/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="LogisticOp_JJ96"]/message_doc[@name="XAverageLogarithm(Beta, Gaussian, Gaussian)"]/*'/>
public static Gaussian XAverageLogarithm([SkipIfUniform] Beta logistic, [Proper, SkipIfUniform] Gaussian x, Gaussian result)
{
if (logistic.IsPointMass)
{
return(LogisticOp.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);
// sigma(x) >= sigma(t) exp((x-t)/2 - a/2*(x^2 - t^2))
double m, v;
x.GetMeanAndVariance(out m, out v);
double t = Math.Sqrt(m * m + v);
double lambda = (t == 0) ? 0.25 : Math.Tanh(t / 2) / (2 * t);
return(Gaussian.FromNatural(scale * 0.5 + shift, scale * lambda));
}
#pragma warning disable 429
#endif
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="LogisticOp_SJ99"]/message_doc[@name="XAverageLogarithm(Beta, Gaussian, Gaussian, double)"]/*'/>
public static Gaussian XAverageLogarithm([SkipIfUniform] Beta logistic, Gaussian x, Gaussian to_x, double a, IPolyrand random = null)
{
if (logistic.IsPointMass)
{
return(LogisticOp.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 scale = logistic.TrueCount + logistic.FalseCount - 2;
if (scale == 0.0)
{
return(Gaussian.Uniform());
}
double shift = -(logistic.FalseCount - 1);
double m, v;
x.GetMeanAndVariance(out m, out v);
double sa;
if (double.IsPositiveInfinity(v))
{
a = 0.5;
sa = MMath.Logistic(m);
}
else
{
sa = MMath.Logistic(m + (1 - 2 * a) * v * 0.5);
}
double precision = a * a + (1 - 2 * a) * sa;
// meanTimesPrecision = m*a*a + 1-2*a*sa;
double meanTimesPrecision = m * precision + 1 - sa;
//double vf = 1/(a*a + (1-2*a)*sa);
//double mf = m + vf*(true ? 1-sa : sa);
//double precision = 1/vf;
//double meanTimesPrecision = mf*precision;
Gaussian result = Gaussian.FromNatural(scale * meanTimesPrecision + shift, scale * precision);
double step
= (LogisticOp_SJ99.global_step == 0.0)
? 1.0
: (Rand.Double(random) * LogisticOp_SJ99.global_step);
// random damping helps convergence, especially with parallel updates
if (false && !x.IsPointMass)
{
// if the update would change the sign of 1-2*sa, send a message to make sa=0.5
double newPrec = x.Precision - to_x.Precision + result.Precision;
double newv = 1 / newPrec;
double newm = newv * (x.MeanTimesPrecision - to_x.MeanTimesPrecision + result.MeanTimesPrecision);
double newarg = newm + (1 - 2 * a) * newv * 0.5;
if ((sa < 0.5 && newarg > 0) || (sa > 0.5 && newarg < 0))
{
// send a message to make newarg=0
// it is sufficient to make (x.MeanTimesPrecision + step*(result.MeanTimesPrecision - to_x.MeanTimesPrecision) + 0.5-a) = 0
double mpOffset = x.MeanTimesPrecision + 0.5 - a;
double precOffset = x.Precision;
double mpScale = result.MeanTimesPrecision - to_x.MeanTimesPrecision;
double precScale = result.Precision - to_x.Precision;
double arg = m + (1 - 2 * a) * v * 0.5;
//arg = 0;
step = (arg * precOffset - mpOffset) / (mpScale - arg * precScale);
//step = (a-0.5-x.MeanTimesPrecision)/(result.MeanTimesPrecision - to_x.MeanTimesPrecision);
//Console.WriteLine(step);
}
}
if (step != 1.0)
{
result.Precision = step * result.Precision + (1 - step) * to_x.Precision;
result.MeanTimesPrecision = step * result.MeanTimesPrecision + (1 - step) * to_x.MeanTimesPrecision;
}
return(result);
}