// Commented out since this test is very slow and does not have any assertions
//[Fact]
internal void GaussianFromMeanAndVarianceVaryTruePrec()
{
double mean = 2.0;
var Nvar = Variable.Observed <int>(50);
var n = new Range(Nvar);
var noisePrecision = 10;
var variancePriors = new double[] { 1, 5, 10 }.Select(i => Gamma.FromShapeAndRate(i, i)).ToArray();
var varPriorVar = Variable.Observed(new Gamma());
var variance_EP = Variable <double> .Random(varPriorVar);
var x_ep = GaussianFromMeanAndVarianceSampleSizeModel(variance_EP, n, true, noisePrecision);
var ie_EP = new InferenceEngine();
ie_EP.ShowWarnings = false;
ie_EP.ShowProgress = false;
var ev = Variable.Bernoulli(.5);
var modelBlock = Variable.If(ev);
var variance_MC = Variable <double> .Random(varPriorVar);
var x_mc = GaussianFromMeanAndVarianceSampleSizeModel(variance_MC, n, true, noisePrecision);
modelBlock.CloseBlock();
var ie_MC = new InferenceEngine();
ie_MC.ShowWarnings = false;
ie_MC.ShowProgress = false;
var precision_VMP = Variable.GammaFromShapeAndRate(1, 1);
var x_vmp = GaussianFromMeanAndVarianceSampleSizeModel(precision_VMP, n, false, noisePrecision);
var ie_VMP = new InferenceEngine(new VariationalMessagePassing());
ie_VMP.ShowWarnings = false;
ie_VMP.ShowProgress = false;
var ie_EP_prec = new InferenceEngine();
ie_EP_prec.ShowWarnings = false;
ie_EP_prec.ShowProgress = false;
Console.WriteLine("var " + variancePriors.Select(i => "EP" + i.Shape).Aggregate((i, j) => i + " " + j) + " "
+ variancePriors.Select(i => "MC" + i.Shape).Aggregate((i, j) => i + " " + j) + " EPp VMP EMP");
for (int j = 0; j < 10; j++)
{
Rand.Restart(2);
//int N = (int)Math.Pow(10, j + 1);
double variance = System.Math.Exp(-5 + j);
var data = Enumerable.Range(0, Nvar.ObservedValue).Select(i => Gaussian.Sample(mean, 1.0 / variance) + Gaussian.Sample(0, noisePrecision)).ToArray();
x_ep.ObservedValue = data;
x_mc.ObservedValue = data;
x_vmp.ObservedValue = data;
var epMeans = variancePriors.Select(i =>
{
double res = double.NaN;
varPriorVar.ObservedValue = i;
try
{
res = ie_EP.Infer <Gamma>(variance_EP).GetMean();
}
catch
{
}
;
return(res);
}).ToArray();
var mcMeans = variancePriors.Select(p =>
{
double varianceSample = 2;
var ge = new GammaEstimator();
varPriorVar.ObservedValue = p;
Converter <double, double> f = vari =>
{
variance_MC.ObservedValue = vari;
return(ie_MC.Infer <Bernoulli>(ev).LogOdds);
};
int burnin = 1000, thin = 5, numSamples = 1000;
var samples = new double[numSamples];
for (int i = 0; i < burnin; i++)
{
varianceSample = NonconjugateVMP2Tests.SliceSampleUnivariate(varianceSample, f, lower_bound: 0);
}
for (int i = 0; i < numSamples; i++)
{
for (int k = 0; k < thin; k++)
{
varianceSample = NonconjugateVMP2Tests.SliceSampleUnivariate(varianceSample, f, lower_bound: 0);
}
samples[i] = varianceSample;
ge.Add(varianceSample);
}
return(samples.Sum() / numSamples);
}).ToArray();
double epMean2 = double.NaN;
try
{
epMean2 = ie_EP_prec.Infer <Gamma>(precision_VMP).GetMeanInverse();
}
catch
{
}
;
double vmpMean = ie_VMP.Infer <Gamma>(precision_VMP).GetMeanInverse();
var empiricalMean = data.Sum() / data.Length;
var empVar = data.Sum(o => o * o) / data.Length - empiricalMean * empiricalMean;
Console.Write("{0:G3} ", variance);
foreach (var i in epMeans)
{
Console.Write("{0:G3} ", i);
}
foreach (var i in mcMeans)
{
Console.Write("{0:G3} ", i);
}
Console.WriteLine("{0:G3} {1:G3} {2:G3}", epMean2, vmpMean, empVar);
}
}
// Commented out since this test is very slow and does not have any assertions
//[Fact]
internal void GaussianFromMeanAndVarianceVaryNoise()
{
double mean = 2.0, variance = 2.0;
var Nvar = Variable.Observed <int>(1);
var n = new Range(Nvar);
var noisePrecision = Variable.Array <double>(n);
var variance_EP = Variable.GammaFromShapeAndRate(1, 1);
var x_ep = GaussianPlusNoiseModel(variance_EP, n, true, noisePrecision);
var ie_EP = new InferenceEngine();
ie_EP.ShowWarnings = false;
ie_EP.ShowProgress = false;
var ev = Variable.Bernoulli(.5);
var modelBlock = Variable.If(ev);
var variance_MC = Variable.GammaFromShapeAndRate(1, 1);
var x_mc = GaussianPlusNoiseModel(variance_MC, n, true, noisePrecision);
modelBlock.CloseBlock();
var ie_MC = new InferenceEngine();
ie_MC.ShowWarnings = false;
ie_MC.ShowProgress = false;
var precision_VMP = Variable.GammaFromShapeAndRate(1, 1);
var x_vmp = GaussianPlusNoiseModel(precision_VMP, n, false, noisePrecision);
var ie_VMP = new InferenceEngine(new VariationalMessagePassing());
ie_VMP.ShowWarnings = false;
ie_VMP.ShowProgress = false;
Console.WriteLine("N EP MC VMP EMP");
for (int j = 0; j < 10; j++)
{
Rand.Restart(2);
//int N = (int)Math.Pow(10, j + 1);
int N = 10 * (j + 1);
var noiseP = Enumerable.Range(0, N).Select(i =>
{
if (i % 3 == 0)
{
return(.1);
}
if (i % 3 == 1)
{
return(1);
}
else
{
return(10);
}
}).ToArray();
var data = noiseP.Select(i => Gaussian.Sample(mean, 1.0 / variance) + Gaussian.Sample(0, i)).ToArray();
Nvar.ObservedValue = N;
noisePrecision.ObservedValue = noiseP;
x_ep.ObservedValue = data;
x_mc.ObservedValue = data;
x_vmp.ObservedValue = data;
double epMean = double.NaN;
try
{
epMean = ie_EP.Infer <Gamma>(variance_EP).GetMean();
}
catch
{
}
;
double vmpMean = ie_VMP.Infer <Gamma>(precision_VMP).GetMeanInverse();
double varianceSample = 2;
var ge = new GammaEstimator();
Converter <double, double> f = vari =>
{
variance_MC.ObservedValue = vari;
return(ie_MC.Infer <Bernoulli>(ev).LogOdds);
};
int burnin = 1000, thin = 5, numSamples = 1000;
var samples = new double[numSamples];
for (int i = 0; i < burnin; i++)
{
varianceSample = NonconjugateVMP2Tests.SliceSampleUnivariate(varianceSample, f, lower_bound: 0);
}
for (int i = 0; i < numSamples; i++)
{
for (int k = 0; k < thin; k++)
{
varianceSample = NonconjugateVMP2Tests.SliceSampleUnivariate(varianceSample, f, lower_bound: 0);
}
samples[i] = varianceSample;
ge.Add(varianceSample);
}
double mcMean = samples.Sum() / numSamples;
var empiricalMean = data.Sum() / data.Length;
var empVar = data.Sum(o => o * o) / data.Length - empiricalMean * empiricalMean;
Console.WriteLine(N + " " + epMean + " " + mcMean + " " + vmpMean + " " + empVar);
}
}
public static Gamma RateAverageConditional([SkipIfUniform] Gamma y, double shape, Gamma rate)
{
if (y.IsPointMass) return RateAverageConditional(y.Point, shape);
// q(y) = y^(a1-1) exp(-b1 y)
// q(b) = b^(a2-1) exp(-b2 b)
// f(y,b) = y^(a-1) b^a exp(-by)
// q(y) q(b) f(y,b) = y^(a+a1-2) b^(a+a2-1) exp(-b2 b - b1 y - b y)
// int over y = b^(a+a2-1) exp(-b2 b) / (b + b1)^(a+a1-1)
// this is dist of ratio Ga(a+1,1)/Ga(a1-2,1) times Ga(a2,b2) pdf
double max = shape/y.GetMean()*10;
int n = 1000;
double inc = max/n;
GammaEstimator est = new GammaEstimator();
for (int i = 0; i < n; i++) {
double b = (i+1)*inc;
double logp = (shape + rate.Shape - 1)*Math.Log(b) - b*rate.Rate - (shape + y.Shape - 1)*Math.Log(b + y.Rate);
est.Add(b, Math.Exp(logp));
}
Gamma post = est.GetDistribution(new Gamma());
//Console.WriteLine("y = {0}, shape = {1}, rate = {2}, post = {3}", y, shape, rate, post);
return post / rate;
//throw new NotSupportedException(NotSupportedMessage);
}
private void GaussianFromMeanAndVarianceTest(double mm, double vm, double mx, double vx, double a, double b)
{
Variable <bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
Variable <double> mean = Variable.GaussianFromMeanAndVariance(mm, vm).Named("mean");
Variable <double> variance = Variable.GammaFromShapeAndRate(a, b).Named("variance");
Variable <double> x = Variable.GaussianFromMeanAndVariance(mean, variance).Named("x");
Variable.ConstrainEqualRandom(x, new Gaussian(mx, vx));
block.CloseBlock();
InferenceEngine engine = new InferenceEngine();
engine.Compiler.RecommendedQuality = QualityBand.Experimental;
double evExpected;
Gaussian xExpected;
Gamma vExpected;
if (a == 1 || a == 2)
{
double c = System.Math.Sqrt(2 * b);
double m = c * (mx - mm);
double v = c * c * (vx + vm);
double Z, mu, m2u;
VarianceGammaTimesGaussianMoments(a, m, v, out Z, out mu, out m2u);
evExpected = System.Math.Log(Z * c);
double vu = m2u - mu * mu;
double r = Double.IsPositiveInfinity(vx) ? 1.0 : vx / (vx + vm);
double mp = r * (mu / c + mm) + (1 - r) * mx;
double vp = r * r * vu / (c * c) + r * vm;
xExpected = new Gaussian(mp, vp);
double Zplus1, Zplus2;
VarianceGammaTimesGaussianMoments(a + 1, m, v, out Zplus1, out mu, out m2u);
VarianceGammaTimesGaussianMoments(a + 2, m, v, out Zplus2, out mu, out m2u);
double vmp = a / b * Zplus1 / Z;
double vm2p = a * (a + 1) / (b * b) * Zplus2 / Z;
double vvp = vm2p - vmp * vmp;
vExpected = Gamma.FromMeanAndVariance(vmp, vvp);
}
else
{
int n = 1000000;
GaussianEstimator est = new GaussianEstimator();
GammaEstimator vEst = new GammaEstimator();
Gaussian xLike = new Gaussian(mx, vx);
for (int i = 0; i < n; i++)
{
double m = Gaussian.Sample(mm, 1 / vm);
double v = Rand.Gamma(a) / b;
double xSample = Gaussian.Sample(m, 1 / v);
double weight = System.Math.Exp(xLike.GetLogProb(xSample));
est.Add(xSample, weight);
vEst.Add(v, weight);
}
evExpected = System.Math.Log(est.mva.Count / n);
xExpected = est.GetDistribution(new Gaussian());
vExpected = vEst.GetDistribution(new Gamma());
}
double evActual = engine.Infer <Bernoulli>(evidence).LogOdds;
Console.WriteLine("evidence = {0} should be {1}", evActual, evExpected);
Gaussian xActual = engine.Infer <Gaussian>(x);
Console.WriteLine("x = {0} should be {1}", xActual, xExpected);
Gamma vActual = engine.Infer <Gamma>(variance);
Console.WriteLine("variance = {0} should be {1}", vActual, vExpected);
Assert.True(MMath.AbsDiff(evExpected, evActual, 1e-10) < 1e-4);
Assert.True(xExpected.MaxDiff(xActual) < 1e-4);
Assert.True(vExpected.MaxDiff(vActual) < 1e-4);
}
public static Gamma YAverageConditional(Gamma y, double shape, [SkipIfUniform] Gamma rate)
{
if (rate.IsPointMass) return YAverageConditional(shape, rate.Point);
// q(b) = b^(a2-1) exp(-b2 b)
// f(y,b) = y^(a-1) b^a exp(-by)
// q(b) f(y,b) = y^(a-1) b^(a+a2-1) exp(-b (y+b2))
// int over b = y^(a-1) / (y + b2)^(a+a2) = ratio of Ga(a,1)/Ga(a2,1/b2)
double max = shape/rate.GetMean()*10;
int n = 1000;
double inc = max/n;
GammaEstimator est = new GammaEstimator();
for (int i = 0; i < n; i++) {
double x = (i+1)*inc;
double logp = (shape + y.Shape - 2)*Math.Log(x) - x*y.Rate - (shape + rate.Shape)*Math.Log(x + rate.Rate);
est.Add(x, Math.Exp(logp));
}
Gamma post = est.GetDistribution(new Gamma());
return post / rate;
//throw new NotSupportedException(NotSupportedMessage);
}