public void GaussianOpMean()
{
Gaussian result = new Gaussian();
Gaussian X0 = Gaussian.FromMeanAndVariance(7, 1.0 / 3);
Gaussian Mean0 = Gaussian.FromMeanAndVariance(3, 0.5);
Gamma Precision0 = Gamma.FromShapeAndScale(3, 3);
// Unknown precision
Gamma Precision = Gamma.FromShapeAndScale(3, 3);
Gaussian X = X0;
Gaussian Mean = Mean0;
// in matlab: test_t_msg
result = GaussianOp.MeanAverageConditional_slow(X, Mean, Precision);
Console.WriteLine(result);
Assert.True(GaussianOp.MeanAverageConditional_slow(X, Mean, Precision).MaxDiff(new Gaussian(-9.9121, -4.5998)) < 1e-0);
X = Gaussian.FromMeanAndVariance(1, 2);
Mean = Gaussian.PointMass(0);
Precision = Gamma.FromShapeAndRate(3, 1);
Gaussian xPostExpected = Gaussian.FromMeanAndVariance(0.178378819440295, 0.365796599498963);
Console.WriteLine(GaussianOp.SampleAverageConditional_slow(X, Mean, Precision) * X);
Assert.True(GaussianOp.SampleAverageConditional_slow(X, Mean, Precision).MaxDiff(xPostExpected / X) < 5e-7);
Console.WriteLine(GaussianOp_Slow.SampleAverageConditional(X, Mean, Precision) * X);
Assert.True(GaussianOp_Slow.SampleAverageConditional(X, Mean, Precision).MaxDiff(xPostExpected / X) < 5e-7);
}
private void GaussianOpX2(Gaussian mean, Gamma precision)
{
Gaussian sample, result, result2;
sample = Gaussian.PointMass(2);
result = GaussianOp.SampleAverageConditional_slow(sample, mean, precision);
result2 = GaussianOp_Slow.SampleAverageConditional(sample, mean, precision);
Console.WriteLine("{0}: {1} {2}", sample, result, result2);
Assert.True(result.MaxDiff(result2) < 1e-8);
double prevDiff = double.PositiveInfinity;
for (int i = 8; i < 30; i++)
{
double v = System.Math.Pow(0.1, i);
sample = Gaussian.FromMeanAndVariance(2, v);
result2 = GaussianOp_Slow.SampleAverageConditional(sample, mean, precision);
double diff = result.MaxDiff(result2);
Console.WriteLine("{0}: {1} diff={2}", sample, result2, diff.ToString("g4"));
Assert.True(diff <= prevDiff || diff < 1e-6);
result2 = GaussianOp.SampleAverageConditional_slow(sample, mean, precision);
diff = result.MaxDiff(result2);
Console.WriteLine("{0}: {1} diff={2}", sample, result2, diff.ToString("g4"));
Assert.True(diff <= prevDiff || diff < 1e-6);
prevDiff = diff;
}
}
internal void StudentIsPositiveTest3()
{
double shape = 1;
Gamma precPrior = Gamma.FromShapeAndRate(shape, shape);
Gaussian meanPrior = Gaussian.PointMass(0);
Gaussian xB = Gaussian.Uniform();
Gaussian xF = GaussianOp.SampleAverageConditional_slow(xB, meanPrior, precPrior);
for (int iter = 0; iter < 100; iter++)
{
xB = IsPositiveOp.XAverageConditional(true, xF);
xF = GetConstrainedMessage(xB, meanPrior, precPrior, xF);
}
Console.WriteLine("xF = {0} x = {1}", xF, xB * xF);
}
private static Gaussian GetConstrainedMessage1(Gaussian sample, Gaussian mean, Gamma precision, Gaussian to_sample)
{
Gaussian sampleMarginal = sample * to_sample;
double m1, v1;
to_sample.GetMeanAndVariance(out m1, out v1);
double m, v;
sampleMarginal.GetMeanAndVariance(out m, out v);
double moment2 = m * m + v;
// vq < moment2 implies 1/vq > 1/moment2
// implies 1/v2 > 1/moment2 - to_sample.Precision
double v2max = 1 / (1 / moment2 - to_sample.Precision);
double v2min = 1e-2;
double[] v2s = EpTests.linspace(v2min, v2max, 100);
double p2min = 1 / moment2 - to_sample.Precision;
if (p2min < 0.0)
{
return(to_sample);
}
double p2max = sample.Precision * 10;
double[] p2s = EpTests.linspace(p2min, p2max, 100);
Gaussian bestResult = to_sample;
double bestScore = double.PositiveInfinity;
for (int i = 0; i < p2s.Length; i++)
{
double p2 = p2s[i];
double vq = 1 / (to_sample.Precision + p2);
double m2 = (System.Math.Sqrt(moment2 - vq) / vq - to_sample.MeanTimesPrecision) / p2;
// check
double mq = vq * (to_sample.MeanTimesPrecision + m2 * p2);
Assert.True(MMath.AbsDiff(mq * mq + vq, moment2) < 1e-10);
Gaussian sample2 = Gaussian.FromMeanAndPrecision(m2, p2);
Gaussian result = GaussianOp.SampleAverageConditional_slow(sample2, mean, precision);
double score = System.Math.Abs(result.MeanTimesPrecision);
if (score < bestScore)
{
bestScore = score;
bestResult = result;
}
}
return(bestResult);
}
public void GaussianOpX()
{
Gaussian uniform = Gaussian.Uniform();
Gaussian X0 = Gaussian.FromMeanAndVariance(3, 0.5);
Gaussian Mean0 = Gaussian.FromMeanAndVariance(7, 1.0 / 3);
double Precision0 = 3;
Gaussian X, Mean;
Gamma Precision, to_precision;
Gaussian xActual, xExpected;
bool testImproper = false;
if (testImproper)
{
// Test the case where precisionIsBetween = false
X = Gaussian.FromNatural(1, 2);
Mean = Gaussian.FromNatural(3, -1);
Precision = Gamma.FromShapeAndRate(4, 5);
to_precision = Gamma.FromShapeAndRate(6, 7);
xActual = GaussianOp.SampleAverageConditional(X, Mean, Precision, to_precision);
}
X = Gaussian.FromNatural(-2.7793306963303595, 0.050822473645365768);
Mean = Gaussian.FromNatural(-5.9447032851878134E-09, 3.2975231004586637E-204);
Precision = Gamma.FromShapeAndRate(318.50907574398883, 9.6226982361933746E+205);
to_precision = Gamma.PointMass(0);
xActual = GaussianOp.SampleAverageConditional(X, Mean, Precision, to_precision);
X = Gaussian.FromNatural(0.1559599323109816, 8.5162535450918462);
Mean = Gaussian.PointMass(0.57957597647840942);
Precision = Gamma.FromShapeAndRate(7.8308812008325587E+30, 8.2854255911709925E+30);
to_precision = Gamma.FromShapeAndRate(1.4709139487775529, 0.14968339171493822);
xActual = GaussianOp.SampleAverageConditional(X, Mean, Precision, to_precision);
X = Gaussian.FromNatural(0.15595993233964134, 8.5162535466550349);
Mean = Gaussian.PointMass(0.57957597647840942);
Precision = Gamma.FromShapeAndRate(3.9206259406339067E+20, 4.1481991194547565E+20);
to_precision = Gamma.FromShapeAndRate(1.4709139487806249, 0.14968339171413536);
xActual = GaussianOp.SampleAverageConditional(X, Mean, Precision, to_precision);
X = Gaussian.FromNatural(0.15595993261634511, 8.5162535617468418);
Mean = Gaussian.PointMass(0.57957597647840942);
Precision = Gamma.FromShapeAndRate(1.825759224425317E+19, 1.9317356258150703E+19);
to_precision = Gamma.FromShapeAndRate(1.4709139487887679, 0.14968339176002607);
xActual = GaussianOp.SampleAverageConditional(X, Mean, Precision, to_precision);
X = Gaussian.FromNatural(0.16501264432785923, 9.01);
Mean = Gaussian.PointMass(0.57957597647840942);
Precision = Gamma.FromShapeAndRate(1.6965139612477539E+21, 1.6965139612889427E+21);
to_precision = Gamma.FromShapeAndRate(1.4695136363119978, 0.14707291154227081);
xActual = GaussianOp.SampleAverageConditional(X, Mean, Precision, to_precision);
// initialized in a bad place, gets stuck in a flat region
X = Gaussian.FromNatural(3.9112579392580757, 11.631097473681082);
Mean = Gaussian.FromNatural(10.449696977834144, 5.5617978202886995);
Precision = Gamma.FromShapeAndRate(1.0112702817305146, 0.026480506235719053);
to_precision = Gamma.FromShapeAndRate(1, 0.029622790537514355);
xActual = GaussianOp.SampleAverageConditional(X, Mean, Precision, to_precision);
X = Gaussian.FromNatural(57788.170908674481, 50207.150004827061);
Mean = Gaussian.PointMass(0);
Precision = Gamma.FromShapeAndRate(19764.051194189466, 0.97190264412377791);
xActual = GaussianOp.SampleAverageConditional_slow(X, Mean, Precision);
// integration bounds should be [-36,4]
X = Gaussian.FromNatural(1.696828485456396, 0.71980672726406147);
Mean = Gaussian.PointMass(-1);
Precision = new Gamma(1, 1);
xActual = GaussianOp.SampleAverageConditional_slow(X, Mean, Precision);
xExpected = GaussianOp_Slow.SampleAverageConditional(X, Mean, Precision);
Assert.True(xExpected.MaxDiff(xActual) < 1e-4);
X = new Gaussian(-1.565, 0.8466);
Mean = new Gaussian(0.0682, 0.3629);
Precision = new Gamma(103.2, 0.009786);
xActual = GaussianOp.SampleAverageConditional_slow(X, Mean, Precision);
xExpected = GaussianOp_Slow.SampleAverageConditional(X, Mean, Precision);
Assert.True(xExpected.MaxDiff(xActual) < 1e-4);
// Fixed precision
X = X0;
Mean = uniform;
Assert.True(GaussianOp.SampleAverageConditional(Mean, Precision0).MaxDiff(uniform) < 1e-10);
Mean = Mean0;
Assert.True(GaussianOp.SampleAverageConditional(Mean, Precision0).MaxDiff(new Gaussian(Mean.GetMean(), Mean.GetVariance() + 1 / Precision0)) < 1e-10);
Mean = Gaussian.PointMass(Mean0.GetMean());
Assert.True(GaussianOp.SampleAverageConditional(Mean, Precision0).MaxDiff(new Gaussian(Mean.GetMean(), 1 / Precision0)) < 1e-10);
// Uniform precision
// the answer should always be uniform
Precision = Gamma.Uniform();
Assert.True(GaussianOp.SampleAverageConditional_slow(X, Mean, Precision).MaxDiff(uniform) < 1e-10);
// Unknown precision
Precision = Gamma.FromShapeAndScale(3, 3);
// Known X
X = Gaussian.PointMass(X0.GetMean());
Mean = uniform;
Assert.True(GaussianOp.SampleAverageConditional_slow(X, Mean, Precision).MaxDiff(uniform) < 1e-10);
// Unknown X
X = X0;
Mean = uniform;
//Console.WriteLine(XAverageConditional2(result));
Assert.True(GaussianOp.SampleAverageConditional_slow(X, Mean, Precision).MaxDiff(uniform) < 1e-10);
X = X0;
Mean = Mean0;
// converge the precision message. (only matters if KeepLastMessage is set).
//for (int i = 0; i < 10; i++) GaussianOp.PrecisionAverageConditional(X, Mean, Precision, precisionMessage);
// in matlab: test_t_msg
if (GaussianOp.ForceProper)
{
Assert.True(GaussianOp.SampleAverageConditional_slow(X, Mean, Precision).MaxDiff(Gaussian.FromNatural(3.1495, 0)) < 1e-4);
}
else
{
Assert.True(GaussianOp.SampleAverageConditional_slow(X, Mean, Precision).MaxDiff(new Gaussian(-9.9121, -4.5998)) < 1e-4);
}
X = X0;
Mean = Gaussian.PointMass(Mean0.GetMean());
// converge the precision message. (only matters if KeepLastMessage is set).
//for (int i = 0; i < 10; i++) GaussianOp.PrecisionAverageConditional(X, Mean, Precision, precisionMessage);
// in matlab: test_t_msg
if (GaussianOp.ForceProper)
{
Assert.True(GaussianOp.SampleAverageConditional_slow(X, Mean, Precision).MaxDiff(Gaussian.FromNatural(2.443, 0)) < 1e-4);
}
else
{
Assert.True(GaussianOp.SampleAverageConditional_slow(X, Mean, Precision).MaxDiff(new Gaussian(0.81394, -1.3948)) < 1e-4);
}
// Uniform X
X = uniform;
Mean = Mean0;
// converge the precision message. (only matters if KeepLastMessage is set).
//for (int i = 0; i < 10; i++) GaussianOp.PrecisionAverageConditional(X, Mean, Precision, precisionMessage);
Assert.True(GaussianOp.SampleAverageConditional_slow(X, Mean, Precision).MaxDiff(new Gaussian(7, 0.5)) < 1e-10);
X = uniform;
Mean = Gaussian.PointMass(Mean0.GetMean());
// converge the precision message. (only matters if KeepLastMessage is set).
//for (int i = 0; i < 10; i++) GaussianOp.PrecisionAverageConditional(X, Mean, Precision, precisionMessage);
Assert.True(GaussianOp.SampleAverageConditional_slow(X, Mean, Precision).MaxDiff(new Gaussian(7, 1.0 / 6)) < 1e-10);
}