Class GaussianOp_Laplace

Provides outgoing messages for the following factors:

• Sample(Double, Double)
• Gaussian(Double, Double)

, given random arguments to the function.

Inheritance

Object

GaussianOpBase

GaussianOp_Laplace

Inherited Members

GaussianOpBase.SampleAverageConditional(Double, Double)

GaussianOpBase.MeanAverageConditional(Double, Double)

GaussianOpBase.PrecisionAverageConditional(Double, Double)

GaussianOpBase.SampleAverageConditional(Gaussian, Double)

GaussianOpBase.MeanAverageConditional(Gaussian, Double)

GaussianOpBase.LogAverageFactor(Double, Double, Double)

GaussianOpBase.LogAverageFactor(Gaussian, Gaussian, Double)

GaussianOpBase.LogAverageFactor(Gaussian, Double, Double)

GaussianOpBase.LogAverageFactor(Double, Gaussian, Double)

GaussianOpBase.LogAverageFactor(Double, Double, Gamma)

GaussianOpBase.TPdfLn(Double, Double, Double)

GaussianOpBase.LogEvidenceRatio(Double, Double, Double)

GaussianOpBase.LogEvidenceRatio(Gaussian, Gaussian, Double)

GaussianOpBase.LogEvidenceRatio(Gaussian, Double, Double)

GaussianOpBase.LogEvidenceRatio(Double, Gaussian, Double)

GaussianOpBase.LogEvidenceRatio(Double, Double, Gamma)

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(Gaussian), "Sample", new Type[]{typeof(double), typeof(double)}, Default = false)]
[FactorMethod(new string[]{"sample", "mean", "precision"}, typeof(Factor), "Gaussian", new Type[]{}, Default = false)]
[Buffers(new string[]{"Q"})]
[Quality(QualityBand.Experimental)]
public class GaussianOp_Laplace : GaussianOpBase

Fields

modified

Declaration

public static bool modified

Field Value

Type	Description
Boolean

modified2

Declaration

public static bool modified2

Field Value

Type	Description
Boolean

Methods

dlogfs(Double, Double, Double)

Derivatives of the factor wrt precision

Declaration

public static double[] dlogfs(double x, double m, double v)

Parameters

Type	Name	Description
Double	x
Double	m
Double	v

Returns

Type	Description
Double[]

dlogfxs(Double, Gamma)

Declaration

public static double[] dlogfxs(double x, Gamma precision)

Parameters

Type	Name	Description
Double	x
Gamma	precision

Returns

Type	Description
Double[]

LaplaceMoments(Gamma, Double[], Double[], out Double, out Double)

Approximate the mean and variance of a function g(x) where x is distributed according to a Gamma times f(x).

Declaration

public static void LaplaceMoments(Gamma q, double[] g, double[] dlogf, out double m, out double v)

Parameters

Type	Name	Description
Gamma	q	The Gamma distribution that multiplies f
Double[]	g	g[0] = g(xhat), g[1] = g'(xhat), g[2] = g''(xhat), and so on.
Double[]	dlogf	dlogf[0] = (logf)'(xhat), dlogf[1] = (logf)''(xhat), and so on.
Double	m
Double	v

LaplaceMoments(Gaussian, Double[], out Double, out Double)

Declaration

public static void LaplaceMoments(Gaussian q, double[] dlogfx, out double m, out double v)

Parameters

Type	Name	Description
Gaussian	q
Double[]	dlogfx
Double	m
Double	v

LaplaceMoments2(Gamma, Double[], Double[], out Double, out Double)

Declaration

public static void LaplaceMoments2(Gamma q, double[] xg, double[] xdlogf, out double m, out double v)

Parameters

Type	Name	Description
Gamma	q
Double[]	xg
Double[]	xdlogf
Double	m
Double	v

LogAverageFactor(Gaussian, Gaussian, Gamma, Gamma)

Evidence message for EP.

Declaration

public static double LogAverageFactor(Gaussian sample, Gaussian mean, Gamma precision, Gamma q)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	precision	Incoming message from precision.
Gamma	q	Buffer q.

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

Exceptions

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

LogEvidenceRatio(Gaussian, Gaussian, Gamma, Gaussian, Gamma)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(Gaussian sample, Gaussian mean, Gamma precision, Gaussian to_sample, Gamma q)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	precision	Incoming message from precision. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	to_sample	Outgoing message to sample.
Gamma	q	Buffer q.

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,precision) p(sample,mean,precision) 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.
ImproperMessageException	precision is not a proper distribution.

LogEvidenceRatio(Double, Gaussian, Gamma, Gamma)

Evidence message for EP.

Declaration

public static double LogEvidenceRatio(double sample, Gaussian mean, Gamma precision, Gamma q)

Parameters

Type	Name	Description
Double	sample	Constant value for sample.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	precision	Incoming message from precision. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	q	Buffer q.

Returns

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

Remarks

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

Exceptions

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

MeanAverageConditional(Gaussian, Gaussian, Gamma, Gamma)

EP message to mean.

Declaration

public static Gaussian MeanAverageConditional(Gaussian sample, Gaussian mean, Gamma precision, Gamma q)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	mean	Incoming message from mean.
Gamma	precision	Incoming message from precision. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	q	Buffer q.

Returns

Type	Description
Gaussian	The outgoing EP message to the mean argument.

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,precision) p(sample,precision) factor(sample,mean,precision)]/p(mean).

Exceptions

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

PrecisionAverageConditional(Gaussian, Gaussian, Gamma, Gamma)

EP message to precision.

Declaration

public static Gamma PrecisionAverageConditional(Gaussian sample, Gaussian mean, Gamma precision, Gamma q)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample. Must be a proper distribution. If uniform, the result will be uniform.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	precision	Incoming message from precision. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	q	Buffer q.

Returns

Type	Description
Gamma	The outgoing EP message to the precision argument.

Remarks

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

Exceptions

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

PrecisionAverageConditional_slow(Gaussian, Gaussian, Gamma)

Declaration

public static Gamma PrecisionAverageConditional_slow(Gaussian sample, Gaussian mean, Gamma precision)

Parameters

Type	Name	Description
Gaussian	sample
Gaussian	mean
Gamma	precision

Returns

Type	Description
Gamma

Q(Gaussian, Gaussian, Gamma, Gamma)

Update the buffer Q.

Declaration

public static Gamma Q(Gaussian sample, Gaussian mean, Gamma precision, Gamma q)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample.
Gaussian	mean	Incoming message from mean.
Gamma	precision	Incoming message from precision.
Gamma	q	Buffer q.

Returns

Type	Description
Gamma	New value of buffer Q.

Remarks

Q_Slow(Gaussian, Gaussian, Gamma)

Declaration

public static Gamma Q_Slow(Gaussian sample, Gaussian mean, Gamma precision)

Parameters

Type	Name	Description
Gaussian	sample
Gaussian	mean
Gamma	precision

Returns

Type	Description
Gamma

QInit()

Initialize the buffer Q.

Declaration

public static Gamma QInit()

Returns

Type	Description
Gamma	Initial value of buffer Q.

Remarks

Qx(Gaussian, Gamma, Gaussian)

Declaration

public static Gaussian Qx(Gaussian y, Gamma precision, Gaussian qx)

Parameters

Type	Name	Description
Gaussian	y
Gamma	precision
Gaussian	qx

Returns

Type	Description
Gaussian

SampleAverageConditional(Gaussian, Gaussian, Gamma, Gamma)

EP message to sample.

Declaration

public static Gaussian SampleAverageConditional(Gaussian sample, Gaussian mean, Gamma precision, Gamma q)

Parameters

Type	Name	Description
Gaussian	sample	Incoming message from sample.
Gaussian	mean	Incoming message from mean. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	precision	Incoming message from precision. Must be a proper distribution. If uniform, the result will be uniform.
Gamma	q	Buffer q.

Returns

Type	Description
Gaussian	The outgoing EP message to the sample argument.

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,precision) p(mean,precision) factor(sample,mean,precision)]/p(sample).

Exceptions

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

xdlogfs(Double, Double, Double)

Derivatives of the factor wrt precision, times powers of x

Declaration

public static double[] xdlogfs(double x, double m, double v)

Parameters

Type	Name	Description
Double	x
Double	m
Double	v

Returns

Type	Description
Double[]