Class SoftmaxOp_KM11_Sparse2

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

Inheritance

Object

SoftmaxOp_KM11_Sparse2

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.Preview)]
[Buffers(new string[]{"Asj", "Abouchard"})]
public static class SoftmaxOp_KM11_Sparse2

Remarks

This implementation uses a generalization of the tilted bound used in Saul Jordan 1999, followed by nonconjugate VMP. This approach is linear in the dimension K.

Methods

Abouchard<GaussianList>(GaussianList, Double)

Update the buffer Abouchard.

Declaration

public static double Abouchard<GaussianList>(GaussianList x, double abouchard)
    where GaussianList : IList<Gaussian>

Parameters

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

Returns

Type	Description
Double	New value of buffer Abouchard.

Type Parameters

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

Remarks

AbouchardInit()

Initialize the buffer Abouchard.

Declaration

public static double AbouchardInit()

Returns

Type	Description
Double	Initial value of buffer Abouchard.

Remarks

Asj(IList<Gaussian>, IList<Double>)

Update the buffer Asj.

Declaration

public static IList<double> Asj(IList<Gaussian> x, IList<double> asj)

Parameters

Type	Name	Description
IList<Gaussian>	x	Incoming message from x. Must be a proper distribution. If any element is uniform, the result will be uniform.
IList<Double>	asj	Buffer asj.

Returns

Type	Description
IList<Double>	New value of buffer Asj.

Remarks

Exceptions

Type	Condition
ImproperMessageException	x is not a proper distribution.

AsjInit(IList<Gaussian>)

Initialize the buffer Asj.

Declaration

public static IList<double> AsjInit(IList<Gaussian> x)

Parameters

Type	Name	Description
IList<Gaussian>	x	Incoming message from x.

Returns

Type	Description
IList<Double>	Initial value of buffer Asj.

Remarks

LogAverageFactor<GaussianList>(GaussianList, IList<Double>, Double, Dirichlet, Dirichlet)

Evidence message for EP.

Declaration

public static double LogAverageFactor<GaussianList>([SkipIfAllUniform] GaussianList x, IList<double> asj, double abouchard, Dirichlet softmax, Dirichlet to_softmax)
    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.
IList<Double>	asj	Buffer asj.
Double	abouchard	Buffer abouchard.
Dirichlet	softmax	Incoming message from softmax.
Dirichlet	to_softmax	Previous outgoing message to softmax.

Returns

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

Type Parameters

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

Remarks

The formula for the result is log(sum_(x,softmax) p(x,softmax) factor(softmax,x)).

Exceptions

Type	Condition
ImproperMessageException	x is not a proper distribution.

SoftmaxAverageLogarithm<GaussianList>(GaussianList, IList<Double>, Double, Dirichlet, Dirichlet)

VMP message to softmax.

Declaration

public static Dirichlet SoftmaxAverageLogarithm<GaussianList>([SkipIfAllUniform] GaussianList x, IList<double> asj, double abouchard, Dirichlet softmax, Dirichlet to_softmax)
    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.
IList<Double>	asj	Buffer asj.
Double	abouchard	Buffer abouchard.
Dirichlet	softmax	Incoming message from softmax.
Dirichlet	to_softmax	Previous outgoing message to softmax.

Returns

Type	Description
Dirichlet	The outgoing VMP message to the softmax argument.

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

VMP message to x.

Declaration

public static GaussianList XAverageLogarithm<GaussianList>([SkipIfAllUniform] GaussianList x, IList<double> asj, double abouchard, Dirichlet softmax, Dirichlet to_softmax, GaussianList to_x)
    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.
IList<Double>	asj	Buffer asj.
Double	abouchard	Buffer abouchard.
Dirichlet	softmax	Incoming message from softmax.
Dirichlet	to_softmax	Previous outgoing message to softmax.
GaussianList	to_x	Previous outgoing message to x.

Returns

Type	Description
GaussianList	The outgoing VMP message to the x argument.

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	x is not a proper distribution.