/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaRatioOp_Laplace"]/message_doc[@name="LogAverageFactor(Gamma, Gamma, Gamma, Gamma)"]/*'/>
public static double LogAverageFactor(Gamma ratio, Gamma A, Gamma B, Gamma q)
{
if (B.IsPointMass)
{
return(GammaRatioOp.LogAverageFactor(ratio, A, B.Point));
}
if (A.IsPointMass)
{
// int Ga(a/b; y_s, y_r) Ga(b; s, r) db
// = int a^(y_s-1) b^(-y_s+1) exp(-a/b y_r) y_r^(y_s)/Gamma(y_s) Ga(b; s, r) db
// = a^(y_s-1) y_r^(y_s)/Gamma(y_s)/Gamma(s) r^s int b^(s-y_s) exp(-a/b y_r -rb) db
// this requires BesselK
throw new NotImplementedException();
}
if (ratio.IsPointMass)
{
return(GammaRatioOp.LogAverageFactor(ratio.Point, A, B));
}
// int Ga(a/b; y_s, y_r) Ga(a; s, r) da = b^s / (br + y_r)^(y_s + s-1) Gamma(y_s+s-1)
double x = q.GetMean();
double shape = A.Shape;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(ratio.Shape, shape);
double logf = shape * Math.Log(x) - shape2 * Math.Log(x * A.Rate + ratio.Rate) +
MMath.GammaLn(shape2) - A.GetLogNormalizer() - ratio.GetLogNormalizer();
double logz = logf + B.GetLogProb(x) - q.GetLogProb(x);
return(logz);
}
public void GammaFromShapeAndRateOpTest2()
{
Gamma sample, rate, result;
double prevDiff;
double shape = 3;
sample = Gamma.FromShapeAndRate(4, 5);
shape = 0.1;
rate = Gamma.FromShapeAndRate(0.1, 0.1);
result = GammaFromShapeAndRateOp_Slow.RateAverageConditional(sample, shape, rate);
Console.WriteLine(result);
shape = 3;
rate = Gamma.PointMass(2);
result = GammaFromShapeAndRateOp_Slow.RateAverageConditional(sample, shape, rate);
Console.WriteLine("{0}: {1}", rate, result);
prevDiff = double.PositiveInfinity;
for (int i = 10; i < 50; i++)
{
double v = System.Math.Pow(0.1, i);
rate = Gamma.FromMeanAndVariance(2, v);
Gamma result2 = GammaFromShapeAndRateOp_Slow.RateAverageConditional(sample, shape, rate);
double diff = result.MaxDiff(result2);
Console.WriteLine("{0}: {1} (diff={2})", rate, result2, diff.ToString("g4"));
Assert.True(diff <= prevDiff || diff < 1e-10);
prevDiff = diff;
}
}
public static Gamma Q(Gamma ratio, [Proper] Gamma A, [Proper] Gamma B)
{
if (B.IsPointMass)
{
return(B);
}
if (ratio.IsPointMass)
{
return(GammaRatioOp.BAverageConditional(ratio.Point, A) * B);
}
double shape1 = A.Shape + B.Shape;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(A.Shape, ratio.Shape);
// find the maximum of the factor marginalized over Ratio and A, times B
// logf = s*log(b) - (s+ya-1)*log(b*r + yb)
// let b' = b*r and maximize over b'
double x = GammaFromShapeAndRateOp_Slow.FindMaximum(shape1, shape2, ratio.Rate, B.Rate / A.Rate);
if (x == 0)
{
return(B);
}
x /= A.Rate;
double[] dlogfss = dlogfs(x, ratio, A);
double dlogf = dlogfss[0];
double ddlogf = dlogfss[1];
return(GammaFromShapeAndRateOp_Laplace.GammaFromDerivatives(B, x, dlogf, ddlogf));
}
public void GammaFromShapeAndRateOpTest4()
{
Gamma sample = Gamma.FromShapeAndRate(2, 0);
Gamma rate = Gamma.FromShapeAndRate(4, 1);
double shape = 1;
Gamma rateExpected = GammaFromShapeAndRateOp_Slow.RateAverageConditional(sample, shape, rate);
Gamma q = GammaFromShapeAndRateOp_Laplace.Q(sample, shape, rate);
Gamma rateActual = GammaFromShapeAndRateOp_Laplace.RateAverageConditional(sample, shape, rate, q);
Assert.True(rateExpected.MaxDiff(rateActual) < 1e-4);
Gamma to_sample2 = GammaFromShapeAndRateOp_Laplace.SampleAverageConditional(sample, shape, rate, q);
double evExpected = GammaFromShapeAndRateOp_Laplace.LogEvidenceRatio(sample, shape, rate, to_sample2, q);
Console.WriteLine("sample = {0} to_sample = {1} evidence = {2}", sample, to_sample2, evExpected);
for (int i = 40; i < 41; i++)
{
sample.Rate = System.Math.Pow(0.1, i);
q = GammaFromShapeAndRateOp_Laplace.Q(sample, shape, rate);
Gamma to_sample = GammaFromShapeAndRateOp_Laplace.SampleAverageConditional(sample, shape, rate, q);
double evActual = GammaFromShapeAndRateOp_Laplace.LogEvidenceRatio(sample, shape, rate, to_sample, q);
Console.WriteLine("sample = {0} to_sample = {1} evidence = {2}", sample, to_sample, evActual);
Assert.True(to_sample2.MaxDiff(to_sample2) < 1e-4);
Assert.True(MMath.AbsDiff(evExpected, evActual) < 1e-4);
}
}
/**I confirmed that the EP using this factor and using 2 Gamma factor
* yields exactly the same result.*/
// http://research.microsoft.com/en-us/um/cambridge/projects/infernet/docs/How%20to%20add%20a%20new%20factor%20and%20message%20operators.aspx
public static Gamma PrecisionAverageConditional(Gamma precision)
{
// This is the default operator.
Console.WriteLine("{0}.PrecisionAverageConditional: precision {1}",
typeof(CGFacOp), precision);
return(GammaFromShapeAndRateOp_Slow.SampleAverageConditional(precision,
CGParams.Shape2, r2FwMsg));
}
/**I confirmed that the EP using this factor and using 2 Gamma factos
* yields exactly the same result.*/
// http://research.microsoft.com/en-us/um/cambridge/projects/infernet/docs/How%20to%20add%20a%20new%20factor%20and%20message%20operators.aspx
public static Gamma PrecisionAverageConditional(Gamma precision, double s1,
double r1, double s2)
{
Console.WriteLine("{0}.PrecisionAverageConditional: precision {1}",
typeof(CGFac4Op), precision);
Gamma r2FwMsg = Gamma.FromShapeAndRate(s1, r1);
return(GammaFromShapeAndRateOp_Slow.SampleAverageConditional(precision,
s2, r2FwMsg));
}
// derivatives of the factor marginalized over Ratio and A
private static double[] dlogfs(double b, Gamma ratio, Gamma A)
{
if (ratio.IsPointMass)
{
// int delta(a/b - y) Ga(a; s, r) da = int b delta(a' - y) Ga(a'b; s, r) da' = b Ga(y*b; s, r)
// logf = s*log(b) - y*r*b
double p = 1 / b;
double p2 = p * p;
double shape = A.Shape;
double dlogf = shape * p - ratio.Point * A.Rate;
double ddlogf = -shape * p2;
double dddlogf = 2 * shape * p * p2;
double d4logf = -6 * shape * p2 * p2;
return(new double[] { dlogf, ddlogf, dddlogf, d4logf });
}
else if (A.IsPointMass)
{
// Ga(a/b; y_a, y_b)
// logf = (1-y_a)*log(b) - y_b*a/b
double p = 1 / b;
double p2 = p * p;
double c = ratio.Rate * A.Point;
double shape = 1 - ratio.Shape;
double dlogf = shape * p + c * p2;
double ddlogf = -shape * p2 - 2 * c * p * p2;
double dddlogf = 2 * shape * p * p2 + 6 * c * p2 * p2;
double d4logf = -6 * shape * p2 * p2 - 24 * c * p2 * p2 * p;
return(new double[] { dlogf, ddlogf, dddlogf, d4logf });
}
else
{
// int Ga(a/b; y_s, y_r) Ga(a; s, r) da = y_r^(y_s) r^s b^s / (br + y_r)^(y_s + s-1)
// logf = s*log(b) - (s+y_s-1)*log(b*r + y_r)
double r = A.Rate;
double r2 = r * r;
double p = 1 / (b * r + ratio.Rate);
double p2 = p * p;
double b2 = b * b;
double shape = A.Shape;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(ratio.Shape, shape);
double dlogf = shape / b - shape2 * p;
double ddlogf = -shape / b2 + shape2 * p2 * r;
double dddlogf = 2 * shape / (b * b2) - 2 * shape2 * p * p2 * r2;
double d4logf = -6 * shape / (b2 * b2) + 6 * shape2 * p2 * p2 * r * r2;
return(new double[] { dlogf, ddlogf, dddlogf, d4logf });
}
}
/// <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 GammaFromShapeAndRateOpTest5()
{
Gamma sample;
Gamma rate;
double shape = 1;
Gamma q, sampleExpected, sampleActual;
sample = Gamma.FromShapeAndRate(101, 6.7234079315458819E-154);
rate = Gamma.FromShapeAndRate(1, 1);
q = GammaFromShapeAndRateOp_Laplace.Q(sample, shape, rate);
Console.WriteLine(q);
Assert.True(!double.IsNaN(q.Rate));
sampleExpected = GammaFromShapeAndRateOp_Slow.SampleAverageConditional(sample, shape, rate);
sampleActual = GammaFromShapeAndRateOp_Laplace.SampleAverageConditional(sample, shape, rate, q);
Console.WriteLine("sample = {0} should be {1}", sampleActual, sampleExpected);
Assert.True(sampleExpected.MaxDiff(sampleActual) < 1e-4);
sample = Gamma.FromShapeAndRate(1.4616957536444839, 6.2203585601953317E+36);
rate = Gamma.FromShapeAndRate(2.5, 0.99222007168007165);
sampleExpected = GammaFromShapeAndRateOp_Slow.SampleAverageConditional(sample, shape, rate);
q = Gamma.FromShapeAndRate(3.5, 0.99222007168007154);
sampleActual = GammaFromShapeAndRateOp_Laplace.SampleAverageConditional(sample, shape, rate, q);
Console.WriteLine("sample = {0} should be {1}", sampleActual, sampleExpected);
Assert.True(sampleExpected.MaxDiff(sampleActual) < 1e-4);
sample = Gamma.FromShapeAndRate(1.9692446124520258, 1.0717828357423075E+77);
rate = Gamma.FromShapeAndRate(101.0, 2.1709591889324445E-80);
sampleExpected = GammaFromShapeAndRateOp_Slow.SampleAverageConditional(sample, shape, rate);
q = GammaFromShapeAndRateOp_Laplace.Q(sample, shape, rate);
sampleActual = GammaFromShapeAndRateOp_Laplace.SampleAverageConditional(sample, shape, rate, q);
Console.WriteLine("sample = {0} should be {1}", sampleActual, sampleExpected);
Assert.True(sampleExpected.MaxDiff(sampleActual) < 1e-4);
Assert.Equal(0.0,
GammaFromShapeAndRateOp_Laplace.LogEvidenceRatio(Gamma.Uniform(), 4.0, Gamma.PointMass(0.01), Gamma.FromShapeAndRate(4, 0.01),
Gamma.PointMass(0.01)));
}
/// <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($"productMarginal = {productMarginal}");
}
}
else
{
// Compute the moments of y = product^(1/product.Power)
// yMean = E[shape2*b/(b y_r + a_r)]
// yVariance = E[shape2*(shape2+1)*b^2/(b y_r + a_r)^2] - yMean^2
// = var(shape2*b/(b y_r + a_r)) + E[shape2*b^2/(b y_r + a_r)^2]
// = shape2^2*var(b/(b y_r + a_r)) + shape2*(var(b/(b y_r + a_r)) + (yMean/shape2)^2)
// Let g = b/(b y_r + a_r)
double denom = qPoint * r + A.Rate;
double denom2 = denom * denom;
double rOverDenom = r / denom;
double[] gDerivatives = (denom == 0)
? new double[] { 0, 0, 0, 0 }
: new double[] { qPoint / denom, A.Rate / denom2, -2 * A.Rate / denom2 * rOverDenom, 6 * A.Rate / denom2 * rOverDenom * rOverDenom };
double gMean, gVariance;
GaussianOp_Laplace.LaplaceMoments(q, gDerivatives, dlogfs(qPoint, product, A), out gMean, out gVariance);
double yMean = shape2 * gMean;
double yVariance = shape2 * shape2 * gVariance + shape2 * (gVariance + gMean * gMean);
productMarginal = GammaPower.FromGamma(Gamma.FromMeanAndVariance(yMean, yVariance), result.Power);
}
result.SetToRatio(productMarginal, product, GammaProductOp_Laplace.ForceProper);
if (double.IsNaN(result.Shape) || double.IsNaN(result.Rate))
{
throw new InferRuntimeException("result is nan");
}
return(result);
}
// derivatives of the factor marginalized over Product and A
internal static double[] dlogfs(double b, GammaPower product, GammaPower A)
{
if (A.Power != product.Power)
{
throw new NotSupportedException($"A.Power ({A.Power}) != product.Power ({product.Power})");
}
if (product.IsPointMass)
{
double productPointPower = Math.Pow(product.Point, 1 / A.Power);
if (productPointPower > double.MaxValue)
{
return new double[] { 0, 0, 0, 0 }
}
;
// int delta(a^pa * b^pb - y) Ga(a; s, r) da
// = int delta(a' - y) Ga(a'^(1/pa)/b^(pb/pa); s, r) a'^(1/pa-1)/b^(pb/pa)/pa da'
// = Ga(y^(1/pa)/b^(pb/pa); s, r) y^(1/pa-1)/b^(pb/pa)/pa
// logf = -s*pb/pa*log(b) - r*y^(1/pa)/b^(pb/pa)
double ib = 1 / b;
double ib2 = ib * ib;
double s = A.Shape;
double c = A.Rate * productPointPower / b;
double dlogf = -s * ib + c * ib;
double ddlogf = s * ib2 - 2 * c * ib2;
double dddlogf = -2 * s * ib * ib2 + 6 * c * ib2 * ib;
double d4logf = 6 * s * ib2 * ib2 - 24 * c * ib2 * ib2;
return(new double[] { dlogf, ddlogf, dddlogf, d4logf });
}
else if (A.IsPointMass)
{
// (a * b^pb)^(y_s/py - 1) exp(-y_r*(a*b^pb)^(1/py))
// logf = (y_s/py-1)*pb*log(b) - y_r*a^(1/py)*b^(pb/py)
double ib = 1 / b;
double ib2 = ib * ib;
double s = product.Shape - product.Power;
double c = product.Rate * Math.Pow(A.Point, 1 / product.Power);
double dlogf = s * ib - c;
double ddlogf = -s * ib2;
double dddlogf = 2 * s * ib * ib2;
double d4logf = -6 * s * ib2 * ib2;
return(new double[] { dlogf, ddlogf, dddlogf, d4logf });
}
else
{
// int (a^pa * b^pb)^(y_s/y_p - 1) exp(-y_r*(a^pa*b^pb)^(1/y_p)) Ga(a; s, r) da
// = int a^(pa*(y_s/y_p-1) + s-1) b^(pb*(y_s/y_p-1)) exp(-y_r a^(pa/y_p) b^(pb/y_p) -r*a) da
// where pa = pb = y_p:
// = int a^(y_s-pa + s-1) b^(y_s-y_p) exp(-(y_r b + r)*a) da
// = b^(y_s-y_p) / (r + b y_r)^(y_s-pa + s)
// logf = (y_s-y_p)*log(b) - (s+y_s-pa)*log(r + b*y_r)
double b2 = b * b;
double s = product.Shape - product.Power;
double c = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(product.Shape, A.Shape) + (1 - A.Power);
double denom = A.Rate / product.Rate + b;
if (product.Rate == 0)
{
c = 0;
denom = double.PositiveInfinity;
}
if (b < 1e-77)
{
double bOverDenom = b / denom;
double bOverDenom2 = bOverDenom * bOverDenom;
double dlogf = (s - c * bOverDenom) / b;
double ddlogf = (-s + c * bOverDenom2) / b / b;
double dddlogf = (2 * s - 2 * c * bOverDenom * bOverDenom2) / b / b / b;
double d4logf = (-6 * s + 6 * c * bOverDenom2 * bOverDenom2) / b / b / b / b;
return(new double[] { dlogf, ddlogf, dddlogf, d4logf });
}
else
{
double denom2 = denom * denom;
double dlogf = s / b - c / denom;
double ddlogf = -s / b2 + c / denom2;
double dddlogf = 2 * s / (b * b2) - 2 * c / (denom * denom2);
double d4logf = -6 * s / (b2 * b2) + 6 * c / (denom2 * denom2);
return(new double[] { dlogf, ddlogf, dddlogf, d4logf });
}
}
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaPowerProductOp_Laplace"]/message_doc[@name="LogAverageFactor(GammaPower, GammaPower, GammaPower, Gamma)"]/*'/>
public static double LogAverageFactor(GammaPower product, GammaPower A, GammaPower B, Gamma q)
{
if (B.Shape < A.Shape)
{
return(LogAverageFactor(product, B, A, q));
}
if (B.IsPointMass)
{
return(GammaProductOp.LogAverageFactor(product, A, B.Point));
}
if (A.IsPointMass)
{
return(GammaProductOp.LogAverageFactor(product, A.Point, B));
}
double qPoint = q.GetMean();
double logf;
if (product.IsPointMass)
{
// Ga(y/q; s, r)/q
if (qPoint == 0)
{
if (product.Point == 0)
{
logf = A.GetLogProb(0);
}
else
{
logf = double.NegativeInfinity;
}
}
else
{
logf = A.GetLogProb(product.Point / qPoint) - Math.Log(qPoint);
}
}
else
{
// int Ga^y_p(a^pa b^pb; y_s, y_r) Ga(a; s, r) da = q^(y_s-y_p) / (r + q y_r)^(y_s + s-pa) Gamma(y_s+s-pa)
double shape = product.Shape - product.Power;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(product.Shape, A.Shape) + (1 - A.Power);
if (IsProper(product) && product.Shape > A.Shape)
{
// same as below but product.GetLogNormalizer() is inlined and combined with other terms
double AShapeMinusPower = A.Shape - A.Power;
logf = shape * Math.Log(qPoint)
- Gamma.FromShapeAndRate(A.Shape, A.Rate).GetLogNormalizer()
- product.Shape * Math.Log(A.Rate / product.Rate + qPoint)
- Math.Log(Math.Abs(product.Power));
if (AShapeMinusPower != 0)
{
logf += AShapeMinusPower * (MMath.RisingFactorialLnOverN(product.Shape, AShapeMinusPower) - Math.Log(A.Rate + qPoint * product.Rate));
}
}
else
{
logf = shape * Math.Log(qPoint)
- shape2 * Math.Log(A.Rate + qPoint * product.Rate)
+ MMath.GammaLn(shape2)
- Gamma.FromShapeAndRate(A.Shape, A.Rate).GetLogNormalizer()
- product.GetLogNormalizer();
// normalizer is -MMath.GammaLn(Shape) + Shape * Math.Log(Rate) - Math.Log(Math.Abs(Power))
}
}
double logz = logf + Gamma.FromShapeAndRate(B.Shape, B.Rate).GetLogProb(qPoint) - q.GetLogProb(qPoint);
return(logz);
}
public static Gamma Q(GammaPower product, [Proper] GammaPower A, [Proper] GammaPower B)
{
// ensure B has the larger shape
if (B.Shape < A.Shape)
{
return(Q(product, B, A));
}
if (B.IsPointMass)
{
return(Gamma.PointMass(B.Point));
}
if (A.IsPointMass)
{
return(Gamma.FromShapeAndRate(B.Shape, B.Rate));
}
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 x;
if (product.IsPointMass)
{
if (product.Point == 0)
{
return(Gamma.PointMass(0));
}
double productPointPower = Math.Pow(product.Point, 1 / A.Power);
// y = product^(1/power)
// logf = -a_s*log(b) - y*a_r/b
// logp = b_s*log(b) - b_r*b
// dlogfp = (b_s-a_s)/b - b_r + y*a_r/b^2 = 0
// -b_r b^2 + (b_s-a_s) b + y*a_r = 0
double shape = B.Shape - A.Shape;
x = (Math.Sqrt(shape * shape + 4 * B.Rate * A.Rate * productPointPower) + shape) / 2 / B.Rate;
}
else
{
double shape1 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(B.Shape, product.Shape) + (1 - product.Power);
if (product.Rate == 0)
{
x = GammaFromShapeAndRateOp_Slow.FindMaximum(shape1, 0, A.Rate, B.Rate);
}
else
{
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(A.Shape, product.Shape) + (1 - A.Power);
// find the maximum of the factor marginalized over Product and A, times B
// From above:
// logf = (y_s/y_p-1)*pb*log(b) - (s+y_s-pa)*log(r + b^(pb/y_p)*y_r)
x = GammaFromShapeAndRateOp_Slow.FindMaximum(shape1, shape2, A.Rate / product.Rate, B.Rate);
}
if (x == 0)
{
x = 1e-100;
}
}
double[] dlogfss = dlogfs(x, product, A);
double dlogf = dlogfss[0];
double ddlogf = dlogfss[1];
return(GammaFromShapeAndRateOp_Laplace.GammaFromDerivatives(Gamma.FromShapeAndRate(B.Shape, B.Rate), x, dlogf, ddlogf));
}