/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="WishartFromShapeAndRateOp_Laplace2"]/message_doc[@name="RateAverageConditional(Wishart, double, Wishart, Wishart, Wishart)"]/*'/>
public static Wishart RateAverageConditional([SkipIfUniform] Wishart sample, double shape, Wishart rate, Wishart to_rate, Wishart result)
{
if (sample.IsPointMass)
{
return(WishartFromShapeAndRateOp.RateAverageConditional(sample.Point, shape, result));
}
// f(Y,R) = |Y|^(a-c) |R|^a exp(-tr(YR))
// p(Y) = |Y|^(a_y-c) exp(-tr(YB_y)
// p(R) = |R|^(a_r-c) exp(-tr(RB_r)
// int_Y f(Y,R) p(Y) dY = |R|^a |R+B_y|^-(a+a_y-c)
int dim = sample.Dimension;
double c = 0.5 * (dim + 1);
double shape2 = shape - c + sample.Shape;
Wishart ratePost = rate * to_rate;
PositiveDefiniteMatrix r = ratePost.GetMean();
PositiveDefiniteMatrix rby = r + sample.Rate;
PositiveDefiniteMatrix invrby = rby.Inverse();
PositiveDefiniteMatrix rInvrby = rby;
rInvrby.SetToProduct(r, invrby);
double xxddlogp = Matrix.TraceOfProduct(rInvrby, rInvrby) * shape2;
double delta = -xxddlogp / dim;
PositiveDefiniteMatrix invR = r.Inverse();
PositiveDefiniteMatrix dlogp = invrby;
dlogp.Scale(-shape2);
LowerTriangularMatrix rChol = new LowerTriangularMatrix(dim, dim);
rChol.SetToCholesky(r);
result.SetDerivatives(rChol, invR, dlogp, xxddlogp, GammaFromShapeAndRateOp.ForceProper, shape);
return(result);
}
public static Vector VectorGaussianScaled(double scaling, PositiveDefiniteMatrix precision)
{
var scaledPrec = new PositiveDefiniteMatrix(precision);
scaledPrec.Scale(scaling);
return(VectorGaussian.FromMeanAndPrecision(Vector.Zero(precision.Cols), scaledPrec).Sample());
}
public void RandWishart()
{
// multivariate Gamma
double a = 2.7;
int d = 3;
PositiveDefiniteMatrix mTrue = new PositiveDefiniteMatrix(d, d);
mTrue.SetToIdentity();
mTrue.SetToProduct(mTrue, a);
LowerTriangularMatrix L = new LowerTriangularMatrix(d, d);
PositiveDefiniteMatrix X = new PositiveDefiniteMatrix(d, d);
PositiveDefiniteMatrix m = new PositiveDefiniteMatrix(d, d);
m.SetAllElementsTo(0);
double s = 0;
for (int i = 0; i < nsamples; i++)
{
Rand.Wishart(a, L);
X.SetToProduct(L, L.Transpose());
m = m + X;
s = s + X.LogDeterminant();
}
double sTrue = 0;
for (int i = 0; i < d; i++)
{
sTrue += MMath.Digamma(a - i * 0.5);
}
m.Scale(1.0 / nsamples);
s = s / nsamples;
Console.WriteLine("");
Console.WriteLine("Multivariate Gamma");
Console.WriteLine("-------------------");
Console.WriteLine("m = \n{0}", m);
double dError = m.MaxDiff(mTrue);
if (dError > TOLERANCE)
{
Assert.True(false, String.Format("Wishart({0}) mean: (should be {0}*I), error = {1}", a, dError));
}
if (System.Math.Abs(s - sTrue) > TOLERANCE)
{
Assert.True(false, string.Format("E[logdet]: {0} (should be {1})", s, sTrue));
}
}
/// <summary>
/// Adds a weighted observation.
/// </summary>
/// <param name="x"></param>
/// <param name="weight"></param>
public void Add(Vector x, double weight)
{
// new_mean = mean + w/(count + w)*(x - mean)
// new_cov = count/(count + w)*(cov + w/(count+w)*(x-mean)*(x-mean)')
count += weight;
if (count == 0)
{
return;
}
diff.SetToDifference(x, mean);
double s = weight / count;
mean.SetToSum(1.0, mean, s, diff);
//outer.SetToOuter(diff,diff2);
// this is more numerically stable:
//outer.SetToOuter(diff, diff).Scale(s);
cov.SetToSumWithOuter(cov, s, diff, diff);
cov.Scale(1 - s);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="WishartFromShapeAndRateOp_Laplace2"]/message_doc[@name="SampleAverageConditional(Wishart, double, Wishart, Wishart, Wishart, Wishart)"]/*'/>
public static Wishart SampleAverageConditional([NoInit] Wishart sample, double shape, [Proper] Wishart rate, [NoInit] Wishart to_rate, [NoInit] Wishart to_sample, Wishart result)
{
if (sample.IsUniform())
{
return(SampleAverageConditional2(shape, rate, to_rate, result));
}
// f(Y,R) = |Y|^(a-c) |R|^a exp(-tr(YR))
// p(Y) = |Y|^(a_y-c) exp(-tr(YB_y)
// p(R) = |R|^(a_r-c) exp(-tr(RB_r)
// int_R f(Y,R) p(R) dR = |Y|^(a-c) |Y+B_r|^-(a+a_r)
int dim = sample.Dimension;
double c = 0.5 * (dim + 1);
double shape2 = shape + rate.Shape;
Wishart samplePost = sample * to_sample;
if (!samplePost.IsProper())
{
return(SampleAverageConditional2(shape, rate, to_rate, result));
}
PositiveDefiniteMatrix y = samplePost.GetMean();
PositiveDefiniteMatrix yPlusBr = y + rate.Rate;
PositiveDefiniteMatrix invyPlusBr = yPlusBr.Inverse();
PositiveDefiniteMatrix yInvyPlusBr = yPlusBr;
yInvyPlusBr.SetToProduct(y, invyPlusBr);
double xxddlogf = shape2 * Matrix.TraceOfProduct(yInvyPlusBr, yInvyPlusBr);
PositiveDefiniteMatrix invY = y.Inverse();
//double delta = -xxddlogf / dim;
//result.Shape = delta + shape;
//result.Rate.SetToSum(delta, invY, shape2, invyPlusBr);
LowerTriangularMatrix yChol = new LowerTriangularMatrix(dim, dim);
yChol.SetToCholesky(y);
PositiveDefiniteMatrix dlogp = invyPlusBr;
dlogp.Scale(-shape2);
result.SetDerivatives(yChol, invY, dlogp, xxddlogf, GammaFromShapeAndRateOp.ForceProper, shape - c);
if (result.Rate.Any(x => double.IsNaN(x)))
{
throw new Exception("result.Rate is nan");
}
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="ProductWishartOp"]/message_doc[@name="ProductAverageLogarithm(Wishart, Gamma, Wishart)"]/*'/>
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));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="ProductWishartOp"]/message_doc[@name="ProductAverageConditional(Wishart, PositiveDefiniteMatrix, Gamma, Gamma, Wishart)"]/*'/>
public static Wishart ProductAverageConditional(Wishart Product, PositiveDefiniteMatrix A, [SkipIfUniform] Gamma B, Gamma to_B, Wishart result)
{
if (B.IsPointMass)
{
return(ProductAverageConditional(A, B.Point, result));
}
Gamma Bpost = B * to_B;
// E[x] = a*E[b]
// E[logdet(x)] = logdet(a) + d*E[log(b)]
PositiveDefiniteMatrix m = new PositiveDefiniteMatrix(A.Rows, A.Cols);
m.SetTo(A);
m.Scale(Bpost.GetMean());
double meanLogDet = A.Rows * Bpost.GetMeanLog() + A.LogDeterminant();
if (m.LogDeterminant() < meanLogDet)
{
throw new MatrixSingularException(m);
}
Wishart.FromMeanAndMeanLogDeterminant(m, meanLogDet, result);
result.SetToRatio(result, Product);
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);
}
