// GammaPower = TruncatedGamma ^ y /////////////////////////////////////////////////////////
public static GammaPower PowAverageConditional([SkipIfUniform] TruncatedGamma x, double y, GammaPower result)
{
if (result.Power == -1)
{
y = -y;
}
else if (result.Power != 1)
{
throw new ArgumentException($"result.Power ({result.Power}) is not 1 or -1", nameof(result));
}
double mean = x.GetMeanPower(y);
if (x.LowerBound > 0)
{
double meanInverse = x.GetMeanPower(-y);
Gamma result1 = GammaFromMeanAndMeanInverse(mean, meanInverse);
return(GammaPower.FromShapeAndRate(result1.Shape, result1.Rate, result.Power));
}
else
{
double variance = x.GetMeanPower(2 * y) - mean * mean;
Gamma result1 = Gamma.FromMeanAndVariance(mean, variance);
return(GammaPower.FromShapeAndRate(result1.Shape, result1.Rate, result.Power));
}
}
public void ExpOpGammaPowerTest()
{
Assert.True(!double.IsNaN(ExpOp.ExpAverageConditional(GammaPower.Uniform(-1), Gaussian.FromNatural(0.046634157098979417, 0.00078302234897204242), Gaussian.Uniform()).Rate));
Assert.True(!double.IsNaN(ExpOp.ExpAverageConditional(GammaPower.Uniform(-1), Gaussian.FromNatural(0.36153121930654075, 0.0005524890062312658), Gaussian.Uniform()).Rate));
Assert.True(ExpOp.DAverageConditional(GammaPower.PointMass(0, -1), new Gaussian(0, 1), Gaussian.Uniform()).Point < double.MinValue);
ExpOp.ExpAverageConditional(GammaPower.FromShapeAndRate(-1, 283.673, -1), Gaussian.FromNatural(0.004859823703146038, 6.6322755562737905E-06), Gaussian.FromNatural(0.00075506803981220758, 8.24487022054953E-07));
GammaPower exp = GammaPower.FromShapeAndRate(0, 0, -1);
Gaussian[] ds = new[]
{
Gaussian.FromNatural(-1.6171314269768655E+308, 4.8976001759138024),
Gaussian.FromNatural(-0.037020622891705768, 0.00034989765084474117),
Gaussian.PointMass(double.NegativeInfinity),
};
foreach (var d in ds)
{
Gaussian to_d = ExpOp.DAverageConditional(exp, d, Gaussian.Uniform());
Gaussian to_d_slow = ExpOp_Slow.DAverageConditional(exp, d);
Assert.True(to_d_slow.MaxDiff(to_d) < 1e-10);
to_d = Gaussian.FromNatural(1, 0);
GammaPower to_exp = ExpOp.ExpAverageConditional(exp, d, to_d);
//Trace.WriteLine($"{to_exp}");
}
ExpOp.ExpAverageConditional(GammaPower.FromShapeAndRate(-1, 883.22399999999993, -1), Gaussian.FromNatural(0.0072160312702854888, 8.1788482512051846E-06), Gaussian.FromNatural(0.00057861649495666474, 5.6316164560235272E-07));
}
public static GammaPower InvGammaFromMeanAndMeanInverse(double mean, double meanInverse)
{
double shape = 1 / (1 - 1 / mean / meanInverse);
double rate = mean * (shape - 1);
return(GammaPower.FromShapeAndRate(shape, rate, -1));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaRatioOp"]/message_doc[@name="RatioAverageConditional(double, Gamma)"]/*'/>
public static GammaPower RatioAverageConditional(double A, Gamma B)
{
if (B.IsPointMass)
{
return(GammaPower.PointMass(A / B.Point, -1));
}
return(GammaPower.FromShapeAndRate(B.Shape, B.Rate * A, -1));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaRatioOp"]/message_doc[@name="BAverageConditional(Gamma, double)"]/*'/>
public static GammaPower BAverageConditional([SkipIfUniform] Gamma ratio, double A)
{
if (ratio.IsPointMass)
{
return(GammaPower.PointMass(BAverageConditional(ratio.Point, A).Point, -1));
}
// Ga(a/b; y_s, y_r) =propto b^(-y_s+1) exp(-a/b y_r)
return(GammaPower.FromShapeAndRate(ratio.Shape - 2, ratio.Rate * A, -1));
}
public static GammaPower XAverageConditional([SkipIfUniform] GammaPower pow, double y, GammaPower result)
{
double power = pow.Power / y;
if (power != result.Power)
{
throw new NotSupportedException("Outgoing message power (" + power + ") does not match the desired power (" + result.Power + ")");
}
return(GammaPower.FromShapeAndRate(pow.Shape, pow.Rate, pow.Power / y));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PlusGammaVmpOp"]/message_doc[@name="AAverageLogarithm(GammaPower, GammaPower, GammaPower)"]/*'/>
public static GammaPower AAverageLogarithm([SkipIfUniform] GammaPower sum, [Proper] GammaPower a, [Proper] GammaPower b, GammaPower to_a, GammaPower to_b)
{
// f = int_sum sum^(ss/c -1)*exp(-sr*sum^(1/c))*delta(sum = a+b) dsum
// = (a+b)^(ss/c -1)*exp(-sr*(a+b)^(1/c))
// log(f) = (ss/c -1)*log(a+b) - sr*(a+b)^(1/c)
// apply a lower bound:
// log(a+b) >= p*log(a) + (1-p)*log(b) - p*log(p) - (1-p)*log(1-p)
// optimal p = exp(a)/(exp(a)+exp(b)) if (a,b) are fixed
// optimal p = exp(E[log(a)])/(exp(E[log(a)])+exp(E[log(b)])) if (a,b) are random
// This generalizes the bound used by Cemgil (2008).
// (a+b)^(1/c) = (a*q/q + b*(1-q)/(1-q))^(1/c)
// <= q*(a/q)^(1/c) + (1-q)*(b/(1-q))^(1/c) if c < 0
// = q^(1-1/c)*a^(1/c) + (1-q)^(1-1/c)*b^(1/c)
// d/dq = (1-1/c)*(q^(-1/c)*a^(1/c) - (1-q)^(-1/c)*b^(1/c))
// optimal q = a/(a + b) if (a,b) are fixed
// optimal q = E[a^(1/c)]^c/(E[a^(1/c)]^c + E[b^(1/c)]^c) if (a,b) are random
// The message to A has shape (ss-c)*p + c and rate sr*q^(1-1/c).
// If sum is a point mass, then the message to A is pointmass(s*p^c*q^(1-c))
if (a.Power != sum.Power)
{
throw new NotSupportedException($"a.Power ({a.Power}) != sum.Power ({sum.Power})");
}
double x = sum.Shape - sum.Power;
GammaPower aPost = a * to_a;
if (aPost.IsUniform())
{
return(sum);
}
GammaPower bPost = b * to_b;
if (bPost.IsUniform())
{
if (sum.IsPointMass)
{
return(sum);
}
return(GammaPower.FromShapeAndRate(sum.Power, sum.Rate, sum.Power));
}
double ma = Math.Exp(aPost.GetMeanLog());
double mb = Math.Exp(bPost.GetMeanLog());
double denom = ma + mb;
double p = (denom == 0) ? 0.5 : ma / (ma + mb);
double m = x * p;
double mac = Math.Exp(a.Power * aPost.GetLogMeanPower(1 / a.Power));
double mbc = Math.Exp(b.Power * bPost.GetLogMeanPower(1 / b.Power));
double denom2 = mac + mbc;
double q = (denom2 == 0) ? 0.5 : mac / (mac + mbc);
if (sum.IsPointMass)
{
return(GammaPower.PointMass(sum.Point * Math.Pow(p / q, sum.Power) * q, sum.Power));
}
return(GammaPower.FromShapeAndRate(m + sum.Power, sum.Rate * Math.Pow(q, 1 - 1 / sum.Power), sum.Power));
}
// GammaPower = Gamma ^ y //////////////////////////////////////////////////////////////
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PowerOp"]/message_doc[@name="PowAverageConditional(Gamma, double)"]/*'/>
public static GammaPower PowAverageConditional([SkipIfUniform] Gamma x, double y)
{
if (x.IsPointMass)
{
return(GammaPower.PointMass(System.Math.Pow(x.Point, y), y));
}
else
{
return(GammaPower.FromShapeAndRate(x.Shape, x.Rate, y));
}
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaProductVmpOp"]/message_doc[@name="ProductAverageLogarithm(double, Gamma)"]/*'/>
public static GammaPower ProductAverageLogarithm(double A, [SkipIfUniform] GammaPower B)
{
if (B.IsPointMass)
{
return(GammaPower.PointMass(A * B.Point, B.Power));
}
if (A == 0)
{
return(GammaPower.PointMass(0, B.Power));
}
return(GammaPower.FromShapeAndRate(B.Shape, B.Rate * Math.Pow(A, -1 / B.Power), B.Power));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaProductOp"]/message_doc[@name="AAverageConditional(double, Gamma)"]/*'/>
public static GammaPower AAverageConditional(double product, Gamma B)
{
if (B.IsPointMass)
{
return(GammaPower.PointMass(B.Point / product, -1));
}
// b' = ab, db' = a db
// int delta(y - ab) Ga(b; b_s, b_r) db
// = int delta(y - b') Ga(b'/a; b_s, b_r)/a db'
// = Ga(y/a; b_s, b_r)/a
// =propto a^(-b_s) exp(-yb_r/a)
return(GammaPower.FromShapeAndRate(B.Shape - 1, product * B.Rate, -1));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaProductOp"]/message_doc[@name="AAverageConditional(GammaPower, double, GammaPower)"]/*'/>
public static GammaPower AAverageConditional([SkipIfUniform] GammaPower Product, double B, GammaPower result)
{
if (Product.IsPointMass)
{
return(AAverageConditional(Product.Point, B, result));
}
if (B == 0)
{
result.SetToUniform();
return(result);
}
// (ab)^(shape/power-1) exp(-rate*(ab)^(1/power))
return(GammaPower.FromShapeAndRate(Product.Shape, Product.Rate * Math.Pow(B, 1 / result.Power), result.Power));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PowerOp"]/message_doc[@name="PowAverageConditional(GammaPower, double, GammaPower)"]/*'/>
public static GammaPower PowAverageConditional([SkipIfUniform] GammaPower x, double y, GammaPower result)
{
GammaPower message;
if (x.IsPointMass)
{
message = GammaPower.PointMass(System.Math.Pow(x.Point, y), y * x.Power);
}
else
{
message = GammaPower.FromShapeAndRate(x.Shape, x.Rate, y * x.Power);
}
return(GammaPowerFromDifferentPower(message, result.Power));
}
/// <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 qPoint = q.GetMean();
GammaPower bMarginal;
// threshold ensures 6/qPoint^4 does not overflow
double threshold = Math.Sqrt(Math.Sqrt(6 / double.MaxValue));
if (result.Power < 0 && qPoint > threshold)
{
double iqMean, iqVariance;
GetIQMoments(product, A, q, qPoint, out iqMean, out iqVariance);
GammaPower iqMarginal = GammaPower.FromMeanAndVariance(iqMean, iqVariance, -1);
bMarginal = GammaPower.FromShapeAndRate(iqMarginal.Shape, iqMarginal.Rate, result.Power);
}
else
{
// B.Shape >= A.Shape therefore Q is the approximate distribution of B^(1/B.Power).
// We compute the approximate moments of q = b^(1/b.Power) to get a Gamma distribution and then raise to B.Power.
double qMean, qVariance;
GetQMoments(product, A, q, qPoint, out qMean, out qVariance);
bMarginal = GammaPower.FromGamma(Gamma.FromMeanAndVariance(qMean, qVariance), result.Power);
}
result.SetToRatio(bMarginal, B, GammaProductOp_Laplace.ForceProper);
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PowerOp"]/message_doc[@name="XAverageConditional(GammaPower, GammaPower, double, GammaPower)"]/*'/>
public static GammaPower XAverageConditional([SkipIfUniform] GammaPower pow, GammaPower x, double y, GammaPower result)
{
// message computed below should be uniform when pow is uniform, but may not due to roundoff error.
if (pow.IsUniform())
{
return(GammaPower.Uniform(result.Power));
}
// Factor is (x^y)^(pow.Shape/pow.Power - 1) * exp(-pow.Rate*(x^y)^1/pow.Power)
// =propto x^(pow.Shape/(pow.Power/y) - y) * exp(-pow.Rate*x^y/pow.Power)
// newShape/(pow.Power/y) - 1 = pow.Shape/(pow.Power/y) - y
// newShape = pow.Shape + (1-y)*(pow.Power/y)
double power = pow.Power / y;
var toPow = PowAverageConditional(x, y, pow);
GammaPower powMarginal = pow * toPow;
// xMarginal2 is the exact distribution of pow^(1/y) where pow has distribution powMarginal
GammaPower xMarginal2 = GammaPower.FromShapeAndRate(powMarginal.Shape, powMarginal.Rate, power);
GammaPower xMarginal = GammaPowerFromDifferentPower(xMarginal2, result.Power);
result.SetToRatio(xMarginal, x, GammaProductOp_Laplace.ForceProper);
return(result);
}
public static GammaPower GammaPowerFromDerivLogZ(GammaPower a, double dlogZ, double ddlogZ)
{
bool method1 = false;
if (method1)
{
GetPosteriorMeanAndVariance(Gamma.FromShapeAndRate(a.Shape, a.Rate), dlogZ, ddlogZ, out double iaMean, out double iaVariance);
Gamma ia = Gamma.FromMeanAndVariance(iaMean, iaVariance);
return(GammaPower.FromShapeAndRate(ia.Shape, ia.Rate, a.Power) / a);
}
else
{
double alpha = -a.Rate * dlogZ;
// dalpha/dr = -dlogZ - r*ddlogZ
// beta = -r * dalpha/dr
double beta = a.Rate * dlogZ + a.Rate * a.Rate * ddlogZ;
Gamma prior = Gamma.FromShapeAndRate(a.Shape, a.Rate);
// ia is the marginal of a^(1/a.Power)
Gamma ia = GaussianOp.GammaFromAlphaBeta(prior, alpha, beta, true) * prior;
return(GammaPower.FromShapeAndRate(ia.Shape, ia.Rate, a.Power) / a);
}
}
private static GammaPower InverseGammaFromMeanAndVarianceOverMeanSquared(double mean, double varianceOverMeanSquared)
{
double shape = 1 / varianceOverMeanSquared + 2;
return(GammaPower.FromShapeAndRate(shape, mean * (shape - 1), -1));
}
/// <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);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PlusGammaOp"]/message_doc[@name="SumAverageConditional(GammaPower, double)"]/*'/>
public static GammaPower SumAverageConditional([SkipIfUniform] GammaPower a, double b)
{
if (double.IsInfinity(b) || double.IsNaN(b))
{
throw new ArgumentOutOfRangeException(nameof(b), b, $"Argument is outside the range of supported values.");
}
if (a.IsUniform() || b == 0)
{
return(a);
}
else if (a.Power == 0)
{
throw new ArgumentException($"Cannot add {b} to {a}");
}
else if (a.IsPointMass)
{
return(GammaPower.PointMass(a.Point + b, a.Power));
}
else if (a.Power < 0)
{
if (a.Shape <= a.Power)
{
return(a); // mode is at zero
}
// The mode is ((Shape - Power)/Rate)^Power
// We want to shift the mode by b, preserving the Shape and Power.
// This implies ((Shape - Power)/newRate)^Power = newMode
// newRate = (Shape - Power)/newMode^(1/Power)
// = (a.Shape - a.Power) * Math.Pow(a.GetMode() + b, -1 / a.Power);
//double logMode = a.Power * (Math.Log(Math.Max(0, a.Shape - a.Power)) - Math.Log(a.Rate));
//if (logMode > double.MaxValue) return a; // mode is at infinity
double logShapeMinusPower = Math.Log(a.Shape - a.Power);
double mode = a.GetMode();
if (mode > double.MaxValue)
{
return(a); // mode is at infinity
}
double newMode = Math.Max(0, mode + b);
double newLogMode = Math.Log(newMode);
// Find newLogRate to satisfy a.Power*(logShapeMinusPower - newLogRate) <= newLogMode
// logShapeMinusPower - newLogRate >= newLogMode/a.Power
// newLogRate - logShapeMinusPower <= -newLogMode/a.Power
double newLogModeOverPower = MMath.LargestDoubleRatio(newLogMode, -a.Power);
double newLogRate = MMath.LargestDoubleSum(logShapeMinusPower, newLogModeOverPower);
if ((double)((logShapeMinusPower - newLogRate) * a.Power) > newLogMode)
{
throw new Exception();
}
// Ideally this would find largest newRate such that log(newRate) <= newLogRate
double newRate = Math.Exp(newLogRate);
if (logShapeMinusPower == newLogRate)
{
newRate = a.Shape - a.Power;
}
if (a.Rate > 0)
{
newRate = Math.Max(double.Epsilon, newRate);
}
if (!double.IsPositiveInfinity(a.Rate))
{
newRate = Math.Min(double.MaxValue, newRate);
}
return(GammaPower.FromShapeAndRate(a.Shape, newRate, a.Power));
}
else if (!a.IsProper())
{
return(a);
}
else
{
// The mean is Math.Exp(Power * (MMath.RisingFactorialLnOverN(Shape, Power) - Math.Log(Rate)))
// We want to shift the mean by b, preserving the Shape and Power.
// This implies log(newRate) = MMath.RisingFactorialLnOverN(Shape, Power) - log(newMean)/Power
double logShape = MMath.RisingFactorialLnOverN(a.Shape, a.Power);
//double logMean = a.GetLogMeanPower(1);
//double newLogMean = (b > 0) ?
// MMath.LogSumExp(logMean, Math.Log(b)) :
// MMath.LogDifferenceOfExp(logMean, Math.Log(-b));
double newMean = Math.Max(0, a.GetMean() + b);
double newLogMean = Math.Log(newMean);
// If logShape is big, this difference can lose accuracy
// Find newLogRate to satisfy logShape - newLogRate <= newLogMean/a.Power
double newLogMeanOverPower = MMath.LargestDoubleRatio(newLogMean, a.Power);
double newLogRate = -MMath.LargestDoubleSum(-logShape, newLogMeanOverPower);
// check: (logShape - newLogRate)*a.Power <= newLogMean
if ((double)((logShape - newLogRate) * a.Power) > newLogMean)
{
throw new Exception();
}
double newRate = Math.Exp(newLogRate);
newRate = Math.Max(double.Epsilon, newRate);
if (!double.IsPositiveInfinity(a.Rate))
{
newRate = Math.Min(double.MaxValue, newRate);
}
return(GammaPower.FromShapeAndRate(a.Shape, newRate, a.Power));
}
}
// GammaPower = Gamma ^ y //////////////////////////////////////////////////////////////
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PowerOp"]/message_doc[@name="PowAverageConditional(Gamma, double)"]/*'/>
public static GammaPower PowAverageConditional([SkipIfUniform] Gamma x, double y)
{
return(GammaPower.FromShapeAndRate(x.Shape, x.Rate, y));
}
public static GammaPower GammaPowerFromDifferentPower(GammaPower message, double newPower)
{
if (message.Power == newPower)
{
return(message); // same as below, but faster
}
if (message.IsUniform())
{
return(GammaPower.Uniform(newPower));
}
// Making two hops ensures that the desired mean powers are finite.
if (message.Power > 0 && newPower < 0 && newPower != -1)
{
return(GammaPowerFromDifferentPower(GammaPowerFromDifferentPower(message, -1), newPower));
}
if (message.Power < 0 && newPower > 0 && newPower != 1)
{
return(GammaPowerFromDifferentPower(GammaPowerFromDifferentPower(message, 1), newPower));
}
// Project the message onto the desired power
if (newPower == 1 || newPower == -1 || newPower == 2)
{
message.GetMeanAndVariance(out double mean, out double variance);
if (!double.IsPositiveInfinity(mean))
{
return(GammaPower.FromMeanAndVariance(mean, variance, newPower));
}
// Fall through
}
bool useMean = false;
if (useMean)
{
// Constraints:
// mean = Gamma(Shape + newPower)/Gamma(Shape)/Rate^newPower =approx (Shape/Rate)^newPower
// mean2 = Gamma(Shape + 2*newPower)/Gamma(Shape)/Rate^(2*newPower) =approx ((Shape + newPower)/Rate)^newPower * (Shape/Rate)^newPower
// mean2/mean^2 = Gamma(Shape + 2*newPower)*Gamma(Shape)/Gamma(Shape + newPower)^2 =approx ((Shape + newPower)/Shape)^newPower
// Shape =approx newPower/((mean2/mean^2)^(1/newPower) - 1)
// Rate = Shape/mean^(1/newPower)
message.GetMeanAndVariance(out double mean, out double variance);
double meanp = System.Math.Pow(mean, 1 / newPower);
double mean2p = System.Math.Pow(variance + mean * mean, 1 / newPower);
double shape = newPower / (mean2p / meanp / meanp - 1);
if (double.IsInfinity(shape))
{
return(GammaPower.PointMass(mean, newPower));
}
double rate = shape / meanp;
return(GammaPower.FromShapeAndRate(shape, rate, newPower));
}
else
{
// Compute the mean and variance of x^1/newPower
double mean = message.GetMeanPower(1 / newPower);
double mean2 = message.GetMeanPower(2 / newPower);
double variance = System.Math.Max(0, mean2 - mean * mean);
if (double.IsPositiveInfinity(mean * mean))
{
variance = mean;
}
return(GammaPower.FromGamma(Gamma.FromMeanAndVariance(mean, variance), newPower));
}
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PowerOp"]/message_doc[@name="PowAverageConditional(GammaPower, double, GammaPower)"]/*'/>
public static GammaPower PowAverageConditional([SkipIfUniform] GammaPower x, double y, GammaPower result)
{
GammaPower message = GammaPower.FromShapeAndRate(x.Shape, x.Rate, y * x.Power);
return(GammaPowerFromDifferentPower(message, result.Power));
}
// Gamma = Gamma ^ y /////////////////////////////////////////////////////////
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PowerOp"]/message_doc[@name="PowAverageConditional(Gamma, double, Gamma)"]/*'/>
public static Gamma PowAverageConditional([SkipIfUniform] Gamma x, double y, Gamma result)
{
GammaPower message = GammaPower.FromShapeAndRate(x.Shape, x.Rate, y);
return(GammaFromGammaPower(message));
}
public static GammaPower InvGammaFromShapeAndMeanInverse(double shape, double meanInverse)
{
return(GammaPower.FromShapeAndRate(shape, shape / meanInverse, -1));
}
