Class VectorGaussianOp

Provides outgoing messages for the following factors:

, given random arguments to the function.

Inheritance

Object

VectorGaussianOp

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(VectorGaussian), "Sample", new Type[]{typeof(Vector), typeof(PositiveDefiniteMatrix)})]
[FactorMethod(new string[]{"sample", "mean", "precision"}, typeof(Factor), "VectorGaussian", new Type[]{})]
[Buffers(new string[]{"SampleMean", "SampleVariance", "MeanMean", "MeanVariance", "PrecisionMean", "PrecisionMeanLogDet"})]
[Quality(QualityBand.Stable)]
public static class VectorGaussianOp

Methods

AverageLogFactor(VectorGaussian, Vector, PositiveDefiniteMatrix, VectorGaussian, Vector, PositiveDefiniteMatrix, Wishart, PositiveDefiniteMatrix, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(VectorGaussian sample, Vector SampleMean, PositiveDefiniteMatrix SampleVariance, VectorGaussian mean, Vector MeanMean, PositiveDefiniteMatrix MeanVariance, Wishart precision, PositiveDefiniteMatrix precisionMean, double precisionMeanLogDet)

Parameters

Type	Name	Description
VectorGaussian	sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	SampleMean	Buffer `SampleMean`.
PositiveDefiniteMatrix	SampleVariance	Buffer `SampleVariance`.
VectorGaussian	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	MeanMean	Buffer `MeanMean`.
PositiveDefiniteMatrix	MeanVariance	Buffer `MeanVariance`.
Wishart	precision	Incoming message from `precision`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	precisionMean	Buffer `precisionMean`.
Double	precisionMeanLogDet	Buffer `precisionMeanLogDet`.

Returns

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

Remarks

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

Exceptions

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

AverageLogFactor(VectorGaussian, Vector, PositiveDefiniteMatrix, VectorGaussian, Vector, PositiveDefiniteMatrix, PositiveDefiniteMatrix)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(VectorGaussian sample, Vector SampleMean, PositiveDefiniteMatrix SampleVariance, VectorGaussian mean, Vector MeanMean, PositiveDefiniteMatrix MeanVariance, PositiveDefiniteMatrix precision)

Parameters

Type	Name	Description
VectorGaussian	sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	SampleMean	Buffer `SampleMean`.
PositiveDefiniteMatrix	SampleVariance	Buffer `SampleVariance`.
VectorGaussian	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	MeanMean	Buffer `MeanMean`.
PositiveDefiniteMatrix	MeanVariance	Buffer `MeanVariance`.
PositiveDefiniteMatrix	precision	Constant value for `precision`.

Returns

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

Remarks

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

Exceptions

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

AverageLogFactor(VectorGaussian, Vector, PositiveDefiniteMatrix, Vector, Wishart, PositiveDefiniteMatrix, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(VectorGaussian sample, Vector SampleMean, PositiveDefiniteMatrix SampleVariance, Vector mean, Wishart precision, PositiveDefiniteMatrix precisionMean, double precisionMeanLogDet)

Parameters

Type	Name	Description
VectorGaussian	sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	SampleMean	Buffer `SampleMean`.
PositiveDefiniteMatrix	SampleVariance	Buffer `SampleVariance`.
Vector	mean	Constant value for `mean`.
Wishart	precision	Incoming message from `precision`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	precisionMean	Buffer `precisionMean`.
Double	precisionMeanLogDet	Buffer `precisionMeanLogDet`.

Returns

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

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`sample` is not a proper distribution.
ImproperMessageException	`precision` is not a proper distribution.

AverageLogFactor(VectorGaussian, Vector, PositiveDefiniteMatrix, Vector, PositiveDefiniteMatrix)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(VectorGaussian sample, Vector SampleMean, PositiveDefiniteMatrix SampleVariance, Vector mean, PositiveDefiniteMatrix precision)

Parameters

Type	Name	Description
VectorGaussian	sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	SampleMean	Buffer `SampleMean`.
PositiveDefiniteMatrix	SampleVariance	Buffer `SampleVariance`.
Vector	mean	Constant value for `mean`.
PositiveDefiniteMatrix	precision	Constant value for `precision`.

Returns

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

Remarks

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

Exceptions

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

AverageLogFactor(Vector, VectorGaussian, Vector, PositiveDefiniteMatrix, Wishart, PositiveDefiniteMatrix, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Vector sample, VectorGaussian mean, Vector MeanMean, PositiveDefiniteMatrix MeanVariance, Wishart precision, PositiveDefiniteMatrix precisionMean, double precisionMeanLogDet)

Parameters

Type	Name	Description
Vector	sample	Constant value for `sample`.
VectorGaussian	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	MeanMean	Buffer `MeanMean`.
PositiveDefiniteMatrix	MeanVariance	Buffer `MeanVariance`.
Wishart	precision	Incoming message from `precision`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	precisionMean	Buffer `precisionMean`.
Double	precisionMeanLogDet	Buffer `precisionMeanLogDet`.

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,precision) p(mean,precision) log(factor(sample,mean,precision)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

Exceptions

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

AverageLogFactor(Vector, VectorGaussian, Vector, PositiveDefiniteMatrix, PositiveDefiniteMatrix)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Vector sample, VectorGaussian mean, Vector MeanMean, PositiveDefiniteMatrix MeanVariance, PositiveDefiniteMatrix precision)

Parameters

Type	Name	Description
Vector	sample	Constant value for `sample`.
VectorGaussian	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	MeanMean	Buffer `MeanMean`.
PositiveDefiniteMatrix	MeanVariance	Buffer `MeanVariance`.
PositiveDefiniteMatrix	precision	Constant value for `precision`.

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) p(mean) log(factor(sample,mean,precision)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

Exceptions

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

AverageLogFactor(Vector, Vector, Wishart, PositiveDefiniteMatrix, Double)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Vector sample, Vector mean, Wishart precision, PositiveDefiniteMatrix precisionMean, double precisionMeanLogDet)

Parameters

Type	Name	Description
Vector	sample	Constant value for `sample`.
Vector	mean	Constant value for `mean`.
Wishart	precision	Incoming message from `precision`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	precisionMean	Buffer `precisionMean`.
Double	precisionMeanLogDet	Buffer `precisionMeanLogDet`.

Returns

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

Remarks

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

Exceptions

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

AverageLogFactor(Vector, Vector, PositiveDefiniteMatrix)

Evidence message for VMP.

Declaration

public static double AverageLogFactor(Vector sample, Vector mean, PositiveDefiniteMatrix precision)

Parameters

Type	Name	Description
Vector	sample	Constant value for `sample`.
Vector	mean	Constant value for `mean`.
PositiveDefiniteMatrix	precision	Constant value for `precision`.

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(sample,mean,precision)). Adding up these values across all factors and variables gives the log-evidence estimate for VMP.

LogAverageFactor(Vector, PositiveDefiniteMatrix, Vector, PositiveDefiniteMatrix, PositiveDefiniteMatrix)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Vector SampleMean, PositiveDefiniteMatrix SampleVariance, Vector MeanMean, PositiveDefiniteMatrix MeanVariance, PositiveDefiniteMatrix Precision)

Parameters

Type	Name	Description
Vector	SampleMean	Buffer `SampleMean`.
PositiveDefiniteMatrix	SampleVariance	Buffer `SampleVariance`.
Vector	MeanMean	Buffer `MeanMean`.
PositiveDefiniteMatrix	MeanVariance	Buffer `MeanVariance`.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.

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(sample,mean,precision)).

LogAverageFactor(Vector, Vector, PositiveDefiniteMatrix)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Vector sample, Vector mean, PositiveDefiniteMatrix precision)

Parameters

Type	Name	Description
Vector	sample	Constant value for `sample`.
Vector	mean	Constant value for `mean`.
PositiveDefiniteMatrix	precision	Constant value for `precision`.

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(sample,mean,precision)).

LogAverageFactor(Vector, Vector, PositiveDefiniteMatrix, PositiveDefiniteMatrix)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Vector Sample, Vector MeanMean, PositiveDefiniteMatrix MeanVariance, PositiveDefiniteMatrix Precision)

Parameters

Type	Name	Description
Vector	Sample	Constant value for `sample`.
Vector	MeanMean	Buffer `MeanMean`.
PositiveDefiniteMatrix	MeanVariance	Buffer `MeanVariance`.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.

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(sample,mean,precision)).

LogEvidenceRatio(VectorGaussian, VectorGaussian, PositiveDefiniteMatrix)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(VectorGaussian sample, VectorGaussian mean, PositiveDefiniteMatrix precision)

Parameters

Type	Name	Description
VectorGaussian	sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
VectorGaussian	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	precision	Constant value for `precision`.

Returns

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

Remarks

The formula for the result is log(sum_(sample,mean) p(sample,mean) factor(sample,mean,precision) / sum_sample p(sample) messageTo(sample)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

Exceptions

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

LogEvidenceRatio(VectorGaussian, Vector, PositiveDefiniteMatrix)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(VectorGaussian sample, Vector mean, PositiveDefiniteMatrix precision)

Parameters

Type	Name	Description
VectorGaussian	sample	Incoming message from `sample`.
Vector	mean	Constant value for `mean`.
PositiveDefiniteMatrix	precision	Constant value for `precision`.

Returns

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

Remarks

The formula for the result is log(sum_(sample) p(sample) factor(sample,mean,precision) / sum_sample p(sample) messageTo(sample)). Adding up these values across all factors and variables gives the log-evidence estimate for EP.

LogEvidenceRatio(Vector, VectorGaussian, Vector, PositiveDefiniteMatrix, PositiveDefiniteMatrix)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(Vector sample, VectorGaussian mean, Vector MeanMean, PositiveDefiniteMatrix MeanVariance, PositiveDefiniteMatrix precision)

Parameters

Type	Name	Description
Vector	sample	Constant value for `sample`.
VectorGaussian	mean	Incoming message from `mean`.
Vector	MeanMean	Buffer `MeanMean`.
PositiveDefiniteMatrix	MeanVariance	Buffer `MeanVariance`.
PositiveDefiniteMatrix	precision	Constant value for `precision`.

Returns

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

Remarks

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

LogEvidenceRatio(Vector, Vector, PositiveDefiniteMatrix)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(Vector sample, Vector mean, PositiveDefiniteMatrix precision)

Parameters

Type	Name	Description
Vector	sample	Constant value for `sample`.
Vector	mean	Constant value for `mean`.
PositiveDefiniteMatrix	precision	Constant value for `precision`.

Returns

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

Remarks

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

MeanAverageConditional(VectorGaussian, PositiveDefiniteMatrix, VectorGaussian)

EP message to mean.

Declaration

public static VectorGaussian MeanAverageConditional(VectorGaussian Sample, PositiveDefiniteMatrix Precision, VectorGaussian result)

Parameters

Type	Name	Description
VectorGaussian	Sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`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_(sample) p(sample) factor(sample,mean,precision)]/p(mean).

Exceptions

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

MeanAverageConditional(Vector, PositiveDefiniteMatrix, VectorGaussian)

EP message to mean.

Declaration

public static VectorGaussian MeanAverageConditional(Vector Sample, PositiveDefiniteMatrix Precision, VectorGaussian result)

Parameters

Type	Name	Description
Vector	Sample	Constant value for `sample`.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

Remarks

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

MeanAverageLogarithm(VectorGaussian, Vector, Wishart, PositiveDefiniteMatrix, VectorGaussian)

VMP message to mean.

Declaration

public static VectorGaussian MeanAverageLogarithm(VectorGaussian Sample, Vector SampleMean, Wishart Precision, PositiveDefiniteMatrix PrecisionMean, VectorGaussian result)

Parameters

Type	Name	Description
VectorGaussian	Sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	SampleMean	Buffer `SampleMean`.
Wishart	Precision	Incoming message from `precision`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	PrecisionMean	Buffer `PrecisionMean`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

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_(sample,precision) p(sample,precision) log(factor(sample,mean,precision))).

Exceptions

Type	Condition
ImproperMessageException	`Sample` is not a proper distribution.
ImproperMessageException	`Precision` is not a proper distribution.

MeanAverageLogarithm(VectorGaussian, Vector, PositiveDefiniteMatrix, VectorGaussian)

VMP message to mean.

Declaration

public static VectorGaussian MeanAverageLogarithm(VectorGaussian Sample, Vector SampleMean, PositiveDefiniteMatrix Precision, VectorGaussian result)

Parameters

Type	Name	Description
VectorGaussian	Sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	SampleMean	Buffer `SampleMean`.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

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_(sample) p(sample) log(factor(sample,mean,precision))).

Exceptions

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

MeanAverageLogarithm(Vector, Wishart, PositiveDefiniteMatrix, VectorGaussian)

VMP message to mean.

Declaration

public static VectorGaussian MeanAverageLogarithm(Vector Sample, Wishart Precision, PositiveDefiniteMatrix PrecisionMean, VectorGaussian result)

Parameters

Type	Name	Description
Vector	Sample	Constant value for `sample`.
Wishart	Precision	Incoming message from `precision`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	PrecisionMean	Buffer `PrecisionMean`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

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_(precision) p(precision) log(factor(sample,mean,precision))).

Exceptions

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

MeanAverageLogarithm(Vector, PositiveDefiniteMatrix, VectorGaussian)

VMP message to mean.

Declaration

public static VectorGaussian MeanAverageLogarithm(Vector Sample, PositiveDefiniteMatrix Precision, VectorGaussian result)

Parameters

Type	Name	Description
Vector	Sample	Constant value for `sample`.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

Remarks

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

MeanConditional(Vector, PositiveDefiniteMatrix, VectorGaussian)

Gibbs message to mean.

Declaration

public static VectorGaussian MeanConditional(Vector Sample, PositiveDefiniteMatrix Precision, VectorGaussian result)

Parameters

Type	Name	Description
Vector	Sample	Constant value for `sample`.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

Remarks

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

MeanMean(VectorGaussian, PositiveDefiniteMatrix, Vector)

Update the buffer MeanMean.

Declaration

public static Vector MeanMean(VectorGaussian Mean, PositiveDefiniteMatrix MeanVariance, Vector result)

Parameters

Type	Name	Description
VectorGaussian	Mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	MeanVariance	Buffer `MeanVariance`.
Vector	result	Modified to contain the outgoing message.

Returns

Type	Description
Vector	`result`

Remarks

Exceptions

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

MeanMeanInit(VectorGaussian)

Initialize the buffer MeanMean.

Declaration

public static Vector MeanMeanInit(VectorGaussian Mean)

Parameters

Type	Name	Description
VectorGaussian	Mean	Incoming message from `mean`.

Returns

Type	Description
Vector	Initial value of buffer `MeanMean`.

Remarks

MeanVariance(VectorGaussian, PositiveDefiniteMatrix)

Update the buffer MeanVariance.

Declaration

public static PositiveDefiniteMatrix MeanVariance(VectorGaussian Mean, PositiveDefiniteMatrix result)

Parameters

Type	Name	Description
VectorGaussian	Mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	result	Modified to contain the outgoing message.

Returns

Type	Description
PositiveDefiniteMatrix	`result`

Remarks

Exceptions

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

MeanVarianceInit(VectorGaussian)

Initialize the buffer MeanVariance.

Declaration

public static PositiveDefiniteMatrix MeanVarianceInit(VectorGaussian Mean)

Parameters

Type	Name	Description
VectorGaussian	Mean	Incoming message from `mean`.

Returns

Type	Description
PositiveDefiniteMatrix	Initial value of buffer `MeanVariance`.

Remarks

PrecisionAverageConditional(Vector, Vector, Wishart)

EP message to precision.

Declaration

public static Wishart PrecisionAverageConditional(Vector Sample, Vector Mean, Wishart result)

Parameters

Type	Name	Description
Vector	Sample	Constant value for `sample`.
Vector	Mean	Constant value for `mean`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

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

PrecisionAverageLogarithm(VectorGaussian, Vector, PositiveDefiniteMatrix, VectorGaussian, Vector, PositiveDefiniteMatrix, Wishart)

VMP message to precision.

Declaration

public static Wishart PrecisionAverageLogarithm(VectorGaussian Sample, Vector SampleMean, PositiveDefiniteMatrix SampleVariance, VectorGaussian Mean, Vector MeanMean, PositiveDefiniteMatrix MeanVariance, Wishart result)

Parameters

Type	Name	Description
VectorGaussian	Sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	SampleMean	Buffer `SampleMean`.
PositiveDefiniteMatrix	SampleVariance	Buffer `SampleVariance`.
VectorGaussian	Mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	MeanMean	Buffer `MeanMean`.
PositiveDefiniteMatrix	MeanVariance	Buffer `MeanVariance`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`Sample` is not a proper distribution.
ImproperMessageException	`Mean` is not a proper distribution.

PrecisionAverageLogarithm(VectorGaussian, Vector, PositiveDefiniteMatrix, Vector, Wishart)

VMP message to precision.

Declaration

public static Wishart PrecisionAverageLogarithm(VectorGaussian Sample, Vector SampleMean, PositiveDefiniteMatrix SampleVariance, Vector Mean, Wishart result)

Parameters

Type	Name	Description
VectorGaussian	Sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	SampleMean	Buffer `SampleMean`.
PositiveDefiniteMatrix	SampleVariance	Buffer `SampleVariance`.
Vector	Mean	Constant value for `mean`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

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

Exceptions

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

PrecisionAverageLogarithm(Vector, VectorGaussian, Vector, PositiveDefiniteMatrix, Wishart)

VMP message to precision.

Declaration

public static Wishart PrecisionAverageLogarithm(Vector Sample, VectorGaussian Mean, Vector MeanMean, PositiveDefiniteMatrix MeanVariance, Wishart result)

Parameters

Type	Name	Description
Vector	Sample	Constant value for `sample`.
VectorGaussian	Mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	MeanMean	Buffer `MeanMean`.
PositiveDefiniteMatrix	MeanVariance	Buffer `MeanVariance`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

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

Exceptions

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

PrecisionAverageLogarithm(Vector, Vector, Wishart)

VMP message to precision.

Declaration

public static Wishart PrecisionAverageLogarithm(Vector Sample, Vector Mean, Wishart result)

Parameters

Type	Name	Description
Vector	Sample	Constant value for `sample`.
Vector	Mean	Constant value for `mean`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

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

PrecisionConditional(Vector, Vector, Wishart)

Gibbs message to precision.

Declaration

public static Wishart PrecisionConditional(Vector Sample, Vector Mean, Wishart result)

Parameters

Type	Name	Description
Vector	Sample	Constant value for `sample`.
Vector	Mean	Constant value for `mean`.
Wishart	result	Modified to contain the outgoing message.

Returns

Type	Description
Wishart	`result`

Remarks

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

PrecisionConditional(Vector, Vector, Wishart, Vector)

Gibbs message to precision.

Declaration

public static Wishart PrecisionConditional(Vector Sample, Vector Mean, Wishart result, Vector diff)

Parameters

Type	Name	Description
Vector	Sample	Constant value for `sample`.
Vector	Mean	Constant value for `mean`.
Wishart	result	Modified to contain the outgoing message.
Vector	diff

Returns

Type	Description
Wishart	`result`

Remarks

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

PrecisionMean(Wishart, PositiveDefiniteMatrix)

Update the buffer PrecisionMean.

Declaration

public static PositiveDefiniteMatrix PrecisionMean(Wishart Precision, PositiveDefiniteMatrix result)

Parameters

Type	Name	Description
Wishart	Precision	Incoming message from `precision`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	result	Modified to contain the outgoing message.

Returns

Type	Description
PositiveDefiniteMatrix	`result`

Remarks

Exceptions

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

PrecisionMeanInit(Wishart)

Initialize the buffer PrecisionMean.

Declaration

public static PositiveDefiniteMatrix PrecisionMeanInit(Wishart Precision)

Parameters

Type	Name	Description
Wishart	Precision	Incoming message from `precision`.

Returns

Type	Description
PositiveDefiniteMatrix	Initial value of buffer `PrecisionMean`.

Remarks

PrecisionMeanLogDet(Wishart)

Update the buffer PrecisionMeanLogDet.

Declaration

public static double PrecisionMeanLogDet(Wishart Precision)

Parameters

Type	Name	Description
Wishart	Precision	Incoming message from `precision`. Must be a proper distribution. If any element is uniform, the result will be uniform.

Returns

Type	Description
Double	New value of buffer `PrecisionMeanLogDet`.

Remarks

Exceptions

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

SampleAverageConditional(VectorGaussian, PositiveDefiniteMatrix, VectorGaussian)

EP message to sample.

Declaration

public static VectorGaussian SampleAverageConditional(VectorGaussian Mean, PositiveDefiniteMatrix Precision, VectorGaussian result)

Parameters

Type	Name	Description
VectorGaussian	Mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

Remarks

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

Exceptions

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

SampleAverageConditional(Vector, PositiveDefiniteMatrix, VectorGaussian)

EP message to sample.

Declaration

public static VectorGaussian SampleAverageConditional(Vector Mean, PositiveDefiniteMatrix Precision, VectorGaussian result)

Parameters

Type	Name	Description
Vector	Mean	Constant value for `mean`.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

Remarks

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

SampleAverageConditionalInit(VectorGaussian)

Declaration

public static VectorGaussian SampleAverageConditionalInit(VectorGaussian Mean)

Parameters

Type	Name	Description
VectorGaussian	Mean	Incoming message from `mean`.

Returns

Type	Description
VectorGaussian

Remarks

SampleAverageConditionalInit(Vector)

Declaration

public static VectorGaussian SampleAverageConditionalInit(Vector Mean)

Parameters

Type	Name	Description
Vector	Mean	Constant value for `mean`.

Returns

Type	Description
VectorGaussian

Remarks

SampleAverageLogarithm(VectorGaussian, Vector, Wishart, PositiveDefiniteMatrix, VectorGaussian)

VMP message to sample.

Declaration

public static VectorGaussian SampleAverageLogarithm(VectorGaussian Mean, Vector MeanMean, Wishart Precision, PositiveDefiniteMatrix PrecisionMean, VectorGaussian result)

Parameters

Type	Name	Description
VectorGaussian	Mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	MeanMean	Buffer `MeanMean`.
Wishart	Precision	Incoming message from `precision`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	PrecisionMean	Buffer `PrecisionMean`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

Remarks

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

Exceptions

Type	Condition
ImproperMessageException	`Mean` is not a proper distribution.
ImproperMessageException	`Precision` is not a proper distribution.

SampleAverageLogarithm(VectorGaussian, Vector, PositiveDefiniteMatrix, VectorGaussian)

VMP message to sample.

Declaration

public static VectorGaussian SampleAverageLogarithm(VectorGaussian mean, Vector MeanMean, PositiveDefiniteMatrix Precision, VectorGaussian result)

Parameters

Type	Name	Description
VectorGaussian	mean	Incoming message from `mean`. Must be a proper distribution. If any element is uniform, the result will be uniform.
Vector	MeanMean	Buffer `MeanMean`.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

Remarks

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

Exceptions

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

SampleAverageLogarithm(Vector, Wishart, PositiveDefiniteMatrix, VectorGaussian)

VMP message to sample.

Declaration

public static VectorGaussian SampleAverageLogarithm(Vector Mean, Wishart Precision, PositiveDefiniteMatrix PrecisionMean, VectorGaussian result)

Parameters

Type	Name	Description
Vector	Mean	Constant value for `mean`.
Wishart	Precision	Incoming message from `precision`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	PrecisionMean	Buffer `PrecisionMean`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

Remarks

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

Exceptions

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

SampleAverageLogarithm(Vector, PositiveDefiniteMatrix, VectorGaussian)

VMP message to sample.

Declaration

public static VectorGaussian SampleAverageLogarithm(Vector Mean, PositiveDefiniteMatrix Precision, VectorGaussian result)

Parameters

Type	Name	Description
Vector	Mean	Constant value for `mean`.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

Remarks

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

SampleAverageLogarithmInit(VectorGaussian)

Declaration

public static VectorGaussian SampleAverageLogarithmInit(VectorGaussian Mean)

Parameters

Type	Name	Description
VectorGaussian	Mean	Incoming message from `mean`.

Returns

Type	Description
VectorGaussian

Remarks

SampleAverageLogarithmInit(Vector)

Declaration

public static VectorGaussian SampleAverageLogarithmInit(Vector Mean)

Parameters

Type	Name	Description
Vector	Mean	Constant value for `mean`.

Returns

Type	Description
VectorGaussian

Remarks

SampleConditional(Vector, PositiveDefiniteMatrix, VectorGaussian)

Gibbs message to sample.

Declaration

public static VectorGaussian SampleConditional(Vector Mean, PositiveDefiniteMatrix Precision, VectorGaussian result)

Parameters

Type	Name	Description
Vector	Mean	Constant value for `mean`.
PositiveDefiniteMatrix	Precision	Constant value for `precision`.
VectorGaussian	result	Modified to contain the outgoing message.

Returns

Type	Description
VectorGaussian	`result`

Remarks

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

SampleMean(VectorGaussian, PositiveDefiniteMatrix, Vector)

Update the buffer SampleMean.

Declaration

public static Vector SampleMean(VectorGaussian Sample, PositiveDefiniteMatrix SampleVariance, Vector result)

Parameters

Type	Name	Description
VectorGaussian	Sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	SampleVariance	Buffer `SampleVariance`.
Vector	result	Modified to contain the outgoing message.

Returns

Type	Description
Vector	`result`

Remarks

Exceptions

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

SampleMeanInit(VectorGaussian)

Initialize the buffer SampleMean.

Declaration

public static Vector SampleMeanInit(VectorGaussian Sample)

Parameters

Type	Name	Description
VectorGaussian	Sample	Incoming message from `sample`.

Returns

Type	Description
Vector	Initial value of buffer `SampleMean`.

Remarks

SampleVariance(VectorGaussian, PositiveDefiniteMatrix)

Update the buffer SampleVariance.

Declaration

public static PositiveDefiniteMatrix SampleVariance(VectorGaussian Sample, PositiveDefiniteMatrix result)

Parameters

Type	Name	Description
VectorGaussian	Sample	Incoming message from `sample`. Must be a proper distribution. If any element is uniform, the result will be uniform.
PositiveDefiniteMatrix	result	Modified to contain the outgoing message.

Returns

Type	Description
PositiveDefiniteMatrix	`result`

Remarks

Exceptions

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

SampleVarianceInit(VectorGaussian)

Initialize the buffer SampleVariance.

Declaration

public static PositiveDefiniteMatrix SampleVarianceInit(VectorGaussian Sample)

Parameters

Type	Name	Description
VectorGaussian	Sample	Incoming message from `sample`.

Returns

Type	Description
PositiveDefiniteMatrix	Initial value of buffer `SampleVariance`.