//-- 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 <c>sample</c>.</param>
/// <param name="logOdds">Incoming message from <c>logOdds</c>. Must be a proper distribution. If uniform, the result will be uniform.</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,logOdds) p(sample,logOdds) log(factor(sample,logOdds))</c>. Adding up these values across all factors and variables gives the log-evidence estimate for VMP.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="logOdds" /> is not a proper distribution.</exception>
public static double AverageLogFactor(Bernoulli sample, [Proper, SkipIfUniform] Gaussian logOdds)
{
// f(sample,logOdds) = exp(sample*logOdds)/(1 + exp(logOdds))
// log f(sample,logOdds) = sample*logOdds - log(1 + exp(logOdds))
double m, v;
logOdds.GetMeanAndVariance(out m, out v);
return(sample.GetProbTrue() * m - MMath.Log1PlusExpGaussian(m, v));
}
/// <summary>
/// VMP message to 'logistic'
/// </summary>
/// <param name="x">Incoming message from 'x'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <returns>The outgoing VMP message to the 'logistic' argument</returns>
/// <remarks><para>
/// The outgoing message is a distribution matching the moments of 'logistic' as the random arguments are varied.
/// The formula is <c>proj[sum_(x) p(x) factor(logistic,x)]</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="x"/> is not a proper distribution</exception>
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));
}
