gov.sandia.cognition.statistics.bayesian

Class GaussianProcessRegression<InputType>

java.lang.Object

gov.sandia.cognition.util.AbstractCloneableSerializable

gov.sandia.cognition.learning.function.kernel.DefaultKernelContainer<InputType>

gov.sandia.cognition.statistics.bayesian.GaussianProcessRegression<InputType>

Type Parameters:

InputType - Type of inputs to map through the kernel

All Implemented Interfaces:

BatchLearner<java.util.Collection<? extends InputOutputPair<? extends InputType,java.lang.Double>>,MultivariateGaussian>, KernelContainer<InputType>, BayesianEstimator<InputOutputPair<? extends InputType,java.lang.Double>,Vector,MultivariateGaussian>, CloneableSerializable, java.io.Serializable, java.lang.Cloneable

@PublicationReference(author="Christopher M. Bishop",title="Pattern Recognition and Machine Learning",type=Book,year=2006,pages={303,312}) @PublicationReference(author="Hanna M. Wallach",title="Introduction to Gaussian Process Regression",type=Misc,year=2005,url="http://www.cs.umass.edu/~wallach/talks/gp_intro.pdf") @PublicationReference(author="Wikipedia",title="Kriging",type=WebPage,year=2010,url="http://en.wikipedia.org/wiki/Kriging")
public class GaussianProcessRegression<InputType>
extends DefaultKernelContainer<InputType>
implements BayesianEstimator<InputOutputPair<? extends InputType,java.lang.Double>,Vector,MultivariateGaussian>

Gaussian Process Regression, is also known as Kriging, is a nonparametric method to interpolate and extrapolate using Bayesian regression, where the expressiveness of the estimator can grow with the data. However, GPR does not scale well as it requires a N-cubed inversion, where N is the number of data points, to compute the predictive distribution.

Since:

3.0

Author:

Kevin R. Dixon

See Also:

Serialized Form

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
class	GaussianProcessRegression.PredictiveDistribution Predictive distribution for Gaussian Process Regression.

Field Summary

Fields

Modifier and Type	Field and Description
static double	DEFAULT_MEASUREMENT_VARIANCE Default assumed variance of the measurements, 1.0.

Fields inherited from class gov.sandia.cognition.learning.function.kernel.DefaultKernelContainer

kernel

Constructor Summary

Constructors

Constructor and Description
GaussianProcessRegression() Creates a new instance of GaussianProcessRegression
GaussianProcessRegression(Kernel<InputType> kernel, double outputVariance) Creates a new instance of GaussianProcessRegression

Method Summary

Modifier and Type	Method and Description
GaussianProcessRegression<InputType>	clone() This makes public the clone method on the Object class and removes the exception that it throws.
GaussianProcessRegression.PredictiveDistribution	createPredictiveDistribution(MultivariateGaussian posterior, java.util.ArrayList<InputType> inputs) Creates the predictive distribution for future points.
double	getOutputVariance() Getter for outputVariance
MultivariateGaussian	learn(java.util.Collection<? extends InputOutputPair<? extends InputType,java.lang.Double>> data) The learn method creates an object of ResultType using data of type DataType, using some form of "learning" algorithm.
void	setOutputVariance(double outputVariance) Getter for outputVariance

Methods inherited from class gov.sandia.cognition.learning.function.kernel.DefaultKernelContainer

getKernel, setKernel

Methods inherited from class java.lang.Object

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

Field Detail

DEFAULT_MEASUREMENT_VARIANCE

public static final double DEFAULT_MEASUREMENT_VARIANCE

Default assumed variance of the measurements, 1.0.

See Also:

Constant Field Values

Constructor Detail

GaussianProcessRegression

public GaussianProcessRegression()

Creates a new instance of GaussianProcessRegression

GaussianProcessRegression

public GaussianProcessRegression(Kernel<InputType> kernel,
                                 double outputVariance)

Creates a new instance of GaussianProcessRegression

Parameters:

kernel - Kernel to map the InputType to the Vector space

outputVariance - Assumed known variance of the outputs (measurements), must be greater than or equal to zero.

Method Detail

clone

public GaussianProcessRegression<InputType> clone()

Description copied from class: AbstractCloneableSerializable

This makes public the clone method on the Object class and removes the exception that it throws. Its default behavior is to automatically create a clone of the exact type of object that the clone is called on and to copy all primitives but to keep all references, which means it is a shallow copy. Extensions of this class may want to override this method (but call super.clone() to implement a "smart copy". That is, to target the most common use case for creating a copy of the object. Because of the default behavior being a shallow copy, extending classes only need to handle fields that need to have a deeper copy (or those that need to be reset). Some of the methods in ObjectUtil may be helpful in implementing a custom clone method. Note: The contract of this method is that you must use super.clone() as the basis for your implementation.

Specified by:

clone in interface CloneableSerializable

Overrides:

clone in class DefaultKernelContainer<InputType>

Returns:

A clone of this object.

learn

public MultivariateGaussian learn(java.util.Collection<? extends InputOutputPair<? extends InputType,java.lang.Double>> data)

Description copied from interface: BatchLearner

The learn method creates an object of ResultType using data of type DataType, using some form of "learning" algorithm.

Specified by:

learn in interface BatchLearner<java.util.Collection<? extends InputOutputPair<? extends InputType,java.lang.Double>>,MultivariateGaussian>

Parameters:

data - The data that the learning algorithm will use to create an object of ResultType.

Returns:

The object that is created based on the given data using the learning algorithm.

getOutputVariance

public double getOutputVariance()

Getter for outputVariance

Returns:

Assumed known variance of the outputs (measurements), must be greater than or equal to zero.

setOutputVariance

public void setOutputVariance(double outputVariance)

Getter for outputVariance

Parameters:

outputVariance - Assumed known variance of the outputs (measurements), must be greater than or equal to zero.

createPredictiveDistribution

public GaussianProcessRegression.PredictiveDistribution createPredictiveDistribution(MultivariateGaussian posterior,
                                                                                     java.util.ArrayList<InputType> inputs)

Creates the predictive distribution for future points.

Parameters:

posterior - Posterior from the fitting of the training data.

inputs - Training data inputs

Returns:

Predictive distribution of the Gaussian Process Regression