//-- VMP -------------------------------------------------------------------------------------------------
/// <summary>
/// Evidence message for VMP
/// </summary>
/// <returns>Zero</returns>
/// <remarks><para>
/// The formula for the result is <c>log(factor(logistic,x))</c>.
/// Adding up these values across all factors and variables gives the log-evidence estimate for VMP.
/// </para></remarks>
//[Skip]
public static double AverageLogFactor([Proper, SkipIfUniform] Gaussian x, Beta logistic, Beta to_logistic)
{
double m, v;
x.GetMeanAndVariance(out m, out v);
double l1pe = v == 0 ? MMath.Log1PlusExp(m) : MMath.Log1PlusExpGaussian(m, v);
return((logistic.TrueCount - 1.0) * (m - l1pe) + (logistic.FalseCount - 1.0) * (-l1pe) - logistic.GetLogNormalizer() - to_logistic.GetAverageLog(logistic));
}
/// <summary>
/// Evidence message for VMP.
/// </summary>
/// <param name="sample">Incoming message from sample</param>
/// <param name="logOdds">Incoming message from logOdds</param>
/// <returns><c>sum_x marginal(x)*log(factor(x))</c></returns>
/// <remarks><para>
/// The formula for the result is <c>int log(f(x)) q(x) dx</c>
/// where <c>x = (sample,logOdds)</c>.
/// </para></remarks>
public static double AverageLogFactor(Beta logistic, [Proper, SkipIfUniform] Gaussian x, Beta to_logistic, double a)
{
double b = logistic.FalseCount;
double scale = logistic.TrueCount + b - 2;
double shift = -(b - 1);
double m, v;
x.GetMeanAndVariance(out m, out v);
double boundOnLog1PlusExp = a * a * v / 2.0 + MMath.Log1PlusExp(m + (1.0 - 2.0 * a) * v / 2.0);
double boundOnLogSigma = m - boundOnLog1PlusExp;
return(scale * boundOnLogSigma + shift * m - logistic.GetLogNormalizer() - to_logistic.GetAverageLog(logistic));
}
/// <summary>
/// Computes the Bernoulli gating function in the log-odds domain.
/// </summary>
/// <param name="x"></param>
/// <param name="gate"></param>
/// <returns></returns>
/// <remarks>
/// The Bernoulli gating function is x if gate = -infinity and 0 if gate = infinity.
/// It is one of the messages sent by a logical OR factor.
/// In the log-odds domain, this is:
/// log (1 + exp(-gate))/(1 + exp(-gate-x))
/// </remarks>
public static double Gate(double x, double gate)
{
if (x == -gate)
{
// avoid subtracting infinities
return(-MMath.Ln2 + MMath.Log1PlusExp(-gate));
}
else if (gate < 0 && x + gate < 0)
{
// factor out -gate and gate+x
return(x + MMath.Log1PlusExp(gate) - MMath.Log1PlusExp(gate + x));
}
else
{
return(MMath.Log1PlusExp(-gate) - MMath.Log1PlusExp(-gate - x));
}
}
/// <summary>Evidence message for VMP.</summary>
/// <param name="sample">Incoming message from <c>sample</c>.</param>
/// <param name="logOdds">Constant value for <c>logOdds</c>.</param>
/// <returns>Average of the factor's log-value across the given argument distributions.</returns>
/// <remarks>
/// <para>The formula for the result is <c>sum_(sample) p(sample) log(factor(sample,logOdds))</c>. Adding up these values across all factors and variables gives the log-evidence estimate for VMP.</para>
/// </remarks>
public static double AverageLogFactor(Bernoulli sample, double logOdds)
{
if (sample.IsPointMass)
{
return(AverageLogFactor(sample.Point, logOdds));
}
// probTrue*log(sigma(logOdds)) + probFalse*log(sigma(-logOdds))
// = -log(1+exp(-logOdds)) + probFalse*(-logOdds)
// = probTrue*logOdds - log(1+exp(logOdds))
if (logOdds >= 0)
{
double probFalse = sample.GetProbFalse();
return(-probFalse * logOdds - MMath.Log1PlusExp(-logOdds));
}
else
{
double probTrue = sample.GetProbTrue();
return(probTrue * logOdds - MMath.Log1PlusExp(logOdds));
}
}
public static double AverageLogFactor(Bernoulli sample, Gaussian logOdds)
{
// This is the non-conjugate VMP update using the Saul and Jordan (1999) bound.
double m, v;
logOdds.GetMeanAndVariance(out m, out v);
double a = 0.5;
// TODO: use a buffer to store the value of 'a', so it doesn't need to be re-optimised each time.
for (int iter = 0; iter < 10; iter++)
{
double aOld = a;
a = MMath.Logistic(m + (1 - 2 * a) * v * 0.5);
if (Math.Abs(a - aOld) < 1e-8)
{
break;
}
}
return(sample.GetProbTrue() * m - .5 * a * a * v - MMath.Log1PlusExp(m + (1 - 2 * a) * v * 0.5));
}
/// <summary>
/// Gets the log normalizer of the distribution
/// </summary>
/// <returns>This equals -log(1-p)</returns>
public double GetLogNormalizer()
{
// equivalent to -log(1-p)
return(MMath.Log1PlusExp(LogOdds));
}
public static double logSumExpBound(double m, double v, double a)
{
return(0.5 * v * a * a + MMath.Log1PlusExp(m + (0.5 - a) * v));
}