[Serializable]
[Quality(QualityBand.Preview)]
[DataContract]
public class SparseGP : IGaussianProcess, IDistribution<IFunction>, IDistribution, ICloneable, Diffable, SettableToUniform, HasPoint<IFunction>, CanGetLogProb<IFunction>, SettableTo<SparseGP>, SettableToProduct<SparseGP>, SettableToProduct<SparseGP, SparseGP>, SettableToRatio<SparseGP>, SettableToRatio<SparseGP, SparseGP>, SettableToPower<SparseGP>, SettableToWeightedSum<SparseGP>, CanGetLogAverageOf<SparseGP>, CanGetLogAverageOfPower<SparseGP>, CanGetAverageLog<SparseGP>, CanGetMean<IFunction>, Sampleable<IFunction>

Remarks

This distribution family comes from the paper "Sparse-posterior Gaussian Processes for general likelihoods" by Qi et al (2010), http://event.cwi.nl/uai2010/papers/UAI2010_0283.pdf

The state of the distribution is represented by (FixedParameters, IncludePrior, InducingDist, pointFunc). The GP prior and basis point locations are stored in FixedParameters. The regression likelihoods are stored as a single VectorGaussian called InducingDist. IncludePrior=false does not include the prior in the distribution (i.e. the distribution is degenerate). If pointFunc != null, the distribution is a point mass. If InducingDist is uniform and IncludePrior is false, the distribution is uniform. The GP prior is assumed to be non-uniform.

Constructors

SparseGP()

Parameterless constructor needed for serialization

Declaration

protected SparseGP()

SparseGP(SparseGP)

Copy constructor

Declaration

public SparseGP(SparseGP that)

Parameters

Type	Name	Description
SparseGP	that

SparseGP(SparseGPFixed)

Constructs sparse GP, given basis etc

Declaration

public SparseGP(SparseGPFixed spgf)

Parameters

Type	Name	Description
SparseGPFixed	spgf	The fixed parameters

SparseGP(SparseGPFixed, Boolean)

Declaration

public SparseGP(SparseGPFixed spgf, bool includePrior)

Parameters

Type	Name	Description
SparseGPFixed	spgf	Fixed parameters
Boolean	includePrior	Whether this instance includes the prior

SparseGP(SparseGPFixed, Boolean, VectorGaussian, IFunction)

Constructor from full specification

Declaration

[Construction(new string[]{"FixedParameters", "IncludePrior", "InducingDist", "Point"})]
public SparseGP(SparseGPFixed spgf, bool includePrior, VectorGaussian InducingDist, IFunction pointFunc)

Parameters

Type	Name	Description
SparseGPFixed	spgf	Fixed parameters
Boolean	includePrior	Whether this instance includes the prior
VectorGaussian	InducingDist	Inducing distribution
IFunction	pointFunc	If not null, set this as a point distribution

Fields

alpha

Field for Alpha property

Declaration

[DataMember]
protected Vector alpha

Field Value

Type	Description
Vector

beta

Field for Beta property

Declaration

[DataMember]
protected PositiveDefiniteMatrix beta

Field Value

Type	Description
PositiveDefiniteMatrix

fixedParameters

Field for FixedParameters property

Declaration

[DataMember]
protected SparseGPFixed fixedParameters

Field Value

Type	Description
SparseGPFixed

IncludePrior

Whether this sparse GP includes the prior

Declaration

[DataMember]
public bool IncludePrior

Field Value

Type	Description
Boolean

InducingDist

The regression likelihoods that modify the prior.

Declaration

[DataMember]
public VectorGaussian InducingDist

Field Value

Type	Description
VectorGaussian

Remarks

If this field is changed, ClearCachedValues() must be called before accessing any other property.

meanB

Field for Mean_B property

Declaration

protected Vector meanB

Field Value

Type	Description
Vector

pointFunc

Use for setting point distribution

Declaration

[DataMember]
protected IFunction pointFunc

Field Value

Type	Description
IFunction

varBB

Field for Var_B_B property

Declaration

protected PositiveDefiniteMatrix varBB

Field Value

Type	Description
PositiveDefiniteMatrix

Properties

Alpha

Alpha - along with beta, this encodes the posterior means and covariances of the Sparse GP

Declaration

[IgnoreDataMember]
public Vector Alpha { get; }

Property Value

Type	Description
Vector

Beta

Beta - along with alpha, this encodes the posterior means and covariances of the Sparse GP

Declaration

[IgnoreDataMember]
public PositiveDefiniteMatrix Beta { get; }

Property Value

Type	Description
PositiveDefiniteMatrix

FixedParameters

Sets and gets the fixed sparse parameters - parameters which are not changed by inference

Declaration

public SparseGPFixed FixedParameters { get; set; }

Property Value

Type	Description
SparseGPFixed

IsPointMass

Asks the distribution whether it is a point mass

Declaration

[IgnoreDataMember]
public bool IsPointMass { get; }

Property Value

Type	Description
Boolean

Mean_B

m(B). This is a calculated Vector maintained by the class

Declaration

[IgnoreDataMember]
public Vector Mean_B { get; }

Property Value

Type	Description
Vector

Point

Sets or Gets a point. If not a point function, the get returns the mean function of the sparse GP

Declaration

[IgnoreDataMember]
public IFunction Point { get; set; }

Property Value

Type	Description
IFunction

Var_B_B

var(B, B). This is a calculated matrix maintained by the class

Declaration

[IgnoreDataMember]
public PositiveDefiniteMatrix Var_B_B { get; }

Property Value

Type	Description
PositiveDefiniteMatrix

Methods

ClearCachedValues()

Function to signal recalculation of calculated parameters. This is called automatically if the fixed parameter class is swapped out, or if the kernel is changed, or if parameters are changed. It should also be called by any external program modifies the kernel or other fixed parameters in place

Declaration

public void ClearCachedValues()

Clone()

Clone. Note that the fixed parameters and the rank1 list are just referenced

Declaration

public object Clone()

Returns

Type	Description
Object	The cloned object

Covariance(Vector, Vector)

Predictive covariance at a given pair of points

Declaration

public double Covariance(Vector x, Vector y)

Parameters

Type	Name	Description
Vector	x
Vector	y

Returns

Type	Description
Double

Covariance(IList<Vector>)

Predictive coariance at a given list of points

Declaration

public PositiveDefiniteMatrix Covariance(IList<Vector> XList)

Parameters

Type	Name	Description
IList<Vector>	XList	List of inputs

Returns

Type	Description
PositiveDefiniteMatrix	Predictive covariance

Equals(Object)

Declaration

public override bool Equals(object obj)

Parameters

Type	Name	Description
Object	obj

Returns

Type	Description
Boolean

Overrides

Object.Equals(Object)

EvaluateMean(Vector)

Evaluates the mean function of the GP

Declaration

public double EvaluateMean(Vector X)

Parameters

Type	Name	Description
Vector	X	Input variable

Returns

Type	Description
Double	Evaulated function value

GetAverageLog(SparseGP)

The expected logarithm of that distribution under this distribution

Declaration

public double GetAverageLog(SparseGP that)

Parameters

Type	Name	Description
SparseGP	that

Returns

Type	Description
Double

Remarks

Not yet implemented

GetHashCode()

Declaration

public override int GetHashCode()

Returns

Type	Description
Int32

Overrides

Object.GetHashCode()

GetLogAverageOf(SparseGP)

Gets the log of the integral of the product of this SparseGP and that SparseGP

Declaration

public double GetLogAverageOf(SparseGP that)

Parameters

Type	Name	Description
SparseGP	that

Returns

Type	Description
Double

GetLogAverageOfPower(SparseGP, Double)

Get the integral of this distribution times another distribution raised to a power.

Declaration

public double GetLogAverageOfPower(SparseGP that, double power)

Parameters

Type	Name	Description
SparseGP	that
Double	power

Returns

Type	Description
Double

GetLogProb(IFunction)

Gets the log density for a given value

Declaration

public double GetLogProb(IFunction value)

Parameters

Type	Name	Description
IFunction	value

Returns

Type	Description
Double

GetMean()

Gets the mean function for the Sparse GP

Declaration

public IFunction GetMean()

Returns

Type	Description
IFunction	The mean function

IsUniform()

Asks the distribution whether it is uniform

Declaration

public bool IsUniform()

Returns

Type	Description
Boolean	True or false

Joint(IList<Vector>)

Predictive distribution at a given list of points

Declaration

public VectorGaussian Joint(IList<Vector> XList)

Parameters

Type	Name	Description
IList<Vector>	XList	List of inputs

Returns

Type	Description
VectorGaussian	Predictive distribution

Marginal(Vector)

Predictive distribution at a given point

Declaration

public Gaussian Marginal(Vector X)

Parameters

Type	Name	Description
Vector	X	Input

Returns

Type	Description
Gaussian	Predictive distribution

MaxDiff(Object)

Max difference between two sparse GPs - used for convergence testing

Declaration

public double MaxDiff(object thatd)

Parameters

Type	Name	Description
Object	thatd	That sparse GP which will be compared to this sparse GP

Returns

Type	Description
Double

Mean(Vector)

Mean at a given point

Declaration

public double Mean(Vector X)

Parameters

Type	Name	Description
Vector	X

Returns

Type	Description
Double

Mean(IList<Vector>)

Mean at a given list of points

Declaration

public Vector Mean(IList<Vector> XList)

Parameters

Type	Name	Description
IList<Vector>	XList	List of inputs

Returns

Type	Description
Vector	Predictive mean vector

PointMass(SparseGPFixed, IFunction)

Creates a sparse GP point mass - i.e. all the mass is at a given function

Declaration

public static SparseGP PointMass(SparseGPFixed sgpf, IFunction value)

Parameters

Type	Name	Description
SparseGPFixed	sgpf
IFunction	value

Returns

Type	Description
SparseGP

Sample()

Samples from the Sparse Gaussian distribution This is only implemented for a 1-dimensional input space, and returns a simple linear spline function

Declaration

public IFunction Sample()

Returns

Type	Description
IFunction	Sample function

Sample(IFunction)

Samples from the Sparse Gaussian distribution This is only implemented for a 1-dimensional input space, and returns a simple linear spline function. result is ignored

This argument is ignored

Declaration

public IFunction Sample(IFunction result)

Parameters

Type	Name	Description
IFunction	result

Returns

Type	Description
IFunction	Sample function

SetTo(SparseGP)

Sets one sparse GP to another. Everything is copied except the FixedParameters and the lsit of rank 1 potentials which are referenced.

Declaration

public void SetTo(SparseGP that)

Parameters

Type	Name	Description
SparseGP	that	The sparse GP to copy

SetToPower(SparseGP, Double)

Sets this sparse GP the the power of another sparse GP

Declaration

public void SetToPower(SparseGP dist, double exponent)

Parameters

Type	Name	Description
SparseGP	dist
Double	exponent

SetToProduct(SparseGP, SparseGP)

Sets this instance to the product of two sparse GPs.

Declaration

public void SetToProduct(SparseGP a, SparseGP b)

Parameters

Type	Name	Description
SparseGP	a	Sparse GP
SparseGP	b	Sparse GP

SetToRatio(SparseGP, SparseGP, Boolean)

Sets this instance to the ratio of two sparse GPs.

Declaration

public void SetToRatio(SparseGP numerator, SparseGP denominator, bool forceProper = false)

Parameters

Type	Name	Description
SparseGP	numerator	Sparse GP
SparseGP	denominator	Sparse GP
Boolean	forceProper

SetToSum(Double, SparseGP, Double, SparseGP)

Sets this SparseGP distribution to the weighted sum of two other such distributions

Declaration

public void SetToSum(double weight1, SparseGP value1, double weight2, SparseGP value2)

Parameters

Type	Name	Description
Double	weight1
SparseGP	value1
Double	weight2
SparseGP	value2

Remarks

Not yet implemented

SetToUniform()

Sets to uniform

Declaration

public void SetToUniform()

ToString()

ToString override

Declaration

public override string ToString()

Returns

Type	Description
String	String representation of instance

Overrides

Object.ToString()

Uniform(SparseGPFixed)

Creates a uniform sparse GP

Declaration

public static SparseGP Uniform(SparseGPFixed sgpf)

Parameters

Type	Name	Description
SparseGPFixed	sgpf

Returns

Type	Description
SparseGP

Variance(Vector)

Predictive Variance at a given point

Declaration

public double Variance(Vector X)

Parameters

Type	Name	Description
Vector	X	Input

Returns

Type	Description
Double	Predictive variance

Operators

Division(SparseGP, SparseGP)

Creates a new SparseGP which the ratio of two other SparseGPs

Declaration

public static SparseGP operator /(SparseGP numerator, SparseGP denominator)

Parameters

Type	Name	Description
SparseGP	numerator	numerator SparseGP
SparseGP	denominator	denominator SparseGP

Returns

Type	Description
SparseGP	Result

Multiply(SparseGP, SparseGP)

Creates a new SparseGP which the product of two other SparseGPs

Declaration

public static SparseGP operator *(SparseGP a, SparseGP b)

Parameters

Type	Name	Description
SparseGP	a	First SparseGP
SparseGP	b	Second SparseGP

Returns

Type	Description
SparseGP	Result

Implements

IGaussianProcess

IDistribution<T>

IDistribution

System.ICloneable

Diffable

SettableToUniform

HasPoint<T>

CanGetLogProb<T>

SettableTo<T>

SettableToProduct<T>

SettableToProduct<T, U>

SettableToRatio<T>

SettableToRatio<T, U>

SettableToPower<T>

SettableToWeightedSum<T>

CanGetLogAverageOf<T>

CanGetLogAverageOfPower<T>

CanGetAverageLog<T>

CanGetMean<MeanType>

Sampleable<T>