/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaRatioOp_Laplace"]/message_doc[@name="BAverageConditional(Gamma, Gamma, Gamma, Gamma)"]/*'/>
public static Gamma BAverageConditional([SkipIfUniform] Gamma ratio, [Proper] Gamma A, [Proper] Gamma B, Gamma q)
{
if (ratio.IsPointMass)
{
// AAverageConditional computes (1st arg)/(2nd arg)
return(GammaRatioOp.BAverageConditional(ratio.Point, A));
}
if (B.IsPointMass)
{
throw new NotImplementedException();
}
if (q.IsUniform())
{
q = Q(ratio, A, B);
}
double x = q.GetMean();
double[] g = new double[] { x, 1, 0, 0 };
double bMean, bVariance;
GaussianOp_Laplace.LaplaceMoments(q, g, dlogfs(x, ratio, A), out bMean, out bVariance);
Gamma bMarginal = Gamma.FromMeanAndVariance(bMean, bVariance);
Gamma result = new Gamma();
result.SetToRatio(bMarginal, B, GammaProductOp_Laplace.ForceProper);
return(result);
}
internal void GaussianOpQ_Timing()
{
Gaussian X, Mean;
Gamma Precision;
Gamma q;
int n = 1;
X = Gaussian.FromNatural(3.9112579392580757, 11.631097473681082);
Mean = Gaussian.FromNatural(10.449696977834144, 5.5617978202886995);
Precision = Gamma.FromShapeAndRate(1.0112702817305146, 0.026480506235719053);
q = Gamma.FromMeanAndVariance(1, 1);
Stopwatch watch = new Stopwatch();
watch.Start();
for (int i = 0; i < n; i++)
{
GaussianOp_Laplace.Q(X, Mean, Precision, q);
}
watch.Stop();
Console.WriteLine("Q = {0}", watch.ElapsedTicks);
watch.Restart();
for (int i = 0; i < n; i++)
{
GaussianOp_Laplace.Q_Slow(X, Mean, Precision);
}
watch.Stop();
Console.WriteLine("Q2 = {0}", watch.ElapsedTicks);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaPowerProductOp_Laplace"]/message_doc[@name="BAverageConditional(GammaPower, GammaPower, GammaPower, Gamma, GammaPower)"]/*'/>
public static GammaPower BAverageConditional([SkipIfUniform] GammaPower product, [Proper] GammaPower A, [Proper] GammaPower B, Gamma q, GammaPower result)
{
if (B.Shape < A.Shape)
{
return(AAverageConditional(product, B, A, q, result));
}
if (A.IsPointMass)
{
return(GammaProductOp.BAverageConditional(product, A.Point, result));
}
if (B.IsPointMass)
{
return(GammaPower.Uniform(result.Power)); // TODO
}
if (product.IsUniform())
{
return(product);
}
if (q.IsUniform())
{
q = Q(product, A, B);
}
double bPoint = q.GetMean();
// derivatives of b
double[] bDerivatives = new double[] { bPoint, 1, 0, 0 };
double bMean, bVariance;
GaussianOp_Laplace.LaplaceMoments(q, bDerivatives, dlogfs(bPoint, product, A), out bMean, out bVariance);
GammaPower bMarginal = GammaPower.FromGamma(Gamma.FromMeanAndVariance(bMean, bVariance), result.Power);
result.SetToRatio(bMarginal, B, GammaProductOp_Laplace.ForceProper);
return(result);
}
private static void GetIQMoments(GammaPower product, GammaPower A, Gamma q, double qPoint, out double iqMean, out double iqVariance)
{
double iq = 1 / qPoint;
double iq2 = iq * iq;
double[] iqDerivatives = new double[] { iq, -iq2, 2 * iq2 * iq, -6 * iq2 * iq2 };
GaussianOp_Laplace.LaplaceMoments(q, iqDerivatives, dlogfs(qPoint, product, A), out iqMean, out iqVariance);
}
internal void StudentIsPositiveTest4()
{
double shape = 1;
Gamma precPrior = Gamma.FromShapeAndRate(shape, shape);
// mean=-1 causes improper messages
double mean = -1;
Gaussian meanPrior = Gaussian.PointMass(mean);
double evExpected;
Gaussian xExpected = StudentIsPositiveExact(mean, precPrior, out evExpected);
GaussianOp.ForceProper = false;
GaussianOp_Laplace.modified = true;
GaussianOp_Laplace.modified2 = true;
Gaussian xF = Gaussian.Uniform();
Gaussian xB = Gaussian.Uniform();
Gamma q = GaussianOp_Laplace.QInit();
double r0 = 0.38;
r0 = 0.1;
for (int iter = 0; iter < 20; iter++)
{
q = GaussianOp_Laplace.Q(xB, meanPrior, precPrior, q);
//xF = GaussianOp_Laplace.SampleAverageConditional(xB, meanPrior, precPrior, q);
xF = Gaussian.FromMeanAndPrecision(mean, r0);
xB = IsPositiveOp.XAverageConditional(true, xF);
Console.WriteLine("xF = {0} xB = {1}", xF, xB);
}
Console.WriteLine("x = {0} should be {1}", xF * xB, xExpected);
double[] precs = EpTests.linspace(1e-3, 5, 100);
double[] evTrue = new double[precs.Length];
double[] evApprox = new double[precs.Length];
double[] evApprox2 = new double[precs.Length];
//r0 = q.GetMean();
double sum = 0, sum2 = 0;
for (int i = 0; i < precs.Length; i++)
{
double r = precs[i];
Gaussian xFt = Gaussian.FromMeanAndPrecision(mean, r);
evTrue[i] = IsPositiveOp.LogAverageFactor(true, xFt) + precPrior.GetLogProb(r);
evApprox[i] = IsPositiveOp.LogAverageFactor(true, xF) + precPrior.GetLogProb(r) + xB.GetLogAverageOf(xFt) - xB.GetLogAverageOf(xF);
evApprox2[i] = IsPositiveOp.LogAverageFactor(true, xF) + precPrior.GetLogProb(r0) + q.GetLogProb(r) - q.GetLogProb(r0);
sum += System.Math.Exp(evApprox[i]);
sum2 += System.Math.Exp(evApprox2[i]);
}
Console.WriteLine("r0 = {0}: {1} {2} {3}", r0, sum, sum2, q.GetVariance() + System.Math.Pow(r0 - q.GetMean(), 2));
//TODO: change path for cross platform using
using (var writer = new MatlabWriter(@"..\..\..\Tests\student.mat"))
{
writer.Write("z", evTrue);
writer.Write("z2", evApprox);
writer.Write("z3", evApprox2);
writer.Write("precs", precs);
}
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaRatioOp_Laplace"]/message_doc[@name="AAverageConditional(Gamma, Gamma, Gamma, Gamma)"]/*'/>
public static Gamma AAverageConditional(Gamma ratio, Gamma A, [SkipIfUniform] Gamma B, Gamma q)
{
if (ratio.IsPointMass)
{
return(GammaRatioOp.AAverageConditional(ratio.Point, B));
}
if (B.IsPointMass)
{
return(GammaRatioOp.AAverageConditional(ratio, B.Point));
}
if (A.IsPointMass)
{
throw new NotImplementedException();
}
double aMean, aVariance;
double x = q.GetMean();
double x2 = x * x;
double p = 1 / (ratio.Rate + A.Rate * x);
double p2 = p * p;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(ratio.Shape, A.Shape);
// aMean = shape2/(y_r/b + a_r)
// aVariance = E[shape2*(shape2+1)/(y_r/b + a_r)^2] - aMean^2 = var(shape2/(y_r/b + a_r)) + E[shape2/(y_r/b + a_r)^2]
// = shape2^2*var(1/(y_r/b + a_r)) + shape2*(var(1/(y_r/b + a_r)) + (aMean/shape2)^2)
double[] g = new double[] { x *p, ratio.Rate *p2, -2 *p2 *p *ratio.Rate *A.Rate, 6 *p2 *p2 *ratio.Rate *A.Rate *A.Rate };
double pMean, pVariance;
GaussianOp_Laplace.LaplaceMoments(q, g, dlogfs(x, ratio, A), out pMean, out pVariance);
aMean = shape2 * pMean;
aVariance = shape2 * shape2 * pVariance + shape2 * (pVariance + pMean * pMean);
Gamma aMarginal = Gamma.FromMeanAndVariance(aMean, aVariance);
Gamma result = new Gamma();
result.SetToRatio(aMarginal, A, GammaProductOp_Laplace.ForceProper);
if (double.IsNaN(result.Shape) || double.IsNaN(result.Rate))
{
throw new InferRuntimeException("result is nan");
}
return(result);
}
public void GaussianOpPrecision()
{
Gamma precMsg, precMsg2;
Gaussian X, Mean;
Gamma Precision;
X = Gaussian.FromNatural(-1.5098177152950143E-09, 1.061649960537027E-168);
Mean = Gaussian.FromNatural(-3.6177299471249587, 0.11664740799025652);
Precision = Gamma.FromShapeAndRate(306.39423695125572, 1.8326832031565403E+170);
precMsg = Gamma.PointMass(0);
precMsg2 = GaussianOp_Slow.PrecisionAverageConditional(X, Mean, Precision);
Assert.True(precMsg.MaxDiff(precMsg2) < 1e-4);
precMsg2 = GaussianOp.PrecisionAverageConditional(X, Mean, Precision);
Assert.True(precMsg.MaxDiff(precMsg2) < 1e-4);
X = Gaussian.FromNatural(-0.55657497231637854, 6.6259783218464713E-141);
Mean = Gaussian.FromNatural(-2.9330116542965374, 0.07513822741674292);
Precision = Gamma.FromShapeAndRate(308.8184220331475, 4.6489382805051884E+142);
precMsg = Gamma.FromShapeAndRate(1.5000000000000628, 3.5279086383286634E+279);
precMsg2 = GaussianOp_Slow.PrecisionAverageConditional(X, Mean, Precision);
Assert.True(precMsg.MaxDiff(precMsg2) < 1e-4);
precMsg2 = GaussianOp.PrecisionAverageConditional(X, Mean, Precision);
Assert.True(precMsg.MaxDiff(precMsg2) < 1e-4);
X = Gaussian.FromNatural(0, 1.0705890985886898E-153);
Mean = Gaussian.PointMass(0);
Precision = Gamma.FromShapeAndRate(1.6461630749684018, 1.0021354807958952E+153);
precMsg = Gamma.FromShapeAndRate(1.3230815374839406, 5.7102212927459039E+151);
precMsg2 = GaussianOp_Slow.PrecisionAverageConditional(X, Mean, Precision);
Assert.True(precMsg.MaxDiff(precMsg2) < 1e-4);
precMsg2 = GaussianOp.PrecisionAverageConditional(X, Mean, Precision);
Assert.True(precMsg.MaxDiff(precMsg2) < 1e-4);
GaussianOp.PrecisionAverageConditional(Gaussian.FromNatural(0, 0.00849303091340374), Gaussian.FromNatural(0.303940178036662, 0.0357912415805232),
Gamma.FromNatural(0.870172077263786 - 1, 0.241027170904459));
GaussianOp.PrecisionAverageConditional(Gaussian.FromNatural(0, 0.932143343115292), Gaussian.FromNatural(0.803368837946732, 0.096549750816333),
Gamma.FromNatural(0.63591693650741 - 1, 0.728459389753854));
GaussianOp.PrecisionAverageConditional(Gaussian.FromNatural(0, 0.799724777601531), Gaussian.FromNatural(0.351882387116497, 0.0795619408970522),
Gamma.FromNatural(0.0398852019756498 - 1, 0.260567798400562));
GaussianOp.PrecisionAverageConditional(Gaussian.FromNatural(0, 0.826197353576402), Gaussian.FromNatural(0.655970732055591, 0.125333868956814),
Gamma.FromNatural(0.202543332801453 - 1, 0.147645744563847));
precMsg = GaussianOp.PrecisionAverageConditional(new Gaussian(-6.235e+207, 1.947e+209), Gaussian.PointMass(11), Gamma.PointMass(7));
Assert.True(!double.IsNaN(precMsg.Rate));
Gaussian X0 = Gaussian.FromMeanAndVariance(3, 0.5);
Gaussian Mean0 = Gaussian.FromMeanAndVariance(7, 1.0 / 3);
Gamma Precision0 = Gamma.FromShapeAndScale(3, 3);
precMsg = GaussianOp_Slow.PrecisionAverageConditional(Gaussian.FromNatural(0.010158033515400506, 0.0041117304509528533),
Gaussian.FromNatural(33.157651455559929, 13.955304749880149),
Gamma.FromShapeAndRate(7.1611372018172794, 1.8190207317123008));
precMsg = GaussianOp_Slow.PrecisionAverageConditional(Gaussian.FromNatural(-0.020177353724675218, 0.0080005002339157711),
Gaussian.FromNatural(-12.303440746896294, 4.6439574387849714),
Gamma.FromShapeAndRate(5.6778922774773992, 1.0667129560350435));
precMsg = GaussianOp_Slow.PrecisionAverageConditional(Gaussian.PointMass(248), Gaussian.FromNatural(0.099086933095776319, 0.00032349393599347853),
Gamma.FromShapeAndRate(0.001, 0.001));
precMsg2 = GaussianOp.PrecisionAverageConditional_slow(Gaussian.PointMass(248), Gaussian.FromNatural(0.099086933095776319, 0.00032349393599347853),
Gamma.FromShapeAndRate(0.001, 0.001));
Assert.True(precMsg.MaxDiff(precMsg2) < 0.3);
precMsg =
GaussianOp_Slow.PrecisionAverageConditional(Gaussian.FromNatural(-0.21769764449791806, 0.0000024898838689952023),
Gaussian.FromNatural(0, 0.5), Gamma.FromShapeAndRate(5, 5));
precMsg2 =
GaussianOp.PrecisionAverageConditional_slow(Gaussian.FromNatural(-0.21769764449791806, 0.0000024898838689952023),
Gaussian.FromNatural(0, 0.5), Gamma.FromShapeAndRate(5, 5));
//Console.WriteLine("{0} should be {1}", precMsg2, precMsg);
Assert.True(precMsg.MaxDiff(precMsg2) < 1e-4);
Gamma precMsg3 =
GaussianOp_Laplace.PrecisionAverageConditional_slow(Gaussian.FromNatural(-0.21769764449791806, 0.0000024898838689952023),
Gaussian.FromNatural(0, 0.5), Gamma.FromShapeAndRate(5, 5));
precMsg2 =
GaussianOp.PrecisionAverageConditional(Gaussian.FromNatural(-0.21769764449791806, 0.0000024898838689952023),
Gaussian.FromNatural(0, 0.5), Gamma.FromShapeAndRate(5, 5));
//Console.WriteLine("{0} should be {1}", precMsg2, precMsg);
Assert.True(precMsg.MaxDiff(precMsg2) < 1e-4);
Assert.True(GaussianOp.PrecisionAverageConditional_slow(Gaussian.FromNatural(-2.3874057896477092, 0.0070584383295080044),
Gaussian.FromNatural(1.3999879871144227, 0.547354438587195), Gamma.FromShapeAndRate(3, 1))
.MaxDiff(Gamma.FromShapeAndRate(1.421, 55546)) < 10);
// Unknown precision
if (GaussianOp.ForceProper)
{
Assert.True(GaussianOp.PrecisionAverageConditional_slow(X0, Mean0, Precision0).MaxDiff(Gamma.FromShapeAndRate(1, 0.3632)) < 1e-4);
}
else
{
Assert.True(GaussianOp.PrecisionAverageConditional_slow(X0, Mean0, Precision0).MaxDiff(Gamma.FromShapeAndRate(-0.96304, -0.092572)) < 1e-4);
}
if (GaussianOp.ForceProper)
{
Assert.True(GaussianOp.PrecisionAverageConditional_slow(Gaussian.PointMass(3.0), Mean0, Precision0).MaxDiff(Gamma.FromShapeAndRate(1, 4.13824)) < 1e-4);
}
else
{
Assert.True(GaussianOp.PrecisionAverageConditional_slow(Gaussian.PointMass(3.0), Mean0, Precision0).MaxDiff(Gamma.FromShapeAndRate(-0.24693, 2.2797)) < 1e-4);
}
Assert.True(GaussianOp.PrecisionAverageConditional(3.0, 7.0).MaxDiff(Gamma.FromShapeAndRate(1.5, 8.0)) < 1e-4);
Assert.True(GaussianOp.PrecisionAverageConditional_slow(new Gaussian(), Gaussian.PointMass(7.0), Precision0).MaxDiff(Gamma.FromShapeAndRate(1.0, 0.0)) < 1e-4);
}
private static void GetQMoments(GammaPower product, GammaPower A, Gamma q, double qPoint, out double qMean, out double qVariance)
{
double[] qDerivatives = new double[] { qPoint, 1, 0, 0 };
GaussianOp_Laplace.LaplaceMoments(q, qDerivatives, dlogfs(qPoint, product, A), out qMean, out qVariance);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaPowerProductOp_Laplace"]/message_doc[@name="AAverageConditional(GammaPower, GammaPower, GammaPower, Gamma, GammaPower)"]/*'/>
public static GammaPower AAverageConditional([SkipIfUniform] GammaPower product, GammaPower A, [SkipIfUniform] GammaPower B, Gamma q, GammaPower result)
{
if (B.Shape < A.Shape)
{
return(BAverageConditional(product, B, A, q, result));
}
if (B.IsPointMass)
{
return(GammaProductOp.AAverageConditional(product, B.Point, result));
}
if (A.IsPointMass)
{
return(GammaPower.Uniform(A.Power)); // TODO
}
if (product.IsUniform())
{
return(product);
}
double qPoint = q.GetMean();
GammaPower aMarginal;
if (product.IsPointMass)
{
// Z = int Ga(y/q; s, r)/q Ga(q; q_s, q_r) dq
// E[a] = E[product/q]
// E[a^2] = E[product^2/q^2]
// aVariance = E[a^2] - aMean^2
double productPoint = product.Point;
if (productPoint == 0)
{
aMarginal = GammaPower.PointMass(0, result.Power);
}
else
{
double iqMean, iqVariance;
GetIQMoments(product, A, q, qPoint, out iqMean, out iqVariance);
double aMean = productPoint * iqMean;
double aVariance = productPoint * productPoint * iqVariance;
aMarginal = GammaPower.FromGamma(Gamma.FromMeanAndVariance(aMean, aVariance), result.Power);
}
}
else
{
if (double.IsPositiveInfinity(product.Rate))
{
return(GammaPower.PointMass(0, result.Power));
}
if (A.Power != product.Power)
{
throw new NotSupportedException($"A.Power ({A.Power}) != product.Power ({product.Power})");
}
if (B.Power != product.Power)
{
throw new NotSupportedException($"B.Power ({B.Power}) != product.Power ({product.Power})");
}
double r = product.Rate;
double g = 1 / (qPoint * r + A.Rate);
double g2 = g * g;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(product.Shape, A.Shape) + (1 - A.Power);
// From above:
// a^(y_s-pa + a_s-1) exp(-(y_r b + a_r)*a)
if (shape2 > 2)
{
// Compute the moments of a^(-1/a.Power)
// Here q = b^(1/b.Power)
// E[a^(-1/a.Power)] = E[(q r + a_r)/(shape2-1)]
// var(a^(-1/a.Power)) = E[(q r + a_r)^2/(shape2-1)/(shape2-2)] - E[a^(-1/a.Power)]^2
// = (var(q r + a_r) + E[(q r + a_r)]^2)/(shape2-1)/(shape2-2) - E[(q r + a_r)]^2/(shape2-1)^2
// = var(q r + a_r)/(shape2-1)/(shape2-2) + E[(q r + a_r)/(shape2-1)]^2/(shape2-2)
// TODO: share this computation with BAverageConditional
double qMean, qVariance;
GetQMoments(product, A, q, qPoint, out qMean, out qVariance);
double iaMean = (qMean * r + A.Rate) / (shape2 - 1);
//double iaVariance = (qVariance * r2 / (shape2 - 1) + iaMean * iaMean) / (shape2 - 2);
// shape = mean^2/variance + 2
//double iaVarianceOverMeanSquared = (qVariance / (shape2 - 1) * r / iaMean * r / iaMean + 1) / (shape2 - 2);
double iaVarianceOverMeanSquared = (qVariance * (shape2 - 1) / (qMean + A.Rate / r) / (qMean + A.Rate / r) + 1) / (shape2 - 2);
//GammaPower iaMarginal = GammaPower.FromMeanAndVariance(iaMean, iaVariance, -1);
GammaPower iaMarginal = InverseGammaFromMeanAndVarianceOverMeanSquared(iaMean, iaVarianceOverMeanSquared);
if (iaMarginal.IsUniform())
{
if (result.Power > 0)
{
return(GammaPower.PointMass(0, result.Power));
}
else
{
return(GammaPower.Uniform(result.Power));
}
}
else
{
aMarginal = GammaPower.FromShapeAndRate(iaMarginal.Shape, iaMarginal.Rate, result.Power);
}
bool check = false;
if (check)
{
// Importance sampling
MeanVarianceAccumulator mvaB = new MeanVarianceAccumulator();
MeanVarianceAccumulator mvaInvA = new MeanVarianceAccumulator();
Gamma bPrior = Gamma.FromShapeAndRate(B.Shape, B.Rate);
q = bPrior;
double shift = (product.Shape - product.Power) * Math.Log(qPoint) - shape2 * Math.Log(A.Rate + qPoint * r) + bPrior.GetLogProb(qPoint) - q.GetLogProb(qPoint);
for (int i = 0; i < 1000000; i++)
{
double bSample = q.Sample();
// logf = (y_s-y_p)*log(b) - (s+y_s-pa)*log(r + b*y_r)
double logf = (product.Shape - product.Power) * Math.Log(bSample) - shape2 * Math.Log(A.Rate + bSample * r) + bPrior.GetLogProb(bSample) - q.GetLogProb(bSample);
double weight = Math.Exp(logf - shift);
mvaB.Add(bSample, weight);
double invA = (bSample * r + A.Rate) / (shape2 - 1);
mvaInvA.Add(invA, weight);
}
Trace.WriteLine($"b = {mvaB}, {qMean}, {qVariance}");
Trace.WriteLine($"invA = {mvaInvA} {mvaInvA.Variance * (shape2 - 1) / (shape2 - 2) + mvaInvA.Mean * mvaInvA.Mean / (shape2 - 2)}, {iaMean}, {iaVarianceOverMeanSquared * iaMean * iaMean}");
Trace.WriteLine($"aMarginal = {aMarginal}");
}
}
else
{
// Compute the moments of a^(1/a.Power)
// aMean = shape2/(b y_r + a_r)
// aVariance = E[shape2*(shape2+1)/(b y_r + a_r)^2] - aMean^2 = var(shape2/(b y_r + a_r)) + E[shape2/(b y_r + a_r)^2]
// = shape2^2*var(1/(b y_r + a_r)) + shape2*(var(1/(b y_r + a_r)) + (aMean/shape2)^2)
double r2 = r * r;
double[] gDerivatives = new double[] { g, -r * g2, 2 * g2 * g * r2, -6 * g2 * g2 * r2 * r };
double gMean, gVariance;
GaussianOp_Laplace.LaplaceMoments(q, gDerivatives, dlogfs(qPoint, product, A), out gMean, out gVariance);
double aMean = shape2 * gMean;
double aVariance = shape2 * shape2 * gVariance + shape2 * (gVariance + gMean * gMean);
aMarginal = GammaPower.FromGamma(Gamma.FromMeanAndVariance(aMean, aVariance), result.Power);
}
}
result.SetToRatio(aMarginal, A, GammaProductOp_Laplace.ForceProper);
if (double.IsNaN(result.Shape) || double.IsNaN(result.Rate))
{
throw new InferRuntimeException("result is nan");
}
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaPowerProductOp_Laplace"]/message_doc[@name="ProductAverageConditional(GammaPower, GammaPower, GammaPower, Gamma, GammaPower)"]/*'/>
public static GammaPower ProductAverageConditional(GammaPower product, [Proper] GammaPower A, [SkipIfUniform] GammaPower B, Gamma q, GammaPower result)
{
if (B.Shape < A.Shape)
{
return(ProductAverageConditional(product, B, A, q, result));
}
if (B.IsPointMass)
{
return(GammaProductOp.ProductAverageConditional(A, B.Point));
}
if (B.IsUniform())
{
return(GammaPower.Uniform(result.Power));
}
if (A.IsPointMass)
{
return(GammaProductOp.ProductAverageConditional(A.Point, B));
}
if (product.IsPointMass)
{
return(GammaPower.Uniform(result.Power)); // TODO
}
if (A.Power != product.Power)
{
throw new NotSupportedException($"A.Power ({A.Power}) != product.Power ({product.Power})");
}
if (B.Power != product.Power)
{
throw new NotSupportedException($"B.Power ({B.Power}) != product.Power ({product.Power})");
}
if (A.Rate == 0)
{
if (B.Rate == 0)
{
return(GammaPower.FromShapeAndRate(Math.Min(A.Shape, B.Shape), 0, result.Power));
}
else
{
return(A);
}
}
if (B.Rate == 0)
{
return(B);
}
double qPoint = q.GetMean();
double r = product.Rate;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(product.Shape, A.Shape) + (1 - A.Power);
GammaPower productMarginal;
// threshold ensures 6/qPoint^4 does not overflow
double threshold = Math.Sqrt(Math.Sqrt(6 / double.MaxValue));
if (shape2 > 2 && result.Power < 0 && qPoint > threshold)
{
// Compute the moments of product^(-1/product.Power)
// Here q = b^(1/b.Power)
// E[a^(-1/a.Power) b^(-1/b.Power)] = E[(q r + a_r)/(shape2-1)/q]
// var(a^(-1/a.Power) b^(-1/b.Power)) = E[(q r + a_r)^2/(shape2-1)/(shape2-2)/q^2] - E[a^(-1/a.Power) b^(-1/b.Power)]^2
// = (var((q r + a_r)/q) + E[(q r + a_r)/q]^2)/(shape2-1)/(shape2-2) - E[(q r + a_r)/q]^2/(shape2-1)^2
// = var((q r + a_r)/q)/(shape2-1)/(shape2-2) + E[(q r + a_r)/(shape2-1)/q]^2/(shape2-2)
double iqMean, iqVariance;
GetIQMoments(product, A, q, qPoint, out iqMean, out iqVariance);
double ipMean = (r + A.Rate * iqMean) / (shape2 - 1);
double ipVariance = (iqVariance * A.Rate * A.Rate / (shape2 - 1) + ipMean * ipMean) / (shape2 - 2);
// TODO: use ipVarianceOverMeanSquared
GammaPower ipMarginal = GammaPower.FromMeanAndVariance(ipMean, ipVariance, -1);
if (ipMarginal.IsUniform())
{
return(GammaPower.Uniform(result.Power));
}
else
{
productMarginal = GammaPower.FromShapeAndRate(ipMarginal.Shape, ipMarginal.Rate, result.Power);
}
bool check = false;
if (check)
{
// Importance sampling
MeanVarianceAccumulator mvaInvQ = new MeanVarianceAccumulator();
MeanVarianceAccumulator mvaInvProduct = new MeanVarianceAccumulator();
Gamma qPrior = Gamma.FromShapeAndRate(B.Shape, B.Rate);
double shift = (product.Shape - product.Power) * Math.Log(qPoint) - shape2 * Math.Log(A.Rate + qPoint * r) + qPrior.GetLogProb(qPoint) - q.GetLogProb(qPoint);
for (int i = 0; i < 1000000; i++)
{
double qSample = q.Sample();
// logf = (y_s-y_p)*log(b) - (s+y_s-pa)*log(r + b*y_r)
double logf = (product.Shape - product.Power) * Math.Log(qSample) - shape2 * Math.Log(A.Rate + qSample * r) + qPrior.GetLogProb(qSample) - q.GetLogProb(qSample);
double weight = Math.Exp(logf - shift);
mvaInvQ.Add(1 / qSample, weight);
double invProduct = (r + A.Rate / qSample) / (shape2 - 1);
mvaInvProduct.Add(invProduct, weight);
}
Trace.WriteLine($"invQ = {mvaInvQ}, {iqMean}, {iqVariance}");
Trace.WriteLine($"invProduct = {mvaInvProduct}");
Trace.WriteLine($"invA = {mvaInvProduct.Variance * (shape2 - 1) / (shape2 - 2) + mvaInvProduct.Mean * mvaInvProduct.Mean / (shape2 - 2)}, {ipMean}, {ipVariance}");
Trace.WriteLine($"productMarginal = {productMarginal}");
}
}
else
{
// Compute the moments of y = product^(1/product.Power)
// yMean = E[shape2*b/(b y_r + a_r)]
// yVariance = E[shape2*(shape2+1)*b^2/(b y_r + a_r)^2] - yMean^2
// = var(shape2*b/(b y_r + a_r)) + E[shape2*b^2/(b y_r + a_r)^2]
// = shape2^2*var(b/(b y_r + a_r)) + shape2*(var(b/(b y_r + a_r)) + (yMean/shape2)^2)
// Let g = b/(b y_r + a_r)
double denom = qPoint * r + A.Rate;
double denom2 = denom * denom;
double rOverDenom = r / denom;
double[] gDerivatives = (denom == 0)
? new double[] { 0, 0, 0, 0 }
: new double[] { qPoint / denom, A.Rate / denom2, -2 * A.Rate / denom2 * rOverDenom, 6 * A.Rate / denom2 * rOverDenom * rOverDenom };
double gMean, gVariance;
GaussianOp_Laplace.LaplaceMoments(q, gDerivatives, dlogfs(qPoint, product, A), out gMean, out gVariance);
double yMean = shape2 * gMean;
double yVariance = shape2 * shape2 * gVariance + shape2 * (gVariance + gMean * gMean);
productMarginal = GammaPower.FromGamma(Gamma.FromMeanAndVariance(yMean, yVariance), result.Power);
}
result.SetToRatio(productMarginal, product, GammaProductOp_Laplace.ForceProper);
if (double.IsNaN(result.Shape) || double.IsNaN(result.Rate))
{
throw new InferRuntimeException("result is nan");
}
return(result);
}
