Class GaussianProductOp_SHG09

Provides outgoing messages for the following factors:

• Product(Double, Double)
• Product_SHG09(Double, Double)

, given random arguments to the function.

Inheritance

Object

GaussianProductOp_SHG09

Inherited Members

Object.Equals(Object)

Object.Equals(Object, Object)

Object.GetHashCode()

Object.GetType()

Object.MemberwiseClone()

Object.ReferenceEquals(Object, Object)

Object.ToString()

Namespace: Microsoft.ML.Probabilistic.Factors

Assembly: Microsoft.ML.Probabilistic.dll

Syntax

[FactorMethod(typeof(Factor), "Product_SHG09", new Type[]{typeof(double), typeof(double)})]
[FactorMethod(typeof(Factor), "Product", new Type[]{typeof(double), typeof(double)})]
[Quality(QualityBand.Preview)]
public static class GaussianProductOp_SHG09

Remarks

This class allows EP to process the product factor as if running VMP, as required by Stern's algorithm. The algorithm comes from "Matchbox: Large Scale Online Bayesian Recommendations" by David Stern, Ralf Herbrich, and Thore Graepel, WWW 2009.

Methods

AAverageConditional(Gaussian, Gaussian, Gaussian)

EP message to a.

Declaration

public static Gaussian AAverageConditional(Gaussian Product, Gaussian B, Gaussian to_B)

Parameters

Type	Name	Description
Gaussian	Product	Incoming message from product. 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_B	Previous outgoing message to B.

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.
ImproperMessageException	B is not a proper distribution.

AAverageConditional(Gaussian, Double)

EP message to a.

Declaration

public static Gaussian AAverageConditional(Gaussian Product, double B)

Parameters

Type	Name	Description
Gaussian	Product	Incoming message from product. Must be a proper distribution. If uniform, the result will be uniform.
Double	B	Constant value for b.

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) p(product) factor(product,a,b)]/p(a).

Exceptions

Type	Condition
ImproperMessageException	Product is not a proper distribution.

BAverageConditional(Gaussian, Gaussian, Gaussian)

EP message to b.

Declaration

public static Gaussian BAverageConditional(Gaussian Product, Gaussian A, 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	to_A	Previous outgoing message to A.

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.
ImproperMessageException	A is not a proper distribution.

BAverageConditional(Gaussian, Double)

EP message to b.

Declaration

public static Gaussian BAverageConditional(Gaussian Product, double A)

Parameters

Type	Name	Description
Gaussian	Product	Incoming message from product. Must be a proper distribution. If uniform, the result will be uniform.
Double	A	Constant value for a.

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) p(product) factor(product,a,b)]/p(b).

Exceptions

Type	Condition
ImproperMessageException	Product is not a proper distribution.

LogEvidenceRatio(Gaussian, Gaussian, Gaussian, Gaussian, Gaussian, Gaussian)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(Gaussian Product, Gaussian A, Gaussian B, Gaussian to_A, Gaussian to_B, Gaussian to_product)

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.
Gaussian	to_B	Previous outgoing message to B.
Gaussian	to_product	Previous outgoing message to product.

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.

LogEvidenceRatio(Gaussian, Gaussian, Double, Gaussian, Gaussian)

Evidence message for EP.

Declaration

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

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.
Double	B	Constant value for b.
Gaussian	to_A	Previous outgoing message to A.
Gaussian	to_product	Previous outgoing message to product.

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) p(product,a) 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.

LogEvidenceRatio(Gaussian, Double, Gaussian, Gaussian, Gaussian)

Evidence message for EP.

Declaration

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

Parameters

Type	Name	Description
Gaussian	Product	Incoming message from product. Must be a proper distribution. If uniform, the result will be uniform.
Double	A	Constant value for a.
Gaussian	B	Incoming message from b. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	to_B	Previous outgoing message to B.
Gaussian	to_product	Previous outgoing message to product.

Returns

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

Remarks

The formula for the result is log(sum_(product,b) p(product,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	B is not a proper distribution.

ProductAverageConditional(Gaussian, Gaussian, Gaussian, Gaussian)

EP message to product.

Declaration

public static Gaussian ProductAverageConditional(Gaussian A, Gaussian B, Gaussian to_A, Gaussian to_B)

Parameters

Type	Name	Description
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.
Gaussian	to_B	Previous outgoing message to B.

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).

Exceptions

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

ProductAverageConditional(Gaussian, Double, Gaussian)

EP message to product.

Declaration

public static Gaussian ProductAverageConditional(Gaussian A, double B, Gaussian to_A)

Parameters

Type	Name	Description
Gaussian	A	Incoming message from a. Must be a proper distribution. If uniform, the result will be uniform.
Double	B	Constant value for b.
Gaussian	to_A	Previous outgoing message to A.

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) p(a) factor(product,a,b)]/p(product).

Exceptions

Type	Condition
ImproperMessageException	A is not a proper distribution.

ProductAverageConditional(Double, Gaussian, Gaussian)

EP message to product.

Declaration

public static Gaussian ProductAverageConditional(double A, Gaussian B, Gaussian to_B)

Parameters

Type	Name	Description
Double	A	Constant value for a.
Gaussian	B	Incoming message from b. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	to_B	Previous outgoing message to B.

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_(b) p(b) factor(product,a,b)]/p(product).

Exceptions

Type	Condition
ImproperMessageException	B is not a proper distribution.

ProductAverageConditional2(Gaussian, Gaussian, Gaussian, Gaussian, Gaussian)

Declaration

public static Gaussian ProductAverageConditional2(Gaussian product, Gaussian A, Gaussian B, Gaussian to_A, Gaussian to_B)

Parameters

Type	Name	Description
Gaussian	product
Gaussian	A
Gaussian	B
Gaussian	to_A
Gaussian	to_B

Returns

Type	Description
Gaussian