/// <summary>
/// VMP message to 'probsTrue'
/// </summary>
/// <param name="sample">Incoming message from 'sample'. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <returns>The outgoing VMP message to the 'probsTrue' argument</returns>
/// <remarks><para>
/// The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except 'probsTrue'.
/// The formula is <c>exp(sum_(sample) p(sample) log(factor(sample,probsTrue)))</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="sample"/> is not a proper distribution</exception>
public static SparseBetaList ProbsTrueAverageLogarithm([Proper] SparseBernoulliListBase sample)
{
// E[x*log(p) + (1-x)*log(1-p)] = E[x]*log(p) + (1-E[x])*log(1-p)
SparseVector ex = sample.GetProbTrueVector();
return(new SparseBetaList((SparseVector)(ex + 1), (SparseVector)(2 - ex)));
}
//-- VMP -------------------------------------------------------------------------------------------
/// <summary>
/// Evidence message for VMP
/// </summary>
/// <param name="sample">Incoming message from 'sample'. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <param name="probsTrue">Incoming message from 'probsTrue'. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <param name="MeanLog">Buffer 'MeanLog'.</param>
/// <param name="MeanLogOneMinus">Buffer 'MeanLogOneMinus'.</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,probsTrue) p(sample,probsTrue) log(factor(sample,probsTrue))</c>.
/// Adding up these values across all factors and variables gives the log-evidence estimate for VMP.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="sample"/> is not a proper distribution</exception>
/// <exception cref="ImproperMessageException"><paramref name="probsTrue"/> is not a proper distribution</exception>
public static double AverageLogFactor([Proper] SparseBernoulliListBase sample,
[Proper] SparseBetaList probsTrue, SparseVector MeanLog, SparseVector MeanLogOneMinus)
{
//var MeanLogOneMinus = probsTrue.GetMeanLogOneMinus();
var p = sample.GetProbTrueVector();
var res = p * MeanLog + (1 - p) * MeanLogOneMinus;
return(res.Sum());
}
