Class MultinomialOp

Provides outgoing messages for the following factors:

• Multinomial(Int32, Vector)
• MultinomialList(Int32, Vector)

, given random arguments to the function.

Inheritance

Object

MultinomialOp

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(new string[]{"sample", "trialCount", "p"}, typeof(Rand), "Multinomial", new Type[]{typeof(int), typeof(Vector)})]
[FactorMethod(typeof(Factor), "MultinomialList", new Type[]{typeof(int), typeof(Vector)})]
[Buffers(new string[]{"MeanLog"})]
[Quality(QualityBand.Preview)]
public static class MultinomialOp

Remarks

The factor is f(sample,p,n) = n!/prod_k sample[k]! prod_k p[k]^sample[k]

Methods

AverageLogFactor(IList<Int32>, Int32, Dirichlet, Vector)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(IList<int> sample, int trialCount, Dirichlet p, Vector MeanLog)

Parameters

Type	Name	Description
IList<Int32>	sample	Incoming message from multinomial.
Int32	trialCount	Constant value for trialCount.
Dirichlet	p	Incoming message from probs.
Vector	MeanLog	Buffer MeanLog.

Returns

Type	Description
Double	Average of the factor's log-value across the given argument distributions.

Remarks

The formula for the result is sum_(multinomial,probs) p(multinomial,probs) log(factor(multinomial,trialCount,probs)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

AverageLogFactor(IList<Int32>, Int32, IList<Double>)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(IList<int> sample, int trialCount, IList<double> p)

Parameters

Type	Name	Description
IList<Int32>	sample	Incoming message from multinomial.
Int32	trialCount	Constant value for trialCount.
IList<Double>	p	Incoming message from probs.

Returns

Type	Description
Double	Average of the factor's log-value across the given argument distributions.

Remarks

The formula for the result is sum_(multinomial,probs) p(multinomial,probs) log(factor(multinomial,trialCount,probs)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

LogAverageFactor(IList<Int32>, Int32, Dirichlet)

Evidence message for EP.

Declaration

public static double LogAverageFactor(IList<int> sample, int trialCount, Dirichlet p)

Parameters

Type	Name	Description
IList<Int32>	sample	Incoming message from multinomial.
Int32	trialCount	Constant value for trialCount.
Dirichlet	p	Incoming message from probs.

Returns

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

Remarks

The formula for the result is log(sum_(multinomial,probs) p(multinomial,probs) factor(multinomial,trialCount,probs)).

LogAverageFactor(IList<Int32>, Int32, IList<Double>)

Evidence message for EP.

Declaration

public static double LogAverageFactor(IList<int> sample, int trialCount, IList<double> p)

Parameters

Type	Name	Description
IList<Int32>	sample	Incoming message from multinomial.
Int32	trialCount	Constant value for trialCount.
IList<Double>	p	Incoming message from probs.

Returns

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

Remarks

The formula for the result is log(sum_(multinomial,probs) p(multinomial,probs) factor(multinomial,trialCount,probs)).

LogEvidenceRatio(IList<Discrete>)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(IList<Discrete> sample)

Parameters

Type	Name	Description
IList<Discrete>	sample	Incoming message from multinomial.

Returns

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

Remarks

The formula for the result is log(sum_(multinomial) p(multinomial) factor(multinomial,trialCount,probs) / sum_multinomial p(multinomial) messageTo(multinomial)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

LogEvidenceRatio(IList<Int32>, Int32, Dirichlet)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(IList<int> sample, int trialCount, Dirichlet p)

Parameters

Type	Name	Description
IList<Int32>	sample	Incoming message from multinomial.
Int32	trialCount	Constant value for trialCount.
Dirichlet	p	Incoming message from probs.

Returns

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

Remarks

The formula for the result is log(sum_(multinomial,probs) p(multinomial,probs) factor(multinomial,trialCount,probs) / sum_multinomial p(multinomial) messageTo(multinomial)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

LogEvidenceRatio(IList<Int32>, Int32, IList<Double>)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(IList<int> sample, int trialCount, IList<double> p)

Parameters

Type	Name	Description
IList<Int32>	sample	Incoming message from multinomial.
Int32	trialCount	Constant value for trialCount.
IList<Double>	p	Incoming message from probs.

Returns

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

Remarks

The formula for the result is log(sum_(multinomial,probs) p(multinomial,probs) factor(multinomial,trialCount,probs) / sum_multinomial p(multinomial) messageTo(multinomial)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

MeanLog(Dirichlet)

Update the buffer MeanLog.

Declaration

public static Vector MeanLog(Dirichlet p)

Parameters

Type	Name	Description
Dirichlet	p	Incoming message from probs.

Returns

Type	Description
Vector	New value of buffer MeanLog.

Remarks

PAverageConditional(IList<Int32>, Int32)

EP message to probs.

Declaration

public static Dirichlet PAverageConditional(IList<int> sample, int trialCount)

Parameters

Type	Name	Description
IList<Int32>	sample	Incoming message from multinomial.
Int32	trialCount	Constant value for trialCount.

Returns

Type	Description
Dirichlet	The outgoing EP message to the probs argument.

Remarks

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

PAverageLogarithm(IList<Int32>, Int32)

VMP message to probs.

Declaration

public static Dirichlet PAverageLogarithm(IList<int> sample, int trialCount)

Parameters

Type	Name	Description
IList<Int32>	sample	Incoming message from multinomial.
Int32	trialCount	Constant value for trialCount.

Returns

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

Remarks

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