gov.sandia.cognition.statistics.bayesian.conjugate

Class MultinomialBayesianEstimator

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.learning.algorithm.AbstractBatchAndIncrementalLearner<ObservationType,BeliefType>

gov.sandia.cognition.statistics.bayesian.conjugate.AbstractConjugatePriorBayesianEstimator<Vector,Vector,MultinomialDistribution,DirichletDistribution>

gov.sandia.cognition.statistics.bayesian.conjugate.MultinomialBayesianEstimator

All Implemented Interfaces:

BatchAndIncrementalLearner<Vector,DirichletDistribution>, BatchLearner<java.util.Collection<? extends Vector>,DirichletDistribution>, IncrementalLearner<Vector,DirichletDistribution>, BayesianEstimator<Vector,Vector,DirichletDistribution>, BayesianEstimatorPredictor<Vector,Vector,DirichletDistribution>, ConjugatePriorBayesianEstimator<Vector,Vector,MultinomialDistribution,DirichletDistribution>, ConjugatePriorBayesianEstimatorPredictor<Vector,Vector,MultinomialDistribution,DirichletDistribution>, RecursiveBayesianEstimator<Vector,Vector,DirichletDistribution>, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

@PublicationReference(author="Wikipedia",
                      title="Conjugate Prior",
                      type=WebPage,
                      year=2009,
                      url="http://en.wikipedia.org/wiki/Conjugate_prior")
public class MultinomialBayesianEstimator
extends AbstractConjugatePriorBayesianEstimator<Vector,Vector,MultinomialDistribution,DirichletDistribution>
implements ConjugatePriorBayesianEstimatorPredictor<Vector,Vector,MultinomialDistribution,DirichletDistribution>

A Bayesian estimator for the parameters of a MultinomialDistribution using its conjugate prior distribution, the DirichletDistribution.

Since:

3.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
static class	MultinomialBayesianEstimator.Parameter Parameter of this conjugate prior relationship.

Field Summary

Fields

Modifier and Type	Field and Description
static int	DEFAULT_NUM_CLASSES Default number of classes/labels, 2.
static int	DEFAULT_NUM_TRIALS Default number of trials, 2.

Fields inherited from class gov.sandia.cognition.statistics.bayesian.conjugate.AbstractConjugatePriorBayesianEstimator

parameter

Constructor Summary

Constructors

Modifier	Constructor and Description
	MultinomialBayesianEstimator() Creates a new instance of MultinomialBayesianEstimator
protected	MultinomialBayesianEstimator(BayesianParameter<Vector,MultinomialDistribution,DirichletDistribution> parameter) Creates a new instance
	MultinomialBayesianEstimator(DirichletDistribution initialBelief, int numTrials) Creates a new instance of MultinomialBayesianEstimator
	MultinomialBayesianEstimator(int numTrials) Creates a new instance of MultinomialBayesianEstimator
	MultinomialBayesianEstimator(int numClasses, int numTrials) Creates a new instance of MultinomialBayesianEstimator
	MultinomialBayesianEstimator(MultinomialDistribution conditional, DirichletDistribution prior) Creates a new instance of PoissonBayesianEstimator

Method Summary

Modifier and Type	Method and Description
double	computeEquivalentSampleSize(DirichletDistribution belief) Computes the equivalent sample size of using the given prior.
MultinomialDistribution	createConditionalDistribution(Vector parameter) Creates an instance of the class conditional distribution, parameterized by the given parameter value.
MultinomialBayesianEstimator.Parameter	createParameter(MultinomialDistribution conditional, DirichletDistribution prior) Creates a parameter linking the conditional and prior distributions
MultivariatePolyaDistribution	createPredictiveDistribution(DirichletDistribution posterior) Creates the predictive distribution of new data given the posterior.
int	getNumTrials() Getter for numTrials
void	setNumTrials(int numTrials) Setter for numTrials
void	update(DirichletDistribution belief, Vector value) The update method updates an object of ResultType using the given new data of type DataType, using some form of "learning" algorithm.

Methods inherited from class gov.sandia.cognition.statistics.bayesian.conjugate.AbstractConjugatePriorBayesianEstimator

clone, createInitialLearnedObject, getInitialBelief, getParameter, setParameter

Methods inherited from class gov.sandia.cognition.learning.algorithm.AbstractBatchAndIncrementalLearner

learn, learn, update

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface gov.sandia.cognition.statistics.bayesian.conjugate.ConjugatePriorBayesianEstimator

getParameter

Methods inherited from interface gov.sandia.cognition.learning.algorithm.BatchLearner

learn

Methods inherited from interface gov.sandia.cognition.util.CloneableSerializable

clone

Methods inherited from interface gov.sandia.cognition.learning.algorithm.IncrementalLearner

createInitialLearnedObject, update

Field Detail

DEFAULT_NUM_TRIALS

public static final int DEFAULT_NUM_TRIALS

Default number of trials, 2.

See Also:

Constant Field Values

DEFAULT_NUM_CLASSES

public static final int DEFAULT_NUM_CLASSES

Default number of classes/labels, 2.

See Also:

Constant Field Values

Constructor Detail

MultinomialBayesianEstimator

public MultinomialBayesianEstimator()

Creates a new instance of MultinomialBayesianEstimator

MultinomialBayesianEstimator

public MultinomialBayesianEstimator(int numTrials)

Creates a new instance of MultinomialBayesianEstimator

Parameters:

numTrials - Number of trials in the distribution, must be greater than 0.

MultinomialBayesianEstimator

public MultinomialBayesianEstimator(int numClasses,
                                    int numTrials)

Creates a new instance of MultinomialBayesianEstimator

Parameters:

numClasses - Number of classes/labels/parameters

numTrials - Number of trials in the distribution, must be greater than 0.

MultinomialBayesianEstimator

public MultinomialBayesianEstimator(DirichletDistribution initialBelief,
                                    int numTrials)

Creates a new instance of MultinomialBayesianEstimator

Parameters:

initialBelief - Initial belief of the prior.

numTrials - Number of trials in the distribution, must be greater than 0.

MultinomialBayesianEstimator

public MultinomialBayesianEstimator(MultinomialDistribution conditional,
                                    DirichletDistribution prior)

Creates a new instance of PoissonBayesianEstimator

Parameters:

prior - Default conjugate prior.

conditional - Conditional distribution of the conjugate prior.

MultinomialBayesianEstimator

protected MultinomialBayesianEstimator(BayesianParameter<Vector,MultinomialDistribution,DirichletDistribution> parameter)

Creates a new instance

Parameters:

parameter - Bayesian hyperparameter relationship between the conditional distribution and the conjugate prior distribution.

Method Detail

createParameter

public MultinomialBayesianEstimator.Parameter createParameter(MultinomialDistribution conditional,
                                                              DirichletDistribution prior)

Description copied from interface: ConjugatePriorBayesianEstimator

Creates a parameter linking the conditional and prior distributions

Specified by:

createParameter in interface ConjugatePriorBayesianEstimator<Vector,Vector,MultinomialDistribution,DirichletDistribution>

Parameters:

conditional - Distribution from which observations are generated

prior - Distribution that generates parameters for the conditional

Returns:

Parameter describing the relationship between the conditional and prior

computeEquivalentSampleSize

public double computeEquivalentSampleSize(DirichletDistribution belief)

Description copied from interface: ConjugatePriorBayesianEstimator

Computes the equivalent sample size of using the given prior. This is effectively how many samples of bias the prior injects into the estimate.

Specified by:

computeEquivalentSampleSize in interface ConjugatePriorBayesianEstimator<Vector,Vector,MultinomialDistribution,DirichletDistribution>

Parameters:

belief - Prior belief to measure.

Returns:

Equivalent sample size of the initial belief.

update

public void update(DirichletDistribution belief,
                   Vector value)

Description copied from interface: IncrementalLearner

The update method updates an object of ResultType using the given new data of type DataType, using some form of "learning" algorithm.

Specified by:

update in interface IncrementalLearner<Vector,DirichletDistribution>

Parameters:

belief - The object to update.

value - The new data for the learning algorithm to use to update the object.

getNumTrials

public int getNumTrials()

Getter for numTrials

Returns:

Number of trials in the distribution, must be greater than 0.

setNumTrials

public void setNumTrials(int numTrials)

Setter for numTrials

Parameters:

numTrials - Number of trials in the distribution, must be greater than 0.

createConditionalDistribution

public MultinomialDistribution createConditionalDistribution(Vector parameter)

Description copied from interface: ConjugatePriorBayesianEstimator

Creates an instance of the class conditional distribution, parameterized by the given parameter value. This is the distribution that we implicitly draw observation samples from.

Specified by:

createConditionalDistribution in interface ConjugatePriorBayesianEstimator<Vector,Vector,MultinomialDistribution,DirichletDistribution>

Overrides:

createConditionalDistribution in class AbstractConjugatePriorBayesianEstimator<Vector,Vector,MultinomialDistribution,DirichletDistribution>

Parameters:

parameter - Parameter used to create the class conditional distribution.

Returns:

Parameterized class conditional distribution.

createPredictiveDistribution

public MultivariatePolyaDistribution createPredictiveDistribution(DirichletDistribution posterior)

Description copied from interface: BayesianEstimatorPredictor

Creates the predictive distribution of new data given the posterior. This is equivalent to evaluating the integral of: p( newdata | data ) = integral( conditional( newdata | data, parameters ) * p( parameters | data ) dparameters )

Specified by:

createPredictiveDistribution in interface BayesianEstimatorPredictor<Vector,Vector,DirichletDistribution>

Parameters:

posterior - Posterior distribution from which to compute the predictive posterior.

Returns:

Predictive distribution of new data given the observed data.