConditional );
}
// Now, update each cluster according to the data assigned to it
this.currentParameter.clusters = this.updateClusters(clusterAssignments);
// Update the alpha parameter
if( this.getReestimateAlpha() )
{
this.currentParameter.alpha =
this.updateAlpha(this.currentParameter.alpha, numObservations);
}
}
/**
* Update each cluster according to the data assigned to it
* @param clusterAssignments
* Observations assigned to each cluster
* @return
* Cluster that contains an update parameter estimate and weighted by
* the number of observations assigned to the cluster
*/
protected ArrayList> updateClusters(
ArrayList> clusterAssignments )
{
final int Kp1 = clusterAssignments.size();
ArrayList> clusters =
new ArrayList>( Kp1 );
for( int k = 0; k < Kp1; k++ )
{
Collection assignments = clusterAssignments.get(k);
if( assignments.size() > 1 )
{
DPMMCluster cluster =
this.createCluster( assignments, this.updater );
if( cluster != null )
{
clusters.add( cluster );
}
}
}
return clusters;
}
/**
* Container for the log conditional likelihood
*/
protected static class DPMMLogConditional
extends AbstractCloneableSerializable
{
/**
* log conditional likelihood
*/
double logConditional;
/**
* Default constructor
*/
public DPMMLogConditional()
{
this.logConditional = 0.0;
}
}
/**
* Assigns observations to each of the K clusters,
* plus the as-yet-uncreated new cluster
* @param K
* Number of clusters
* @param logConditional
* The log of the conditional.
* @return
* Assignments from observations to clusters
*/
protected ArrayList> assignObservationsToClusters(
int K,
DPMMLogConditional logConditional )
{
// This is just a convenience to keep us from re-creating this
// array every time.
if( (this.clusterWeights == null) ||
(this.clusterWeights.length != K+1) )
{
this.clusterWeights = new double[K+1];
}
// This assigns observations to each of the K clusters, plus the
// as-yet-uncreated new cluster
ArrayList> clusterAssignments =
new ArrayList>( K+1 );
for( int k = 0; k < K+1; k++ )
{
clusterAssignments.add( new LinkedList() );
}
// Assign each observation to a cluster, including the possibility
// of assigning the point to a new, as-yet-undefined new cluster
for( ObservationType observation : this.data )
{
// Figure out which cluster this observation is assigned to.
int clusterAssignment = this.assignObservationToCluster(
observation, this.clusterWeights, logConditional );
clusterAssignments.get(clusterAssignment).add(observation);
}
return clusterAssignments;
}
/**
* Probabilistically assigns an observation to a cluster
* @param observation
* Observation that we're assigning
* @param weights
* Place holder for the weights that this method will create
* @param logConditional
* The log of the conditional.
* @return
* Index of the cluster to assign the observation to. This will be
* [0,K-1] for an existing cluster and "K" for an as-yet-undecided new
* cluster.
*/
protected int assignObservationToCluster(
ObservationType observation,
double[] weights,
DPMMLogConditional logConditional )
{
final double alpha = this.currentParameter.alpha;
final int K = this.currentParameter.getNumClusters();
// Weight of assigning the data point to a brand-new cluster
final double newClusterWeight =
alpha*this.conditionalPriorPredictive.evaluate(observation);
weights[K] = newClusterWeight;
double weightSum = newClusterWeight;
// The weight of each cluster is proporationate to the number of
// points assigned to each cluster
double conditional = 1e-100;
for( int k = 0; k < K; k++ )
{
// This is an approximation. We're really supposed to subtract
// "1.0" from the weight of the cluster that the observation has
// been assigned to. However, that book-keeping gets really
// expensive. In any case, by subtracting "1.0" from all weights
// we eliminate that nasty condition of assigning a cluster to
// a single data point and getting infinite likelihood.
DPMMCluster cluster =
this.currentParameter.clusters.get(k);
int num = cluster.getMembers().size();
if( num > 0 )
{
final double c = cluster.getProbabilityFunction().evaluate(observation);
final double weight = (num-1)*c;
weights[k] = weight;
weightSum += weight;
conditional += num*c;
}
else
{
weights[k] = 0.0;
}
}
logConditional.logConditional += Math.log( conditional );
// Choose a uniform number on [0,weightSum] to figure out which
// cluster to assign this observation to
double p = weightSum * this.random.nextDouble();
for( int k = 0; k < K+1; k++ )
{
p -= weights[k];
if( p <= 0.0 )
{
return k;
}
}
// You should/will never get here.
throw new IllegalArgumentException(
"Did not select cluster: " + weightSum );
}
/**
* Creates a cluster from the given cluster assignment
* @param clusterAssignment
* Observations assigned to a particular cluster
* @param localUpdater
* Updater that recomputes the cluster parameters, needed to ensure
* thread safety in the parallel implementation
* @return
* Cluster that contains an update parameter estimate and weighted by
* the number of observations assigned to the cluster
*/
protected DPMMCluster createCluster(
Collection clusterAssignment,
Updater localUpdater )
{
if( clusterAssignment == null )
{
return null;
}
double weight = clusterAssignment.size();
if( weight <= 0.0 )
{
return null;
}
else
{
ProbabilityFunction probabilityFunction =
localUpdater.createClusterPosterior( clusterAssignment, this.random );
return new DPMMCluster( clusterAssignment, probabilityFunction );
}
}
/**
* Creates a new value of "eta" which, in turn, helps sample a new alpha.
*/
transient protected BetaDistribution etaSampler;
/**
* Samples a new alpha-inverse.
*/
transient protected GammaDistribution alphaInverseSampler;
/**
* Runs the Gibbs sampler for the concentration parameter, alpha, given
* the data.
* @param alpha
* Current value of the concentration parameter
* @param numObservations
* Number of observations we're sampling over
* @return
* Updated estimate of alpha
*/
protected double updateAlpha(
double alpha,
int numObservations )
{
// Gibbs Sampler for updating "alpha"
// Escobar & West: Equation 14 on page 585.
if( this.etaSampler == null )
{
this.etaSampler = new BetaDistribution();
}
this.etaSampler.setAlpha(alpha+1.0);
this.etaSampler.setBeta(numObservations);
final double eta = this.etaSampler.sample(this.random);
final double logEta = Math.log(eta);
// Parameterize the Gamma according to the mixture,
// Escobar & West: Equation 13 on page 585.
final double a = 1.0;
final double b = 1.0;
final int updatedK = this.currentParameter.getNumClusters();
double etaWeight = (a+updatedK-1.0) / (numObservations*(b-logEta));
double pEta = this.random.nextDouble();
if( this.alphaInverseSampler == null )
{
this.alphaInverseSampler = new GammaDistribution();
}
if( pEta < etaWeight )
// if( pEta < eta )
{
this.alphaInverseSampler.setShape( a + updatedK );
}
else
{
this.alphaInverseSampler.setShape( a + updatedK - 1.0 );
}
this.alphaInverseSampler.setScale( b - logEta );
return 1.0/this.alphaInverseSampler.sample(this.random);
}
@Override
public DirichletProcessMixtureModel.Sample createInitialLearnedObject()
{
ArrayList> clusters =
new ArrayList>(
this.getNumInitialClusters() );
ProbabilityFunction probabilityFunction =
this.updater.createClusterPosterior( this.data, this.random );
ArrayList dataArray =
CollectionUtil.asArrayList(this.data);
for( int k = 0; k < this.getNumInitialClusters(); k++ )
{
clusters.add( new DPMMCluster(
dataArray, probabilityFunction ) );
}
return new Sample(this.getInitialAlpha(),clusters);
}
/**
* Getter for updater
* @return
* Creates the clusters and predictive prior distributions
*/
public DirichletProcessMixtureModel.Updater getUpdater()
{
return this.updater;
}
/**
* Setter for updater
* @param updater
* Creates the clusters and predictive prior distributions
*/
public void setUpdater(
DirichletProcessMixtureModel.Updater updater)
{
this.updater = updater;
}
/**
* Getter for numInitialClusters
* @return
* Number of clusters to initialize
*/
public int getNumInitialClusters()
{
return this.numInitialClusters;
}
/**
* Getter for numInitialClusters
* @param numInitialClusters
* Number of clusters to initialize
*/
public void setNumInitialClusters(
int numInitialClusters)
{
this.numInitialClusters = numInitialClusters;
}
/**
* Getter for reestimateAlpha
* @return
* Flag to automatically re-estimate the alpha parameter
*/
public boolean getReestimateAlpha()
{
return this.reestimateAlpha;
}
/**
* Setter for reestimateAlpha
* @param reestimateAlpha
* Flag to automatically re-estimate the alpha parameter
*/
public void setReestimateAlpha(
boolean reestimateAlpha)
{
this.reestimateAlpha = reestimateAlpha;
}
/**
* Getter for initialAlpha
* @return
* Initial value of alpha, the concentration parameter of the
* Dirichlet Process
*/
public double getInitialAlpha()
{
return this.initialAlpha;
}
/**
* Setter for initialAlpha
* @param initialAlpha
* Initial value of alpha, the concentration parameter of the
* Dirichlet Process
*/
public void setInitialAlpha(
double initialAlpha)
{
this.initialAlpha = initialAlpha;
}
/**
* Cluster for a step in the DPMM
* @param
* Types of observations of the DPMM
*/
public static class DPMMCluster
extends DefaultCluster
{
/**
* Probability function describing the assigned data
*/
private ProbabilityFunction probabilityFunction;
/**
* Creates a new instance of DPMMCluster
* @param assignedData
* Data assigned to the cluster
* @param probabilityFunction
* Probability function describing the assigned data
*/
public DPMMCluster(
Collection assignedData,
ProbabilityFunction probabilityFunction )
{
super( assignedData );
this.setProbabilityFunction(probabilityFunction);
}
@Override
@SuppressWarnings("unchecked")
public DPMMCluster clone()
{
DPMMCluster clone =
(DPMMCluster) super.clone();
clone.setProbabilityFunction(
ObjectUtil.cloneSafe( this.getProbabilityFunction() ) );
return clone;
}
/**
* Getter for probabilityFunction
* @return
* Probability function describing the assigned data
*/
public ProbabilityFunction getProbabilityFunction()
{
return this.probabilityFunction;
}
/**
* Setter for probabilityFunction
* @param probabilityFunction
* Probability function describing the assigned data
*/
public void setProbabilityFunction(
ProbabilityFunction probabilityFunction)
{
this.probabilityFunction = probabilityFunction;
}
}
/**
* A sample from the Dirichlet Process Mixture Model.
* @param
* Type of observations handled by the mixture model
*/
public static class Sample
extends AbstractCloneableSerializable
{
/**
* Scaling parameter which defines the strength of the base distribution,
* must be greater than zero.
*/
protected double alpha;
/**
* Point mass realizations from the base distribution.
*/
protected ArrayList> clusters;
/**
* Posterior log likelihood of the sample
*/
private Double posteriorLogLikelihood;
/**
* Creates a new instance of Sample
* @param alpha
* Scaling parameter which defines the strength of the base distribution,
* must be greater than zero.
* @param clusters
* Point mass realizations from the base distribution.
*/
public Sample(
double alpha,
ArrayList> clusters )
{
this.setAlpha(alpha);
this.setClusters(clusters);
this.setPosteriorLogLikelihood(null);
}
@Override
public Sample clone()
{
@SuppressWarnings("unchecked")
Sample clone = (Sample) super.clone();
clone.setClusters(
ObjectUtil.cloneSmartElementsAsArrayList( this.getClusters() ) );
// The reason this is null is so that the we know to compute
// the conditional on the next MCMC step
clone.setPosteriorLogLikelihood( null );
return clone;
}
/**
* Computes the posterior log likelihood of the data given the clusters
* and the prior probability of the clustering from a
* Chinese Restaurant Process
* @param data
* Data to consider
* @return
* Posterior log likelihood of the data
*/
public double computePosteriorLogLikelihood(
Iterable data )
{
final int K = this.getNumClusters();
final int numObservations = CollectionUtil.size(data);
double logSum = 0.0;
for( ObservationType value : data )
{
double p = 1e-100;
for( int k = 0; k < K; k++ )
{
DPMMCluster cluster = this.clusters.get(k);
final int weight = cluster.getMembers().size();
final double likelihood =
cluster.getProbabilityFunction().evaluate(value);
p += weight * likelihood;
}
logSum += Math.log(p);
}
ChineseRestaurantProcess.PMF pmf = new ChineseRestaurantProcess.PMF(
this.getAlpha(), numObservations );
Vector counts = VectorFactory.getDefault().createVector(K);
for( int k = 0; k < K; k++ )
{
counts.setElement(k, this.clusters.get(k).getMembers().size() );
}
logSum += pmf.logEvaluate( counts );
return logSum;
}
/**
* Computes the posterior log likelihood of the Sample
* @param numObservations
* Number of observations in the Sample
* @param logConditional
* Log conditional likelihood of the data given the sample
* @return
* Posterior log likelihood
*/
public double computePosteriorLogLikelihood(
int numObservations,
double logConditional )
{
final int K = this.getNumClusters();
ChineseRestaurantProcess.PMF pmf = new ChineseRestaurantProcess.PMF(
this.getAlpha(), numObservations );
Vector counts = VectorFactory.getDefault().createVector(K);
for( int k = 0; k < K; k++ )
{
counts.setElement(k, this.clusters.get(k).getMembers().size() );
}
double logPrior = pmf.logEvaluate( counts );
double logPosterior = logPrior + logConditional;
return logPosterior;
}
/**
* Removes the unused clusters from the Sample.
*/
public void removeUnusedClusters()
{
for( int j = 0; j < this.getNumClusters(); j++ )
{
DPMMCluster cluster = this.clusters.get(j);
if( cluster.getMembers().size() <= 0 )
{
this.clusters.remove(j);
j--;
}
}
}
/**
* Getter for alpha
* @return
* Scaling parameter which defines the strength of the base distribution,
* must be greater than zero.
*/
public double getAlpha()
{
return this.alpha;
}
/**
* Setter for alpha
* @param alpha
* Scaling parameter which defines the strength of the base distribution,
* must be greater than zero.
*/
protected void setAlpha(
double alpha)
{
if( alpha <= 0.0 )
{
throw new IllegalArgumentException(
"Alpha must be > 0.0 " );
}
this.alpha = alpha;
}
/**
* Gets the number of clusters in the Sample
* @return
* Number of clusters in the Sample.
*/
public int getNumClusters()
{
return this.clusters.size();
}
/**
* Getter for clusters
* @return
* Point mass realizations from the base distribution.
*/
public ArrayList> getClusters()
{
return this.clusters;
}
/**
* Setter for clusters
* @param clusters
* Point mass realizations from the base distribution.
*/
protected void setClusters(
ArrayList> clusters)
{
this.clusters = clusters;
}
/**
* Gets the posterior log-likelihood.
*
* @return
* The posterior log-likelihood.
*/
public Double getPosteriorLogLikelihood()
{
return this.posteriorLogLikelihood;
}
/**
* sets the posterior log-likelihood.
*
* @param posteriorLogLikelihood
* The posterior log-likelihood.
*/
public void setPosteriorLogLikelihood(
Double posteriorLogLikelihood)
{
this.posteriorLogLikelihood = posteriorLogLikelihood;
}
}
/**
* Updater for the DPMM
* @param
* Type of observations handled by the mixture model
*/
public static interface Updater
extends CloneableSerializable
{
/**
* Creates the prior predictive distribution from the data.
* @param data
* Data from which to create the prior predictive
* @return
* Prior predictive distribution from the data
*/
public ProbabilityFunction createPriorPredictive(
Iterable data );
/**
* Updates the cluster from the values assigned to it
* @param values
* Values assigned to the cluster
* @param random
* Random number generator
* @return
* Updated cluster value
*/
public ProbabilityFunction createClusterPosterior(
Iterable values,
Random random );
}
/**
* Updater that creates specified clusters with distinct means and covariances
*/
public static class MultivariateMeanCovarianceUpdater
extends AbstractCloneableSerializable
implements Updater
{
/**
* Bayesian estimator for the parameters
*/
private MultivariateGaussianMeanCovarianceBayesianEstimator estimator;
/**
* Default constructor
*/
public MultivariateMeanCovarianceUpdater()
{
this( null );
}
/**
* Creates a new instance of MultivariateMeanCovarianceUpdater
* @param dimensionality
* Dimensionality of the Vectors
*/
public MultivariateMeanCovarianceUpdater(
int dimensionality )
{
this( new MultivariateGaussianMeanCovarianceBayesianEstimator(dimensionality) );
}
/**
* Creates a new instance of MultivariateMeanCovarianceUpdater
* @param estimator
* Bayesian estimator for the parameters
*/
public MultivariateMeanCovarianceUpdater(
MultivariateGaussianMeanCovarianceBayesianEstimator estimator)
{
this.estimator = estimator;
}
@Override
public MultivariateMeanCovarianceUpdater clone()
{
MultivariateMeanCovarianceUpdater clone =
(MultivariateMeanCovarianceUpdater) super.clone();
clone.estimator = ObjectUtil.cloneSafe(this.estimator);
return clone;
}
public MultivariateStudentTDistribution.PDF createPriorPredictive(
Iterable data)
{
NormalInverseWishartDistribution posterior =
this.estimator.learn(data);
return this.estimator.createPredictiveDistribution(posterior).getProbabilityFunction();
}
public MultivariateGaussian.PDF createClusterPosterior(
Iterable values,
Random random )
{
NormalInverseWishartDistribution posterior =
this.estimator.learn(values);
Matrix parameters = posterior.sample(random);
return this.estimator.createConditionalDistribution(parameters).getProbabilityFunction();
}
}
/**
* Updater that creates specified clusters with identical covariances
*/
public static class MultivariateMeanUpdater
extends AbstractCloneableSerializable
implements Updater
{
/**
* Bayesian estimator for the parameters
*/
protected MultivariateGaussianMeanBayesianEstimator estimator;
/**
* Default constructor
*/
public MultivariateMeanUpdater()
{
this( null );
}
/**
* Creates a new instance of MeanCovarianceUpdater
* @param dimensionality
* Dimensionality of the Vectors
*/
public MultivariateMeanUpdater(
int dimensionality )
{
this( new MultivariateGaussianMeanBayesianEstimator(dimensionality) );
}
/**
* Creates a new instance of MeanUpdater
* @param estimator
* Bayesian estimator for the parameters
*/
public MultivariateMeanUpdater(
MultivariateGaussianMeanBayesianEstimator estimator)
{
this.estimator = estimator;
}
@Override
public MultivariateMeanUpdater clone()
{
MultivariateMeanUpdater clone =
(MultivariateMeanUpdater) super.clone();
clone.estimator = ObjectUtil.cloneSafe(this.estimator);
return clone;
}
public MultivariateGaussian.PDF createPriorPredictive(
Iterable data)
{
MultivariateGaussian posterior = this.estimator.learn(data);
return this.estimator.createPredictiveDistribution(posterior).getProbabilityFunction();
}
public MultivariateGaussian.PDF createClusterPosterior(
Iterable values,
Random random )
{
MultivariateGaussian posterior = this.estimator.learn(values);
Vector parameters = posterior.sample(random);
return this.estimator.createConditionalDistribution(parameters).getProbabilityFunction();
}
}
}