Class SoftmaxOp_Bouchard_Sparse

Provides outgoing messages for Softmax(IList<Double>), given random arguments to the function.

Inheritance

Object

SoftmaxOp_Bouchard_Sparse

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(MMath), "Softmax", new Type[]{typeof(IList<double>)})]
[Quality(QualityBand.Experimental)]
[Buffers(new string[]{"A"})]
public static class SoftmaxOp_Bouchard_Sparse

Remarks

This implementation uses the simple first order Taylor series expansion from Blei et al. 06, followed by optimization using LBFGS. This approach is linear in the dimension K.

Methods

A<GaussianList>(GaussianList, Double)

Update the buffer A.

Declaration

public static double A<GaussianList>(GaussianList x, double a)
    where GaussianList : IList<Gaussian>

Parameters

Type	Name	Description
GaussianList	x	Incoming message from x.
Double	a	Buffer a.

Returns

Type	Description
Double	New value of buffer A.

Type Parameters

Name	Description
GaussianList	The type of the incoming message from x.

Remarks

AInit()

Initialize the buffer A.

Declaration

public static double AInit()

Returns

Type	Description
Double	Initial value of buffer A.

Remarks

AverageLogFactor<GaussianList>(GaussianList, Dirichlet, Dirichlet, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor<GaussianList>(GaussianList x, Dirichlet softmax, Dirichlet to_softmax, double a)
    where GaussianList : IList<Gaussian>

Parameters

Type	Name	Description
GaussianList	x	Incoming message from x.
Dirichlet	softmax	Incoming message from softmax.
Dirichlet	to_softmax	Previous outgoing message to softmax.
Double	a	Buffer a.

Returns

Type	Description
Double	Zero.

Type Parameters

Name	Description
GaussianList	The type of the incoming message from x.

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.

logSumExp<GaussianList>(GaussianList, Double)

Declaration

public static double logSumExp<GaussianList>(GaussianList x, double a)
    where GaussianList : IList<Gaussian>

Parameters

Type	Name	Description
GaussianList	x
Double	a

Returns

Type	Description
Double

Type Parameters

Name	Description
GaussianList

SoftmaxAverageLogarithm<GaussianList>(GaussianList, Double, Dirichlet)

VMP message to softmax.

Declaration

public static Dirichlet SoftmaxAverageLogarithm<GaussianList>([SkipIfAllUniform] GaussianList x, double a, Dirichlet result)
    where GaussianList : IList<Gaussian>

Parameters

Type	Name	Description
GaussianList	x	Incoming message from x. Must be a proper distribution. If all elements are uniform, the result will be uniform.
Double	a	Buffer a.
Dirichlet	result	Modified to contain the outgoing message.

Returns

Type	Description
Dirichlet	result

Type Parameters

Name	Description
GaussianList	The type of the incoming message from x.

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	x is not a proper distribution.

XAverageLogarithm<GaussianList>(Dirichlet, GaussianList, Double, GaussianList)

VMP message to x.

Declaration

public static GaussianList XAverageLogarithm<GaussianList>(Dirichlet softmax, [SkipIfAllUniform] GaussianList x, double a, GaussianList result)
    where GaussianList : IList<Gaussian>

Parameters

Type	Name	Description
Dirichlet	softmax	Incoming message from softmax. Must be a proper distribution. If any element is uniform, the result will be uniform.
GaussianList	x	Incoming message from x. Must be a proper distribution. If all elements are uniform, the result will be uniform.
Double	a	Buffer a.
GaussianList	result	Modified to contain the outgoing message.

Returns

Type	Description
GaussianList	result

Type Parameters

Name	Description
GaussianList	The type of the incoming message from x and the outgoing message.

Remarks

The outgoing message is the factor viewed as a function of x with softmax integrated out. The formula is sum_softmax p(softmax) factor(softmax,x).

Exceptions

Type	Condition
ImproperMessageException	softmax is not a proper distribution.
ImproperMessageException	x is not a proper distribution.