Class SoftmaxOp_KM11_LBFGS

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

Inheritance

Object

SoftmaxOp_KM11_LBFGS

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[]{"A"})]
public static class SoftmaxOp_KM11_LBFGS

Remarks

This implementation uses the bound in Knowles and Minka (2011), followed by optimization using LBFGS. This approach is linear in the dimension K.

Methods

A(IList<Gaussian>, Vector)

Update the buffer A.

Declaration

public static Vector A(IList<Gaussian> x, Vector a)

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.
Vector	a	Buffer a.

Returns

Type	Description
Vector	New value of buffer A.

Remarks

Exceptions

Type	Condition
ImproperMessageException	x is not a proper distribution.

AInit(IList<Gaussian>)

Initialize the buffer A.

Declaration

public static Vector AInit(IList<Gaussian> x)

Parameters

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

Returns

Type	Description
Vector	Initial value of buffer A.

Remarks

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

Evidence message for VMP.

Declaration

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

Parameters

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

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.

GradientAndValueAtPoint(Double[], Double[], Vector, Vector, Vector, Vector)

Function to evaluate this factor's KL divergence contribution, and gradient (if grad is not null).

Declaration

public static double GradientAndValueAtPoint(double[] mu, double[] s2, Vector a, Vector x, Vector ns, Vector grad)

Parameters

Type	Name	Description
Double[]	mu	Prior means
Double[]	s2	Prior variances
Vector	a	Variational parameter vector a
Vector	x	x[1..K]: posterior mean, x[K+1..2K]: posterior log variance
Vector	ns	Dirichlet counts-1
Vector	grad	Vector to store the gradient in

Returns

Type	Description
Double	KL divergence

SoftmaxAverageLogarithm<GaussianList>(GaussianList, Vector, Dirichlet)

VMP message to softmax.

Declaration

public static Dirichlet SoftmaxAverageLogarithm<GaussianList>([SkipIfAllUniform] GaussianList x, Vector 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.
Vector	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.

SoftmaxAverageLogarithmInit(IList<Gaussian>)

Declaration

public static Dirichlet SoftmaxAverageLogarithmInit(IList<Gaussian> x)

Parameters

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

Returns

Type	Description
Dirichlet

Remarks

XAverageLogarithm<GaussianList>(Dirichlet, IList<Gaussian>, Vector, GaussianList)

VMP message to x.

Declaration

public static GaussianList XAverageLogarithm<GaussianList>(Dirichlet softmax, [SkipIfAllUniform] IList<Gaussian> x, Vector 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.
IList<Gaussian>	x	Incoming message from x. Must be a proper distribution. If all elements are uniform, the result will be uniform.
Vector	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 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.