Class DirichletOp

Provides outgoing messages for DirichletFromMeanAndTotalCount(Vector, Double), given random arguments to the function.

Inheritance

Object

DirichletOp

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), "DirichletFromMeanAndTotalCount", new Type[]{})]
[Quality(QualityBand.Preview)]
public static class DirichletOp

Fields

damping

How much damping to use to prevent improper messages. Higher values result in more damping.

Declaration

public static double damping

Field Value

Type	Description
Double

Methods

AverageLogFactor(Dirichlet, Dirichlet, Gamma)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Dirichlet prob, Dirichlet mean, Gamma totalCount)

Parameters

Type	Name	Description
Dirichlet	prob	Incoming message from `prob`.
Dirichlet	mean	Incoming message from `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.

Returns

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

Remarks

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

Exceptions

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

AverageLogFactor(Dirichlet, Vector, Gamma)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Dirichlet prob, Vector mean, Gamma totalCount)

Parameters

Type	Name	Description
Dirichlet	prob	Incoming message from `prob`.
Vector	mean	Constant value for `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.

Returns

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

Remarks

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

Exceptions

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

AverageLogFactor(Vector, Dirichlet, Gamma)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Vector prob, Dirichlet mean, Gamma totalCount)

Parameters

Type	Name	Description
Vector	prob	Constant value for `prob`.
Dirichlet	mean	Incoming message from `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.

Returns

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

Remarks

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

Exceptions

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

AverageLogFactor(Vector, Vector, Gamma)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Vector prob, Vector mean, Gamma totalCount)

Parameters

Type	Name	Description
Vector	prob	Constant value for `prob`.
Vector	mean	Constant value for `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.

Returns

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

Remarks

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

Exceptions

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

AverageLogFactor(Vector, Vector, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Vector prob, Vector mean, double totalCount)

Parameters

Type	Name	Description
Vector	prob	Constant value for `prob`.
Vector	mean	Constant value for `mean`.
Double	totalCount	Constant value for `totalCount`.

Returns

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

Remarks

The formula for the result is log(factor(prob,mean,totalCount)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

EvidenceMessageExpectations(Dirichlet, Gamma)

Perform the quadrature required for the VMP evidence message

Declaration

public static Vector EvidenceMessageExpectations(Dirichlet meanQ, Gamma totalCountQ)

Parameters

Type	Name	Description
Dirichlet	meanQ	Incoming message from m='mean'.
Gamma	totalCountQ	Incoming message from s='totalCount'.

Returns

Type	Description
Vector	Vector of E[ LogGamma(s*m_k)].

Remarks

The quadrature over 'totalCount' (which is Gamma-distributed) is peformed by a change of variable x=log(s) followed by Gauss-Hermite quadrature. The quadrature over m is performed using Gauss-Legendre.

LogAverageFactor(Dirichlet, Dirichlet, Gamma)

Evidence message for EP.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static double LogAverageFactor(Dirichlet prob, Dirichlet mean, Gamma totalCount)

Parameters

Type	Name	Description
Dirichlet	prob	Incoming message from `prob`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.

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_(prob,mean,totalCount) p(prob,mean,totalCount) factor(prob,mean,totalCount)).

Exceptions

Type	Condition
ImproperMessageException	`prob` is not a proper distribution.
ImproperMessageException	`mean` is not a proper distribution.
ImproperMessageException	`totalCount` is not a proper distribution.

LogAverageFactor(Dirichlet, Dirichlet, Double)

Evidence message for EP.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static double LogAverageFactor(Dirichlet prob, Dirichlet mean, double totalCount)

Parameters

Type	Name	Description
Dirichlet	prob	Incoming message from `prob`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Double	totalCount	Constant value for `totalCount`.

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_(prob,mean) p(prob,mean) factor(prob,mean,totalCount)).

Exceptions

Type	Condition
ImproperMessageException	`prob` is not a proper distribution.
ImproperMessageException	`mean` is not a proper distribution.

LogAverageFactor(Dirichlet, Vector, Dirichlet, Double)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Dirichlet prob, Vector mean, Dirichlet to_prob, double totalCount)

Parameters

Type	Name	Description
Dirichlet	prob	Incoming message from `prob`.
Vector	mean	Constant value for `mean`.
Dirichlet	to_prob	Previous outgoing message to `prob`.
Double	totalCount	Constant value for `totalCount`.

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_(prob) p(prob) factor(prob,mean,totalCount)).

LogAverageFactor(Dirichlet, Vector, Gamma)

Evidence message for EP.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static double LogAverageFactor(Dirichlet prob, Vector mean, Gamma totalCount)

Parameters

Type	Name	Description
Dirichlet	prob	Incoming message from `prob`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	mean	Constant value for `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.

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_(prob,totalCount) p(prob,totalCount) factor(prob,mean,totalCount)).

Exceptions

Type	Condition
ImproperMessageException	`prob` is not a proper distribution.
ImproperMessageException	`totalCount` is not a proper distribution.

LogAverageFactor(Vector, Dirichlet, Gamma)

Evidence message for EP.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static double LogAverageFactor(Vector prob, Dirichlet mean, Gamma totalCount)

Parameters

Type	Name	Description
Vector	prob	Constant value for `prob`.
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.

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_(mean,totalCount) p(mean,totalCount) factor(prob,mean,totalCount)).

Exceptions

Type	Condition
ImproperMessageException	`mean` is not a proper distribution.
ImproperMessageException	`totalCount` is not a proper distribution.

LogAverageFactor(Vector, Dirichlet, Double)

Evidence message for EP.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static double LogAverageFactor(Vector prob, Dirichlet mean, double totalCount)

Parameters

Type	Name	Description
Vector	prob	Constant value for `prob`.
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Double	totalCount	Constant value for `totalCount`.

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_(mean) p(mean) factor(prob,mean,totalCount)).

Exceptions

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

LogAverageFactor(Vector, Vector, Gamma)

Evidence message for EP.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static double LogAverageFactor(Vector prob, Vector mean, Gamma totalCount)

Parameters

Type	Name	Description
Vector	prob	Constant value for `prob`.
Vector	mean	Constant value for `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.

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_(totalCount) p(totalCount) factor(prob,mean,totalCount)).

Exceptions

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

LogAverageFactor(Vector, Vector, Double)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Vector prob, Vector mean, double totalCount)

Parameters

Type	Name	Description
Vector	prob	Constant value for `prob`.
Vector	mean	Constant value for `mean`.
Double	totalCount	Constant value for `totalCount`.

Returns

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

Remarks

The formula for the result is log(factor(prob,mean,totalCount)).

LogEvidenceRatio(Vector, Vector, Double)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(Vector prob, Vector mean, double totalCount)

Parameters

Type	Name	Description
Vector	prob	Constant value for `prob`.
Vector	mean	Constant value for `mean`.
Double	totalCount	Constant value for `totalCount`.

Returns

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

Remarks

The formula for the result is log(factor(prob,mean,totalCount)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

MeanAverageConditional(Dirichlet, Gamma, Dirichlet, Dirichlet)

EP message to mean.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Dirichlet MeanAverageConditional(Dirichlet mean, Gamma totalCount, Dirichlet prob, Dirichlet result)

Parameters

Type	Name	Description
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.
Dirichlet	prob	Incoming message from `prob`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Dirichlet	result	Modified to contain the outgoing message.

Returns

Type	Description
Dirichlet	`result`

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`mean` is not a proper distribution.
ImproperMessageException	`totalCount` is not a proper distribution.
ImproperMessageException	`prob` is not a proper distribution.

MeanAverageConditional(Dirichlet, Gamma, Vector, Dirichlet)

EP message to mean.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Dirichlet MeanAverageConditional(Dirichlet mean, Gamma totalCount, Vector prob, Dirichlet result)

Parameters

Type	Name	Description
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.
Vector	prob	Constant value for `prob`.
Dirichlet	result	Modified to contain the outgoing message.

Returns

Type	Description
Dirichlet	`result`

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`mean` is not a proper distribution.
ImproperMessageException	`totalCount` is not a proper distribution.

MeanAverageConditional(Dirichlet, Double, Dirichlet, Dirichlet)

EP message to mean.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Dirichlet MeanAverageConditional(Dirichlet mean, double totalCount, Dirichlet prob, Dirichlet result)

Parameters

Type	Name	Description
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Double	totalCount	Constant value for `totalCount`.
Dirichlet	prob	Incoming message from `prob`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Dirichlet	result	Modified to contain the outgoing message.

Returns

Type	Description
Dirichlet	`result`

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`mean` is not a proper distribution.
ImproperMessageException	`prob` is not a proper distribution.

MeanAverageConditional(Dirichlet, Double, Vector, Dirichlet)

EP message to mean.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Dirichlet MeanAverageConditional(Dirichlet mean, double totalCount, Vector prob, Dirichlet result)

Parameters

Type	Name	Description
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Double	totalCount	Constant value for `totalCount`.
Vector	prob	Constant value for `prob`.
Dirichlet	result	Modified to contain the outgoing message.

Returns

Type	Description
Dirichlet	`result`

Remarks

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

Exceptions

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

MeanAverageLogarithm(Dirichlet, Gamma, Dirichlet, Dirichlet)

VMP message to mean.

Declaration

public static Dirichlet MeanAverageLogarithm(Dirichlet mean, Gamma totalCount, Dirichlet prob, Dirichlet to_mean)

Parameters

Type	Name	Description
Dirichlet	mean	Incoming message from `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.
Dirichlet	prob	Incoming message from `prob`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Dirichlet	to_mean	Previous outgoing message to `mean`.

Returns

Type	Description
Dirichlet	The outgoing VMP message to the `mean` argument.

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`totalCount` is not a proper distribution.
ImproperMessageException	`prob` is not a proper distribution.

MeanMessageExpectations(Vector, Gamma, out Double[], out Double[], out Double[])

Perform the quadrature required for the Nonconjugate VMP message to 'mean'

Declaration

public static void MeanMessageExpectations(Vector meanQPseudoCount, Gamma totalCountQ, out double[] EELogGamma, out double[] EELogMLogGamma, out double[] EELogOneMinusMLogGamma)

Parameters

Type	Name	Description
Vector	meanQPseudoCount	Incoming message from 'mean'.
Gamma	totalCountQ	Incoming message from 'totalCount'.
Double[]	EELogGamma	Array to be filled with E[LogGamma(s*m_k)].
Double[]	EELogMLogGamma	Array to be filled with E[Log(m_k)LogGamma(sm_k)].
Double[]	EELogOneMinusMLogGamma	Array to be filled with E[Log(1-m_k)LogGamma(sm_k)].

Remarks

All three arrays are calculated simultaneously for efficiency. The quadrature over 'totalCount' (which is Gamma-distributed) is performed by a change of variable x=log(s) followed by Gauss-Hermite quadrature. The quadrature over m is performed using Gauss-Legendre.

ProbAverageConditional(Dirichlet, Gamma)

EP message to prob.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Dirichlet ProbAverageConditional(Dirichlet mean, Gamma totalCount)

Parameters

Type	Name	Description
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Dirichlet	The outgoing EP message to the `prob` argument.

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`mean` is not a proper distribution.
ImproperMessageException	`totalCount` is not a proper distribution.

ProbAverageConditional(Dirichlet, Double)

EP message to prob.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Dirichlet ProbAverageConditional(Dirichlet mean, double totalCount)

Parameters

Type	Name	Description
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Double	totalCount	Constant value for `totalCount`.

Returns

Type	Description
Dirichlet	The outgoing EP message to the `prob` argument.

Remarks

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

Exceptions

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

ProbAverageConditional(Vector, Gamma)

EP message to prob.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Dirichlet ProbAverageConditional(Vector mean, Gamma totalCount)

Parameters

Type	Name	Description
Vector	mean	Constant value for `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.

Returns

Type	Description
Dirichlet	The outgoing EP message to the `prob` argument.

Remarks

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

Exceptions

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

ProbAverageConditional(Vector, Double)

EP message to prob.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Dirichlet ProbAverageConditional(Vector mean, double totalCount)

Parameters

Type	Name	Description
Vector	mean	Constant value for `mean`.
Double	totalCount	Constant value for `totalCount`.

Returns

Type	Description
Dirichlet	The outgoing EP message to the `prob` argument.

Remarks

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

ProbAverageConditional(Vector, Double, Dirichlet)

Declaration

public static Dirichlet ProbAverageConditional(Vector mean, double totalCount, Dirichlet result)

Parameters

Type	Name	Description
Vector	mean
Double	totalCount
Dirichlet	result

Returns

Type	Description
Dirichlet

ProbAverageLogarithm(Dirichlet, Gamma, Dirichlet)

Declaration

public static Dirichlet ProbAverageLogarithm(Dirichlet mean, Gamma totalCount, Dirichlet result)

Parameters

Type	Name	Description
Dirichlet	mean
Gamma	totalCount
Dirichlet	result

Returns

Type	Description
Dirichlet

ProbAverageLogarithm(Dirichlet, Double, Dirichlet)

Declaration

public static Dirichlet ProbAverageLogarithm(Dirichlet mean, double totalCount, Dirichlet result)

Parameters

Type	Name	Description
Dirichlet	mean
Double	totalCount
Dirichlet	result

Returns

Type	Description
Dirichlet

ProbAverageLogarithm(Vector, Gamma, Dirichlet)

Declaration

public static Dirichlet ProbAverageLogarithm(Vector mean, Gamma totalCount, Dirichlet result)

Parameters

Type	Name	Description
Vector	mean
Gamma	totalCount
Dirichlet	result

Returns

Type	Description
Dirichlet

ProbAverageLogarithm(Vector, Double, Dirichlet)

Declaration

public static Dirichlet ProbAverageLogarithm(Vector mean, double totalCount, Dirichlet result)

Parameters

Type	Name	Description
Vector	mean
Double	totalCount
Dirichlet	result

Returns

Type	Description
Dirichlet

TotalCountAverageConditional(Dirichlet, Gamma, Dirichlet, Gamma)

EP message to totalCount.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Gamma TotalCountAverageConditional(Dirichlet mean, Gamma totalCount, Dirichlet prob, Gamma result)

Parameters

Type	Name	Description
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.
Dirichlet	prob	Incoming message from `prob`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	result	Modified to contain the outgoing message.

Returns

Type	Description
Gamma	`result`

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`mean` is not a proper distribution.
ImproperMessageException	`totalCount` is not a proper distribution.
ImproperMessageException	`prob` is not a proper distribution.

TotalCountAverageConditional(Dirichlet, Gamma, Vector, Gamma)

EP message to totalCount.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Gamma TotalCountAverageConditional(Dirichlet mean, Gamma totalCount, Vector prob, Gamma result)

Parameters

Type	Name	Description
Dirichlet	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.
Vector	prob	Constant value for `prob`.
Gamma	result	Modified to contain the outgoing message.

Returns

Type	Description
Gamma	`result`

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`mean` is not a proper distribution.
ImproperMessageException	`totalCount` is not a proper distribution.

TotalCountAverageConditional(Vector, Gamma, Dirichlet, Gamma)

EP message to totalCount.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Gamma TotalCountAverageConditional(Vector mean, Gamma totalCount, Dirichlet prob, Gamma result)

Parameters

Type	Name	Description
Vector	mean	Constant value for `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.
Dirichlet	prob	Incoming message from `prob`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	result	Modified to contain the outgoing message.

Returns

Type	Description
Gamma	`result`

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`totalCount` is not a proper distribution.
ImproperMessageException	`prob` is not a proper distribution.

TotalCountAverageConditional(Vector, Gamma, Vector, Gamma)

EP message to totalCount.

Declaration

[NotSupported("Expectation Propagation does not currently support Dirichlet distributions with stochastic arguments")]
public static Gamma TotalCountAverageConditional(Vector mean, Gamma totalCount, Vector prob, Gamma result)

Parameters

Type	Name	Description
Vector	mean	Constant value for `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.
Vector	prob	Constant value for `prob`.
Gamma	result	Modified to contain the outgoing message.

Returns

Type	Description
Gamma	`result`

Remarks

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

Exceptions

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

TotalCountAverageLogarithm(Dirichlet, Gamma, Dirichlet, Gamma)

VMP message to totalCount.

Declaration

public static Gamma TotalCountAverageLogarithm(Dirichlet mean, Gamma totalCount, Dirichlet prob, Gamma to_totalCount)

Parameters

Type	Name	Description
Dirichlet	mean	Incoming message from `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.
Dirichlet	prob	Incoming message from `prob`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	to_totalCount	Previous outgoing message to `totalCount`.

Returns

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

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`totalCount` is not a proper distribution.
ImproperMessageException	`prob` is not a proper distribution.

TotalCountAverageLogarithm(Vector, Gamma, Dirichlet, Gamma)

VMP message to totalCount.

Declaration

public static Gamma TotalCountAverageLogarithm(Vector mean, Gamma totalCount, Dirichlet prob, Gamma to_totalCount)

Parameters

Type	Name	Description
Vector	mean	Constant value for `mean`.
Gamma	totalCount	Incoming message from `totalCount`. Must be a proper distribution. If uniform, the result will be uniform.
Dirichlet	prob	Incoming message from `prob`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Gamma	to_totalCount	Previous outgoing message to `totalCount`.

Returns

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

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`totalCount` is not a proper distribution.
ImproperMessageException	`prob` is not a proper distribution.

TotalCountMessageExpectations(Vector, Gamma, out Double[], out Double[], out Double[])

Perform the quadrature required for the Nonconjugate VMP message to 'totalCount'

Declaration

public static void TotalCountMessageExpectations(Vector meanQPseudoCount, Gamma totalCountQ, out double[] EELogGamma, out double[] EELogSLogGamma, out double[] EEMSDigamma)

Parameters

Type	Name	Description
Vector	meanQPseudoCount	Incoming message from 'mean'.
Gamma	totalCountQ	Incoming message from 'totalCount'.
Double[]	EELogGamma	Array to be filled with E[LogGamma(s*m_k)].
Double[]	EELogSLogGamma	Array to be filled with E[Log(s)LogGamma(sm_k)].
Double[]	EEMSDigamma	Array to be filled with E[sm_kDigamma(s*m_k)].

Remarks

All three arrays are calculated simultaneously for efficiency. The quadrature over 'totalCount' (which is Gamma-distributed) is peformed by a change of variable x=log(s) followed by Gauss-Hermite quadrature. The quadrature over m is performed using Gauss-Legendre.