/// <summary>
/// Evidence message for VMP
/// </summary>
/// <param name="sample">Incoming message from 'sample'. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <param name="SampleMean">Buffer 'SampleMean'.</param>
/// <param name="SampleVariance">Buffer 'SampleVariance'.</param>
/// <param name="mean">Incoming message from 'mean'. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <param name="MeanMean">Buffer 'MeanMean'.</param>
/// <param name="MeanVariance">Buffer 'MeanVariance'.</param>
/// <param name="precision">Constant value for 'precision'.</param>
/// <returns>Average of the factor's log-value across the given argument distributions</returns>
/// <remarks><para>
/// The formula for the result is <c>sum_(sample,mean) p(sample,mean) log(factor(sample,mean,precision))</c>.
/// Adding up these values across all factors and variables gives the log-evidence estimate for VMP.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="sample"/> is not a proper distribution</exception>
/// <exception cref="ImproperMessageException"><paramref name="mean"/> is not a proper distribution</exception>
public static double AverageLogFactor(
[Proper] VectorGaussian sample,
[Fresh] Vector SampleMean,
[Fresh] PositiveDefiniteMatrix SampleVariance,
[Proper] VectorGaussian mean,
[Fresh] Vector MeanMean,
[Fresh] PositiveDefiniteMatrix MeanVariance,
PositiveDefiniteMatrix precision)
{
if (sample.IsPointMass)
return AverageLogFactor(sample.Point, mean, MeanMean, MeanVariance, precision);
if (mean.IsPointMass)
return AverageLogFactor(sample, SampleMean, SampleVariance, mean.Point, precision);
return ComputeAverageLogFactor(SampleMean, SampleVariance, MeanMean, MeanVariance, precision.LogDeterminant(ignoreInfinity: true), precision);
}
/// <summary>
/// Evidence message for VMP
/// </summary>
/// <param name="sample">Constant value for 'sample'.</param>
/// <param name="mean">Constant value for 'mean'.</param>
/// <param name="precision">Constant value for 'precision'.</param>
/// <returns>Average of the factor's log-value across the given argument distributions</returns>
/// <remarks><para>
/// The formula for the result is <c>log(factor(sample,mean,precision))</c>.
/// Adding up these values across all factors and variables gives the log-evidence estimate for VMP.
/// </para></remarks>
public static double AverageLogFactor(Vector sample, Vector mean, PositiveDefiniteMatrix precision)
{
return ComputeAverageLogFactor(sample, mean, precision.LogDeterminant(ignoreInfinity: true), precision);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="WishartFromShapeAndRateOp_Laplace2"]/message_doc[@name="LogAverageFactor(Wishart, double, Wishart, Wishart)"]/*'/>
public static double LogAverageFactor(Wishart sample, double shape, Wishart rate, [Fresh] Wishart to_sample)
{
// int_R f(Y,R) p(R) dR = |Y|^(a-c) |Y+B_r|^-(a+a_r) Gamma_d(a+a_r)/Gamma_d(a)/Gamma_d(a_r) |B_r|^a_r
int dim = sample.Dimension;
double c = 0.5 * (dim + 1);
double shape2 = shape + rate.Shape;
Wishart samplePost = sample * to_sample;
PositiveDefiniteMatrix y = samplePost.GetMean();
PositiveDefiniteMatrix yPlusBr = y + rate.Rate;
double result = (shape - c) * y.LogDeterminant() - shape2 * yPlusBr.LogDeterminant() + sample.GetLogProb(y) - samplePost.GetLogProb(y);
result += MMath.GammaLn(shape2, dim) - MMath.GammaLn(shape, dim) - MMath.GammaLn(rate.Shape, dim);
result += rate.Shape * rate.Rate.LogDeterminant();
return(result);
}
/// <summary>
/// VMP message to 'product'
/// </summary>
/// <param name="B">Incoming message from 'a'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="A">Incoming message from 'b'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <returns>The outgoing VMP message to the 'product' argument</returns>
/// <remarks><para>
/// The outgoing message is a distribution matching the moments of 'product' as the random arguments are varied.
/// The formula is <c>proj[sum_(a,b) p(a,b) factor(product,a,b)]</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="B"/> is not a proper distribution</exception>
/// <exception cref="ImproperMessageException"><paramref name="A"/> is not a proper distribution</exception>
public static Wishart ProductAverageLogarithm([SkipIfUniform] Wishart A, [SkipIfUniform] Gamma B, Wishart result)
{
if (B.IsPointMass) return ProductAverageLogarithm(A, B.Point, result);
// E[x] = E[a]*E[b]
// E[log(x)] = E[log(a)]+E[log(b)]
PositiveDefiniteMatrix m = new PositiveDefiniteMatrix(A.Dimension, A.Dimension);
A.GetMean(m);
m.Scale(B.GetMean());
double meanLogDet = A.Dimension*B.GetMeanLog() + A.GetMeanLogDeterminant();
if (m.LogDeterminant() < meanLogDet) throw new MatrixSingularException(m);
return Wishart.FromMeanAndMeanLogDeterminant(m, meanLogDet, result);
}
/// <summary>
/// Update the buffer 'PrecisionMeanLogDet'
/// </summary>
/// <param name="Precision">Incoming message from 'precision'.</param>
/// <returns>New value of buffer 'PrecisionMeanLogDet'</returns>
/// <remarks><para>
///
/// </para></remarks>
public static double PrecisionMeanLogDet([Proper] PositiveDefiniteMatrix Precision)
{
return(Precision.LogDeterminant());
}
