/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaProductOp"]/message_doc[@name="LogAverageFactor(double, GammaPower, double)"]/*'/>
public static double LogAverageFactor(double product, GammaPower a, double b)
{
if (b == 0)
{
return((product == 0) ? 0.0 : double.NegativeInfinity);
}
GammaPower to_product = GammaProductOp.ProductAverageConditional(a, b);
return(to_product.GetLogProb(product));
}
/// <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);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaProductOp"]/message_doc[@name="LogAverageFactor(GammaPower, GammaPower, double)"]/*'/>
public static double LogAverageFactor(GammaPower product, GammaPower a, double b)
{
GammaPower to_product = GammaProductOp.ProductAverageConditional(a, b);
return(to_product.GetLogAverageOf(product));
}