[FactorMethod(typeof(Factor), "Product", new Type[]{typeof(double), typeof(double)})]
[Buffers(new string[]{"ahat"})]
[Quality(QualityBand.Experimental)]
public class GaussianProductOp_Laplace : GaussianProductOpEvidenceBase

Remarks

This class allows EP to process the product factor using Laplace's method.

Methods

AAverageConditional(Gaussian, Gaussian, Gaussian, Double)

EP message to a.

Declaration

public static Gaussian AAverageConditional(Gaussian Product, Gaussian A, Gaussian B, double ahat)

Parameters

Type	Name	Description
Gaussian	Product	Incoming message from `product`. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	A	Incoming message from `a`.
Gaussian	B	Incoming message from `b`.
Double	ahat	Buffer `ahat`.

Returns

Type	Description
Gaussian	The outgoing EP message to the `a` argument.

Remarks

The outgoing message is a distribution matching the moments of a as the random arguments are varied. The formula is proj[p(a) sum_(product,b) p(product,b) factor(product,a,b)]/p(a).

Exceptions

Type	Condition
ImproperMessageException	`Product` is not a proper distribution.

Ahat(Gaussian, Gaussian, Gaussian, Double)

Declaration

public static double Ahat(Gaussian Product, Gaussian A, Gaussian B, double ahat)

Parameters

Type	Name	Description
Gaussian	Product
Gaussian	A
Gaussian	B
Double	ahat

Returns

Type	Description
Double

AhatInit(Gaussian)

Declaration

public static double AhatInit(Gaussian a)

Parameters

Type	Name	Description
Gaussian	a

Returns

Type	Description
Double

BAverageConditional(Gaussian, Gaussian, Gaussian, Double)

EP message to b.

Declaration

public static Gaussian BAverageConditional(Gaussian Product, Gaussian A, Gaussian B, double ahat)

Parameters

Type	Name	Description
Gaussian	Product	Incoming message from `product`. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	A	Incoming message from `a`.
Gaussian	B	Incoming message from `b`.
Double	ahat	Buffer `ahat`.

Returns

Type	Description
Gaussian	The outgoing EP message to the `b` argument.

Remarks

The outgoing message is a distribution matching the moments of b as the random arguments are varied. The formula is proj[p(b) sum_(product,a) p(product,a) factor(product,a,b)]/p(b).

Exceptions

Type	Condition
ImproperMessageException	`Product` is not a proper distribution.

GetMoments(Int32, Gaussian, Gaussian, Gaussian, Double)

Declaration

public static Gaussian GetMoments(int index, Gaussian Product, Gaussian A, Gaussian B, double ahat)

Parameters

Type	Name	Description
Int32	index
Gaussian	Product
Gaussian	A
Gaussian	B
Double	ahat

Returns

Type	Description
Gaussian

LogAverageFactor(Gaussian, Gaussian, Gaussian, Gaussian)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Gaussian Product, Gaussian A, Gaussian B, Gaussian to_A)

Parameters

Type	Name	Description
Gaussian	Product	Incoming message from `product`. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	A	Incoming message from `a`. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	B	Incoming message from `b`. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	to_A	Previous outgoing message to `A`.

Returns

Type	Description
Double	Logarithm of the factor's average value across the given argument distributions.

Remarks

The formula for the result is log(sum_(product,a,b) p(product,a,b) factor(product,a,b)).

Exceptions

Type	Condition
ImproperMessageException	`Product` is not a proper distribution.
ImproperMessageException	`A` is not a proper distribution.
ImproperMessageException	`B` is not a proper distribution.

LogEvidenceRatio(Gaussian, Gaussian, Gaussian)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(Gaussian Product, Gaussian A, Gaussian B)

Parameters

Type	Name	Description
Gaussian	Product	Incoming message from `product`. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	A	Incoming message from `a`. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	B	Incoming message from `b`. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Double	Logarithm of the factor's contribution the EP model evidence.

Remarks

The formula for the result is log(sum_(product,a,b) p(product,a,b) factor(product,a,b) / sum_product p(product) messageTo(product)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

Exceptions

Type	Condition
ImproperMessageException	`Product` is not a proper distribution.
ImproperMessageException	`A` is not a proper distribution.
ImproperMessageException	`B` is not a proper distribution.

ProductAverageConditional(Gaussian, Gaussian, Gaussian, Double)

EP message to product.

Declaration

public static Gaussian ProductAverageConditional(Gaussian Product, Gaussian A, Gaussian B, double ahat)

Parameters

Type	Name	Description
Gaussian	Product	Incoming message from `product`.
Gaussian	A	Incoming message from `a`.
Gaussian	B	Incoming message from `b`.
Double	ahat	Buffer `ahat`.

Returns

Type	Description
Gaussian	The outgoing EP message to the `product` argument.

Remarks

The outgoing message is a distribution matching the moments of product as the random arguments are varied. The formula is proj[p(product) sum_(a,b) p(a,b) factor(product,a,b)]/p(product).