Class ProductWishartOp

Provides outgoing messages for the following factors:

, given random arguments to the function.

Inheritance

Object

ProductWishartOp

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", new Type[]{typeof(PositiveDefiniteMatrix), typeof(double)})]
[FactorMethod(new string[]{"Product", "b", "a"}, typeof(Factor), "Product", new Type[]{typeof(double), typeof(PositiveDefiniteMatrix)})]
[Quality(QualityBand.Experimental)]
public static class ProductWishartOp

Methods

AAverageConditional(Wishart, Double, Wishart)

EP message to a.

Declaration

public static Wishart AAverageConditional(Wishart Product, double B, Wishart result)

Parameters

Type	Name	Description
Wishart	Product	Incoming message from `product`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Double	B	Constant value for `b`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

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.

AAverageLogarithm(Wishart, Gamma, Wishart)

VMP message to a.

Declaration

public static Wishart AAverageLogarithm(Wishart Product, Gamma B, Wishart result)

Parameters

Type	Name	Description
Wishart	Product	Incoming message from `product`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	B	Incoming message from `b`. Must be a proper distribution. If uniform, the result will be uniform.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except a. Because the factor is deterministic, product is integrated out before taking the logarithm. The formula is exp(sum_(b) p(b) log(sum_product p(product) factor(product,a,b))).

Exceptions

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

AAverageLogarithm(Wishart, Double, Wishart)

VMP message to a.

Declaration

public static Wishart AAverageLogarithm(Wishart Product, double B, Wishart result)

Parameters

Type	Name	Description
Wishart	Product	Incoming message from `product`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Double	B	Constant value for `b`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

The outgoing message is the factor viewed as a function of a with product integrated out. The formula is sum_product p(product) factor(product,a,b).

Exceptions

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

AAverageLogarithm(PositiveDefiniteMatrix, Gamma, Wishart)

VMP message to a.

Declaration

[NotSupported("Variational Message Passing does not support a Product factor with fixed output and two random inputs.")]
public static Wishart AAverageLogarithm(PositiveDefiniteMatrix Product, Gamma B, Wishart result)

Parameters

Type	Name	Description
PositiveDefiniteMatrix	Product	Constant value for `product`.
Gamma	B	Incoming message from `b`. Must be a proper distribution. If uniform, the result will be uniform.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except a. The formula is exp(sum_(b) p(b) log(factor(product,a,b))).

Exceptions

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

AAverageLogarithm(PositiveDefiniteMatrix, Double, Wishart)

VMP message to a.

Declaration

public static Wishart AAverageLogarithm(PositiveDefiniteMatrix Product, double B, Wishart result)

Parameters

Type	Name	Description
PositiveDefiniteMatrix	Product	Constant value for `product`.
Double	B	Constant value for `b`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

The outgoing message is the factor viewed as a function of a conditioned on the given values.

AverageLogFactor(Wishart)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Wishart product)

Parameters

Type	Name	Description
Wishart	product	Incoming message from `product`.

Returns

Type	Description
Double	Zero.

Remarks

In Variational Message Passing, the evidence contribution of a deterministic factor is zero. Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

BAverageConditional(Wishart, PositiveDefiniteMatrix)

EP message to b.

Declaration

public static Gamma BAverageConditional(Wishart Product, PositiveDefiniteMatrix A)

Parameters

Type	Name	Description
Wishart	Product	Incoming message from `product`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	A	Constant value for `a`.

Returns

Type	Description
Gamma	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.

BAverageConditional(PositiveDefiniteMatrix, PositiveDefiniteMatrix)

EP message to b.

Declaration

public static Gamma BAverageConditional(PositiveDefiniteMatrix Product, PositiveDefiniteMatrix A)

Parameters

Type	Name	Description
PositiveDefiniteMatrix	Product	Constant value for `product`.
PositiveDefiniteMatrix	A	Constant value for `a`.

Returns

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

Remarks

The outgoing message is the factor viewed as a function of b conditioned on the given values.

BAverageLogarithm(Wishart, Wishart)

VMP message to b.

Declaration

public static Gamma BAverageLogarithm(Wishart Product, Wishart A)

Parameters

Type	Name	Description
Wishart	Product	Incoming message from `product`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Wishart	A	Incoming message from `a`. Must be a proper distribution. If any element is uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing VMP message to the `b` argument.

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except b. Because the factor is deterministic, product is integrated out before taking the logarithm. The formula is exp(sum_(a) p(a) log(sum_product p(product) factor(product,a,b))).

Exceptions

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

BAverageLogarithm(Wishart, PositiveDefiniteMatrix)

VMP message to b.

Declaration

public static Gamma BAverageLogarithm(Wishart Product, PositiveDefiniteMatrix A)

Parameters

Type	Name	Description
Wishart	Product	Incoming message from `product`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	A	Constant value for `a`.

Returns

Type	Description
Gamma	The outgoing VMP message to the `b` argument.

Remarks

The outgoing message is the factor viewed as a function of b with product integrated out. The formula is sum_product p(product) factor(product,a,b).

Exceptions

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

BAverageLogarithm(PositiveDefiniteMatrix, Wishart)

VMP message to b.

Declaration

[NotSupported("Variational Message Passing does not support a Product factor with fixed output and two random inputs.")]
public static Gamma BAverageLogarithm(PositiveDefiniteMatrix Product, Wishart A)

Parameters

Type	Name	Description
PositiveDefiniteMatrix	Product	Constant value for `product`.
Wishart	A	Incoming message from `a`. Must be a proper distribution. If any element is uniform, the result will be uniform.

Returns

Type	Description
Gamma	The outgoing VMP message to the `b` argument.

Remarks

The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except b. The formula is exp(sum_(a) p(a) log(factor(product,a,b))).

Exceptions

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

BAverageLogarithm(PositiveDefiniteMatrix, PositiveDefiniteMatrix)

VMP message to b.

Declaration

public static Gamma BAverageLogarithm(PositiveDefiniteMatrix Product, PositiveDefiniteMatrix A)

Parameters

Type	Name	Description
PositiveDefiniteMatrix	Product	Constant value for `product`.
PositiveDefiniteMatrix	A	Constant value for `a`.

Returns

Type	Description
Gamma	The outgoing VMP message to the `b` argument.

Remarks

The outgoing message is the factor viewed as a function of b conditioned on the given values.

LogEvidenceRatio(Wishart, Wishart, Double)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(Wishart product, Wishart a, double b)

Parameters

Type	Name	Description
Wishart	product	Incoming message from `product`.
Wishart	a	Incoming message from `a`.
Double	b	Constant value for `b`.

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.

LogEvidenceRatio(Wishart, PositiveDefiniteMatrix, Gamma)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(Wishart product, PositiveDefiniteMatrix a, Gamma b)

Parameters

Type	Name	Description
Wishart	product	Incoming message from `product`.
PositiveDefiniteMatrix	a	Constant value for `a`.
Gamma	b	Incoming message from `b`.

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.

LogEvidenceRatio(PositiveDefiniteMatrix, Wishart, Double)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(PositiveDefiniteMatrix product, Wishart a, double b)

Parameters

Type	Name	Description
PositiveDefiniteMatrix	product	Constant value for `product`.
Wishart	a	Incoming message from `a`.
Double	b	Constant value for `b`.

Returns

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

Remarks

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

ProductAverageConditional(Wishart, PositiveDefiniteMatrix, Gamma, Gamma, Wishart)

EP message to product.

Declaration

public static Wishart ProductAverageConditional(Wishart Product, PositiveDefiniteMatrix A, Gamma B, Gamma to_B, Wishart result)

Parameters

Type	Name	Description
Wishart	Product	Incoming message from `product`.
PositiveDefiniteMatrix	A	Constant value for `a`.
Gamma	B	Incoming message from `b`. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	to_B	Previous outgoing message to `B`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

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.

ProductAverageConditional(Wishart, Double, Wishart)

EP message to product.

Declaration

public static Wishart ProductAverageConditional(Wishart A, double B, Wishart result)

Parameters

Type	Name	Description
Wishart	A	Incoming message from `a`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Double	B	Constant value for `b`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

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(PositiveDefiniteMatrix, Double, Wishart)

EP message to product.

Declaration

public static Wishart ProductAverageConditional(PositiveDefiniteMatrix A, double B, Wishart result)

Parameters

Type	Name	Description
PositiveDefiniteMatrix	A	Constant value for `a`.
Double	B	Constant value for `b`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

The outgoing message is the factor viewed as a function of product conditioned on the given values.

ProductAverageLogarithm(Wishart, Gamma, Wishart)

VMP message to product.

Declaration

public static Wishart ProductAverageLogarithm(Wishart A, Gamma B, Wishart result)

Parameters

Type	Name	Description
Wishart	A	Incoming message from `a`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	B	Incoming message from `b`. Must be a proper distribution. If uniform, the result will be uniform.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

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

Exceptions

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

ProductAverageLogarithm(Wishart, Double, Wishart)

VMP message to product.

Declaration

public static Wishart ProductAverageLogarithm(Wishart A, double B, Wishart result)

Parameters

Type	Name	Description
Wishart	A	Incoming message from `a`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Double	B	Constant value for `b`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

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

Exceptions

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