/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="LogisticOp"]/message_doc[@name="LogisticAverageLogarithm(Gaussian)"]/*'/>
public static Beta LogisticAverageLogarithm([Proper] Gaussian x)
{
double m, v;
x.GetMeanAndVariance(out m, out v);
#if true
// for consistency with XAverageLogarithm
double eLogOneMinusP = BernoulliFromLogOddsOp.AverageLogFactor(false, x);
#else
// E[log (1-sigma(x))] = E[log sigma(-x)] = -E[log(1+exp(x))]
double eLogOneMinusP = -MMath.Log1PlusExpGaussian(m, v);
#endif
// E[log sigma(x)] = -E[log(1+exp(-x))] = -E[log(1+exp(x))-x] = -E[log(1+exp(x))] + E[x]
double eLogP = eLogOneMinusP + m;
return(Beta.FromMeanLogs(eLogP, eLogOneMinusP));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="LogisticOp"]/message_doc[@name="XAverageLogarithm(Beta, Gaussian, Gaussian)"]/*'/>
public static Gaussian XAverageLogarithm([SkipIfUniform] Beta logistic, [Proper, SkipIfUniform] Gaussian x, Gaussian to_X)
{
if (logistic.IsPointMass)
{
return(XAverageLogarithm(logistic.Point));
}
// f(x) = sigma(x)^(a-1) sigma(-x)^(b-1)
// = sigma(x)^(a+b-2) exp(-x(b-1))
// since sigma(-x) = sigma(x) exp(-x)
double a = logistic.TrueCount;
double b = logistic.FalseCount;
double scale = a + b - 2;
if (scale == 0.0)
{
return(Gaussian.Uniform());
}
double shift = -(b - 1);
Gaussian toLogOddsPrev = Gaussian.FromNatural((to_X.MeanTimesPrecision - shift) / scale, to_X.Precision / scale);
Gaussian toLogOdds = BernoulliFromLogOddsOp.LogOddsAverageLogarithm(true, x, toLogOddsPrev);
return(Gaussian.FromNatural(scale * toLogOdds.MeanTimesPrecision + shift, scale * toLogOdds.Precision));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="LogisticOp"]/message_doc[@name="FalseMsg(Beta, Gaussian, Gaussian)"]/*'/>
public static Gaussian FalseMsg([SkipIfUniform] Beta logistic, [Proper] Gaussian x, Gaussian falseMsg)
{
// falseMsg approximates sigma(-x)
// logistic(sigma(x)) N(x;m,v)
// = sigma(x)^(a-1) sigma(-x)^(b-1) N(x;m,v)
// = e^((a-1)x) sigma(-x)^(a+b-2) N(x;m,v)
// = sigma(-x)^(a+b-2) N(x;m+(a-1)v,v) exp((a-1)m + (a-1)^2 v/2)
// = sigma(-x) (prior)
// where prior = sigma(-x)^(a+b-3) N(x;m+(a-1)v,v)
double tc1 = logistic.TrueCount - 1;
double fc1 = logistic.FalseCount - 1;
double m, v;
x.GetMeanAndVariance(out m, out v);
if (tc1 + fc1 == 0)
{
falseMsg.SetToUniform();
return(falseMsg);
}
else if (tc1 + fc1 < 0)
{
// power EP update, using 1/sigma(-x) as the factor
Gaussian prior = new Gaussian(m + tc1 * v, v) * (falseMsg ^ (tc1 + fc1 + 1));
double mprior, vprior;
prior.GetMeanAndVariance(out mprior, out vprior);
// posterior moments can be computed exactly
double w = MMath.Logistic(mprior + 0.5 * vprior);
Gaussian post = new Gaussian(mprior + w * vprior, vprior * (1 + w * (1 - w) * vprior));
return(prior / post);
}
else
{
// power EP update
Gaussian prior = new Gaussian(m + tc1 * v, v) * (falseMsg ^ (tc1 + fc1 - 1));
Gaussian newMsg = BernoulliFromLogOddsOp.LogOddsAverageConditional(false, prior);
//Console.WriteLine("prior = {0}, falseMsg = {1}, newMsg = {2}", prior, falseMsg, newMsg);
if (string.Empty.Length == 0)
{
// adaptive damping scheme
Gaussian ratio = newMsg / falseMsg;
if ((ratio.MeanTimesPrecision < 0 && prior.MeanTimesPrecision > 0) ||
(ratio.MeanTimesPrecision > 0 && prior.MeanTimesPrecision < 0))
{
// if the update would change the sign of the mean, take a fractional step so that the new prior has exactly zero mean
// newMsg = falseMsg * (ratio^step)
// newPrior = prior * (ratio^step)^(tc1+fc1-1)
// 0 = prior.mp + ratio.mp*step*(tc1+fc1-1)
double step = -prior.MeanTimesPrecision / (ratio.MeanTimesPrecision * (tc1 + fc1 - 1));
if (step > 0 && step < 1)
{
newMsg = falseMsg * (ratio ^ step);
// check that newPrior has zero mean
//Gaussian newPrior = prior * ((ratio^step)^(tc1+fc1-1));
//Console.WriteLine(newPrior);
}
}
}
else
{
for (int iter = 0; iter < 10; iter++)
{
newMsg = falseMsg * ((newMsg / falseMsg) ^ 0.5);
falseMsg = newMsg;
//Console.WriteLine("prior = {0}, falseMsg = {1}, newMsg = {2}", prior, falseMsg, newMsg);
prior = new Gaussian(m + tc1 * v, v) * (falseMsg ^ (tc1 + fc1 - 1));
newMsg = BernoulliFromLogOddsOp.LogOddsAverageConditional(false, prior);
}
}
return(newMsg);
}
}