/// <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); }
/// <summary> /// EP message to 'product' /// </summary> /// <param name="A">Constant value for 'a'.</param> /// <param name="BMean">Buffer 'BMean'.</param> /// <param name="BVariance">Buffer 'BVariance'.</param> /// <param name="result">Modified to contain the outgoing message</param> /// <returns><paramref name="result"/></returns> /// <remarks><para> /// The outgoing message is the factor viewed as a function of 'product' conditioned on the given values. /// </para></remarks> public static VectorGaussian ProductAverageConditional(Matrix A, [Fresh] Vector BMean, [Fresh] PositiveDefiniteMatrix BVariance, VectorGaussian result) { // P.mean = A*B.mean // P.var = A*B.var*A' // if A is invertible, then // P.prec = inv(A)'*inv(B.var)*inv(A) // P.precTimesMean = inv(A)'*B.precTimesMean Vector rmean = A * BMean; PositiveDefiniteMatrix rvariance = new PositiveDefiniteMatrix(result.Dimension, result.Dimension); Matrix temp = (A * BVariance).Transpose(); rvariance.SetToProduct(A, temp); result.SetMeanAndVariance(rmean, rvariance); return(result); }
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)); } }
/// <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); }
private static void GetProductMoments(Matrix A, Vector BMean, PositiveDefiniteMatrix BVariance, Vector mean, PositiveDefiniteMatrix variance) { // P.mean = A*B.mean // P.var = A*B.var*A' mean.SetToProduct(A, BMean); if (UseAccurateMethod) { int dim = BVariance.Rows; LowerTriangularMatrix cholesky = new LowerTriangularMatrix(dim, dim); cholesky.SetToCholesky(BVariance); Matrix AL = A * cholesky; variance.SetToOuter(AL); } else { variance.SetToProduct(A, (A * BVariance).Transpose()); variance.Symmetrize(); } }
public static VectorGaussianWishart Combine(VectorGaussian position, Wishart orientation, VectorGaussianWishart result) { if (orientation.IsUniform()) { result.SetToUniform(); } else if (position.IsUniform()) { result.SetTo(orientation.Shape, orientation.Rate, Vector.Zero(2), 0); } else { PositiveDefiniteMatrix rateTimesPrecision = new PositiveDefiniteMatrix(2, 2); rateTimesPrecision.SetToProduct(orientation.Rate, position.Precision); double trace = MathHelpers.Invert(rateTimesPrecision).Trace(); Vector positionMean = position.MeanTimesPrecision * MathHelpers.Invert(position.Precision); result.SetTo(orientation.Shape, orientation.Rate, positionMean, orientation.Dimension / (orientation.Shape * trace)); } return result; }
/// <summary> /// EP message to 'product' /// </summary> /// <param name="A">Constant value for 'a'.</param> /// <param name="BMean">Buffer 'BMean'.</param> /// <param name="BVariance">Buffer 'BVariance'.</param> /// <param name="result">Modified to contain the outgoing message</param> /// <returns><paramref name="result"/></returns> /// <remarks><para> /// The outgoing message is the factor viewed as a function of 'product' conditioned on the given values. /// </para></remarks> public static VectorGaussian ProductAverageConditional(Matrix A, [Fresh] Vector BMean, [Fresh] PositiveDefiniteMatrix BVariance, VectorGaussian result) { // P.mean = A*B.mean // P.var = A*B.var*A' // if A is invertible, then // P.prec = inv(A)'*inv(B.var)*inv(A) // P.precTimesMean = inv(A)'*B.precTimesMean Vector rmean = A * BMean; PositiveDefiniteMatrix rvariance = new PositiveDefiniteMatrix(result.Dimension, result.Dimension); Matrix temp = (A*BVariance).Transpose(); rvariance.SetToProduct(A, temp); result.SetMeanAndVariance(rmean, rvariance); return result; }