public void SparseGaussianListFactor() { SparseGaussianList.DefaultTolerance = 1e-10; var calcSuffix = ": calculation differs between sparse and dense"; var sparsitySuffix = ": result is not sparse as expected"; var calcErrMsg = ""; var sparsityErrMsg = ""; var tolerance = 1e-10; Rand.Restart(12347); int listSize = 50; // True distribution for the means var sparseMeanDist = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(1, 2), tolerance); sparseMeanDist[3] = Gaussian.FromMeanAndPrecision(4, 5); sparseMeanDist[6] = Gaussian.FromMeanAndPrecision(7, 8); var meanDist = sparseMeanDist.ToArray(); var sparseMeanPoint = SparseList <double> .Constant(listSize, 0.1); sparseMeanPoint[3] = 0.7; sparseMeanPoint[6] = 0.8; var meanPoint = sparseMeanPoint.ToArray(); // True distribution for the precisions var sparsePrecDist = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(1.1, 1.2), tolerance); sparsePrecDist[3] = Gamma.FromShapeAndRate(2.3, 2.4); sparsePrecDist[6] = Gamma.FromShapeAndRate(3.4, 4.5); var precDist = sparsePrecDist.ToArray(); var sparsePrecPoint = SparseList <double> .Constant(listSize, 0.1); sparsePrecPoint[3] = 5.6; sparsePrecPoint[6] = 0.5; var precPoint = sparsePrecPoint.ToArray(); var sparseSampleDist = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 1.5), tolerance); sparseSampleDist[3] = Gaussian.FromMeanAndPrecision(-0.5, 2.0); sparseSampleDist[9] = Gaussian.FromMeanAndPrecision(1.6, 0.4); var sampleDist = sparseSampleDist.ToArray(); var sparseSamplePoint = SparseList <double> .Constant(listSize, 0.5); sparseSamplePoint[3] = 0.1; sparseSamplePoint[9] = 2.3; var samplePoint = sparseSamplePoint.ToArray(); var toSparseSampleDist = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(-0.2, 0.3), tolerance); toSparseSampleDist[3] = Gaussian.FromMeanAndPrecision(2.1, 3.2); toSparseSampleDist[4] = Gaussian.FromMeanAndPrecision(1.3, 0.7); var toSampleDist = toSparseSampleDist.ToArray(); var toSparsePrecDist = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(2.3, 3.4), tolerance); toSparsePrecDist[3] = Gamma.FromShapeAndRate(3.4, 4.5); toSparsePrecDist[4] = Gamma.FromShapeAndRate(5.6, 6.7); var toPrecDist = toSparsePrecDist.ToArray(); // --------------------------- // Check average log factor // --------------------------- calcErrMsg = "Average log factor" + calcSuffix; // Dist, dist, dist var sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSampleDist, sparseMeanDist, sparsePrecDist); var avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(sampleDist[i], meanDist[i], precDist[i])).Sum(); TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg); // Dist, dist, point sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSampleDist, sparseMeanDist, sparsePrecPoint); avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(sampleDist[i], meanDist[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg); // Dist, point, dist sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSampleDist, sparseMeanPoint, sparsePrecDist); avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(sampleDist[i], meanPoint[i], precDist[i])).Sum(); TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg); // Dist, point, point sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSampleDist, sparseMeanPoint, sparsePrecPoint); avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(sampleDist[i], meanPoint[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg); // Point, dist, dist sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSamplePoint, sparseMeanDist, sparsePrecDist); avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(samplePoint[i], meanDist[i], precDist[i])).Sum(); TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg); // Point, dist, point sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSamplePoint, sparseMeanDist, sparsePrecPoint); avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(samplePoint[i], meanDist[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg); // Point, point, dist sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSamplePoint, sparseMeanPoint, sparsePrecDist); avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(samplePoint[i], meanPoint[i], precDist[i])).Sum(); TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg); // Point, point, point sparseAvgLog = SparseGaussianListOp.AverageLogFactor(sparseSamplePoint, sparseMeanPoint, sparsePrecPoint); avgLog = Util.ArrayInit(listSize, i => GaussianOp.AverageLogFactor(samplePoint[i], meanPoint[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(avgLog - sparseAvgLog) < tolerance, calcErrMsg); // --------------------------- // Check log average factor // --------------------------- calcErrMsg = "Log average factor" + calcSuffix; var sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSampleDist, sparseMeanDist, sparsePrecDist, toSparsePrecDist); var logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(sampleDist[i], meanDist[i], precDist[i], toPrecDist[i])).Sum(); TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg); // Dist, dist, point sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSampleDist, sparseMeanDist, sparsePrecPoint); logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(sampleDist[i], meanDist[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg); // Dist, point, dist sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSampleDist, sparseMeanPoint, sparsePrecDist, toSparsePrecDist); logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(sampleDist[i], meanPoint[i], precDist[i], toPrecDist[i])).Sum(); TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg); // Dist, point, point sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSampleDist, sparseMeanPoint, sparsePrecPoint); logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(sampleDist[i], meanPoint[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg); // Point, dist, dist sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSamplePoint, sparseMeanDist, sparsePrecDist, toSparsePrecDist); logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(samplePoint[i], meanDist[i], precDist[i], toPrecDist[i])).Sum(); TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg); // Point, dist, point sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSamplePoint, sparseMeanDist, sparsePrecPoint); logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(samplePoint[i], meanDist[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg); // Point, point, dist sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSamplePoint, sparseMeanPoint, sparsePrecDist); logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(samplePoint[i], meanPoint[i], precDist[i])).Sum(); TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg); // Point, point, point sparseLogAvg = SparseGaussianListOp.LogAverageFactor(sparseSamplePoint, sparseMeanPoint, sparsePrecPoint); logAvg = Util.ArrayInit(listSize, i => GaussianOp.LogAverageFactor(samplePoint[i], meanPoint[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(logAvg - sparseLogAvg) < tolerance, calcErrMsg); // --------------------------- // Check log evidence ratio // --------------------------- calcErrMsg = "Log evidence ratio" + calcSuffix; var sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSampleDist, sparseMeanDist, sparsePrecDist, toSparseSampleDist, toSparsePrecDist); var evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(sampleDist[i], meanDist[i], precDist[i], toSampleDist[i], toPrecDist[i])).Sum(); TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg); // Dist, dist, point sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSampleDist, sparseMeanDist, sparsePrecPoint); evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(sampleDist[i], meanDist[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg); // Dist, point, dist sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSampleDist, sparseMeanPoint, sparsePrecDist, toSparseSampleDist, toSparsePrecDist); evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(sampleDist[i], meanPoint[i], precDist[i], toSampleDist[i], toPrecDist[i])).Sum(); TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg); // Dist, point, point sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSampleDist, sparseMeanPoint, sparsePrecPoint); evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(sampleDist[i], meanPoint[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg); // Point, dist, dist sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSamplePoint, sparseMeanDist, sparsePrecDist, toSparsePrecDist); evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(samplePoint[i], meanDist[i], precDist[i], toPrecDist[i])).Sum(); TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg); // Point, dist, point sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSamplePoint, sparseMeanDist, sparsePrecPoint); evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(samplePoint[i], meanDist[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg); // Point, point, dist sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSamplePoint, sparseMeanPoint, sparsePrecDist); evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(samplePoint[i], meanPoint[i], precDist[i])).Sum(); TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg); // Point, point, point sparseEvidRat = SparseGaussianListOp.LogEvidenceRatio(sparseSamplePoint, sparseMeanPoint, sparsePrecPoint); evidRat = Util.ArrayInit(listSize, i => GaussianOp.LogEvidenceRatio(samplePoint[i], meanPoint[i], precPoint[i])).Sum(); TAssert.True(System.Math.Abs(evidRat - sparseEvidRat) < tolerance, calcErrMsg); // --------------------------- // Check SampleAverageConditional // --------------------------- calcErrMsg = "SampleAverageConditional" + calcSuffix; sparsityErrMsg = "SampleAverageConditional" + sparsitySuffix; // Use different common value to ensure this gets properly set var sparseSampleAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance); sparseSampleAvgConditional = SparseGaussianListOp.SampleAverageConditional(sparseSampleDist, sparseMeanDist, sparsePrecDist, toSparsePrecDist, sparseSampleAvgConditional); var sampleAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.SampleAverageConditional(sampleDist[i], meanDist[i], precDist[i], toPrecDist[i])); TAssert.True(3 == sparseSampleAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparseSampleAvgConditional.MaxDiff(sampleAvgConditional) < tolerance, calcErrMsg); sparseSampleAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance); sparseSampleAvgConditional = SparseGaussianListOp.SampleAverageConditional(sparseSampleDist, sparseMeanPoint, sparsePrecDist, toSparsePrecDist, sparseSampleAvgConditional); sampleAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.SampleAverageConditional(sampleDist[i], meanPoint[i], precDist[i], toPrecDist[i])); TAssert.True(3 == sparseSampleAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparseSampleAvgConditional.MaxDiff(sampleAvgConditional) < tolerance, calcErrMsg); sparseSampleAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance); sparseSampleAvgConditional = SparseGaussianListOp.SampleAverageConditional(sparseMeanDist, sparsePrecPoint, sparseSampleAvgConditional); sampleAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.SampleAverageConditional(meanDist[i], precPoint[i])); TAssert.True(2 == sparseSampleAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparseSampleAvgConditional.MaxDiff(sampleAvgConditional) < tolerance, calcErrMsg); sparseSampleAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance); sparseSampleAvgConditional = SparseGaussianListOp.SampleAverageConditional(sparseMeanPoint, sparsePrecPoint, sparseSampleAvgConditional); sampleAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.SampleAverageConditional(meanPoint[i], precPoint[i])); TAssert.True(2 == sparseSampleAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparseSampleAvgConditional.MaxDiff(sampleAvgConditional) < tolerance, calcErrMsg); // --------------------------- // Check MeanAverageConditional // --------------------------- calcErrMsg = "MeanAverageConditional" + calcSuffix; sparsityErrMsg = "MeanAverageConditional" + sparsitySuffix; // Use different common value to ensure this gets properly set var sparseMeanAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance); sparseMeanAvgConditional = SparseGaussianListOp.MeanAverageConditional(sparseSampleDist, sparseMeanDist, sparsePrecDist, toSparsePrecDist, sparseMeanAvgConditional); var meanAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.MeanAverageConditional(sampleDist[i], meanDist[i], precDist[i], toPrecDist[i])); TAssert.True(3 == sparseMeanAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparseMeanAvgConditional.MaxDiff(meanAvgConditional) < tolerance, calcErrMsg); sparseMeanAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance); sparseMeanAvgConditional = SparseGaussianListOp.MeanAverageConditional(sparseSamplePoint, sparseMeanDist, sparsePrecDist, toSparsePrecDist, sparseMeanAvgConditional); meanAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.MeanAverageConditional(samplePoint[i], meanDist[i], precDist[i], toPrecDist[i])); TAssert.True(3 == sparseMeanAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparseMeanAvgConditional.MaxDiff(meanAvgConditional) < tolerance, calcErrMsg); sparseMeanAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance); sparseMeanAvgConditional = SparseGaussianListOp.MeanAverageConditional(sparseSampleDist, sparsePrecPoint, sparseMeanAvgConditional); meanAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.MeanAverageConditional(sampleDist[i], precPoint[i])); TAssert.True(3 == sparseMeanAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparseMeanAvgConditional.MaxDiff(meanAvgConditional) < tolerance, calcErrMsg); sparseMeanAvgConditional = SparseGaussianList.Constant(listSize, Gaussian.FromMeanAndPrecision(0.5, 0.6), tolerance); sparseMeanAvgConditional = SparseGaussianListOp.MeanAverageConditional(sparseSamplePoint, sparsePrecPoint, sparseMeanAvgConditional); meanAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.MeanAverageConditional(samplePoint[i], precPoint[i])); TAssert.True(3 == sparseMeanAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparseMeanAvgConditional.MaxDiff(meanAvgConditional) < tolerance, calcErrMsg); // --------------------------- // Check PrecisionAverageConditional // --------------------------- calcErrMsg = "PrecisionAverageConditional" + calcSuffix; sparsityErrMsg = "PrecisionAverageConditional" + sparsitySuffix; // Use different common value to ensure this gets properly set var sparsePrecAvgConditional = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(2.1, 3.2), tolerance); sparsePrecAvgConditional = SparseGaussianListOp.PrecisionAverageConditional(sparseSampleDist, sparseMeanDist, sparsePrecDist, sparsePrecAvgConditional); var precAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.PrecisionAverageConditional(sampleDist[i], meanDist[i], precDist[i])); TAssert.True(3 == sparsePrecAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparsePrecAvgConditional.MaxDiff(precAvgConditional) < tolerance, calcErrMsg); sparsePrecAvgConditional = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(2.1, 3.2), tolerance); sparsePrecAvgConditional = SparseGaussianListOp.PrecisionAverageConditional(sparseSamplePoint, sparseMeanDist, sparsePrecDist, sparsePrecAvgConditional); precAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.PrecisionAverageConditional(Gaussian.PointMass(samplePoint[i]), meanDist[i], precDist[i])); TAssert.True(3 == sparsePrecAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparsePrecAvgConditional.MaxDiff(precAvgConditional) < tolerance, calcErrMsg); sparsePrecAvgConditional = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(2.1, 3.2), tolerance); sparsePrecAvgConditional = SparseGaussianListOp.PrecisionAverageConditional(sparseSampleDist, sparseMeanPoint, sparsePrecDist, sparsePrecAvgConditional); precAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.PrecisionAverageConditional(sampleDist[i], Gaussian.PointMass(meanPoint[i]), precDist[i])); TAssert.True(3 == sparsePrecAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparsePrecAvgConditional.MaxDiff(precAvgConditional) < tolerance, calcErrMsg); sparsePrecAvgConditional = SparseGammaList.Constant(listSize, Gamma.FromShapeAndRate(2.1, 3.2), tolerance); sparsePrecAvgConditional = SparseGaussianListOp.PrecisionAverageConditional(sparseSamplePoint, sparseMeanPoint, sparsePrecAvgConditional); precAvgConditional = Util.ArrayInit(listSize, i => GaussianOp.PrecisionAverageConditional(samplePoint[i], meanPoint[i])); TAssert.True(3 == sparsePrecAvgConditional.SparseCount, sparsityErrMsg); TAssert.True(sparsePrecAvgConditional.MaxDiff(precAvgConditional) < tolerance, calcErrMsg); }