/// <summary>Update the buffer <c>Buffer</c>.</summary>
/// <param name="Buffer">Buffer <c>Buffer</c>.</param>
/// <param name="list">Incoming message from <c>list</c>.</param>
/// <param name="IndexOfMaximumDouble">Constant value for <c>indexOfMaximumDouble</c>.</param>
/// <returns>New value of buffer <c>Buffer</c>.</returns>
/// <remarks>
/// <para />
/// </remarks>
/// <typeparam name="GaussianList">The type of an incoming message from <c>list</c>.</typeparam>
public static IndexOfMaximumBuffer Buffer <GaussianList>(
IndexOfMaximumBuffer Buffer, GaussianList list, int IndexOfMaximumDouble) // redundant parameters required for correct dependency graph
where GaussianList : IList <Gaussian>
{
var max_marginal = Buffer.to_list[IndexOfMaximumDouble] * list[IndexOfMaximumDouble];
Gaussian product = Gaussian.Uniform();
//var order = Rand.Perm(list.Count);
for (int i = 0; i < list.Count; i++)
{
//int c = order[i];
int c = i;
if (c != IndexOfMaximumDouble)
{
var msg_to_sum = max_marginal / Buffer.MessagesToMax[c];
var msg_to_positiveop = DoublePlusOp.AAverageConditional(Sum: msg_to_sum, b: list[c]);
var msgFromPositiveOp = IsPositiveOp.XAverageConditional(true, msg_to_positiveop);
Buffer.MessagesToMax[c] = DoublePlusOp.SumAverageConditional(list[c], msgFromPositiveOp);
Buffer.to_list[c] = DoublePlusOp.AAverageConditional(Sum: msg_to_sum, b: msgFromPositiveOp);
max_marginal = msg_to_sum * Buffer.MessagesToMax[c];
product.SetToProduct(product, Buffer.MessagesToMax[c]);
}
}
//Buffer.to_list[IndexOfMaximumDouble] = max_marginal / list[IndexOfMaximumDouble];
Buffer.to_list[IndexOfMaximumDouble] = product;
return(Buffer);
}
/// <summary>Evidence message for EP.</summary>
/// <param name="Buffer">Buffer <c>Buffer</c>.</param>
/// <param name="list">Incoming message from <c>list</c>.</param>
/// <param name="IndexOfMaximumDouble">Constant value for <c>indexOfMaximumDouble</c>.</param>
/// <returns>Logarithm of the factor's average value across the given argument distributions.</returns>
/// <remarks>
/// <para>The formula for the result is <c>log(sum_(list) p(list) factor(indexOfMaximumDouble,list))</c>.</para>
/// </remarks>
/// <typeparam name="GaussianList">The type of an incoming message from <c>list</c>.</typeparam>
public static double LogAverageFactor <GaussianList>(IndexOfMaximumBuffer Buffer, GaussianList list, int IndexOfMaximumDouble)
where GaussianList : IList <Gaussian>
{
double evidence = 0;
var max_marginal = list[IndexOfMaximumDouble] * Buffer.to_list[IndexOfMaximumDouble];
for (int c = 0; c < list.Count; c++)
{
if (c != IndexOfMaximumDouble)
{
var msg_to_sum = max_marginal / Buffer.MessagesToMax[c];
var msg_to_positiveop = DoublePlusOp.AAverageConditional(Sum: msg_to_sum, b: list[c]);
evidence += IsPositiveOp.LogEvidenceRatio(true, msg_to_positiveop);
// sum operator does not contribute because no projection is involved
// the x[index]-x[c] variable does not contribute because it only connects to two factors
evidence -= msg_to_sum.GetLogAverageOf(Buffer.MessagesToMax[c]);
if (max_marginal.IsPointMass)
{
evidence += Buffer.MessagesToMax[c].GetLogAverageOf(max_marginal);
}
else
{
evidence -= Buffer.MessagesToMax[c].GetLogNormalizer();
}
}
}
//evidence += ReplicateOp.LogEvidenceRatio<Gaussian>(MessagesToMax, list[IndexOfMaximumDouble], MessagesToMax.Select(o => max_marginal / o).ToArray());
if (!max_marginal.IsPointMass)
{
evidence += max_marginal.GetLogNormalizer() - list[IndexOfMaximumDouble].GetLogNormalizer();
}
//evidence -= Buffer.MessagesToMax.Sum(o => o.GetLogNormalizer());
//evidence -= Buffer.MessagesToMax.Sum(o => (max_marginal / o).GetLogAverageOf(o));
return(evidence);
}
// redundant parameters required for correct dependency graph
public static IndexOfMaximumBuffer Buffer <GaussianList>(IndexOfMaximumBuffer Buffer, GaussianList list, int IndexOfMaximumDouble)
where GaussianList : IList <Gaussian>
{
var max_marginal = Buffer.to_list[IndexOfMaximumDouble] * list[IndexOfMaximumDouble];
//var order = Rand.Perm(list.Count);
for (int i = 0; i < list.Count; i++)
{
//int c = order[i];
int c = i;
if (c != IndexOfMaximumDouble)
{
var msg_to_sum = max_marginal / Buffer.MessagesToMax[c];
var msg_to_positiveop = DoublePlusOp.AAverageConditional(Sum: msg_to_sum, b: list[c]);
var msgFromPositiveOp = IsPositiveOp.XAverageConditional(true, msg_to_positiveop);
Buffer.MessagesToMax[c] = DoublePlusOp.SumAverageConditional(list[c], msgFromPositiveOp);
Buffer.to_list[c] = DoublePlusOp.AAverageConditional(Sum: msg_to_sum, b: msgFromPositiveOp);
max_marginal = msg_to_sum * Buffer.MessagesToMax[c];
}
}
Buffer.to_list[IndexOfMaximumDouble] = max_marginal / list[IndexOfMaximumDouble];
return(Buffer);
}
/// <summary>
/// Returns the probability that A>B
/// </summary>
/// <param name="A"></param>
/// <param name="B"></param>
/// <returns></returns>
private static Bernoulli ProbGreater(Gaussian A, Gaussian B)
{
Gaussian diff = DoublePlusOp.AAverageConditional(Sum: A, b: B);
return(IsPositiveOp.IsPositiveAverageConditional(diff));
}
/// <summary>EP message to <c>x</c>.</summary>
/// <param name="isPositive">Incoming message from <c>isPositive</c>. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="x">Incoming message from <c>x</c>. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <returns>The outgoing EP message to the <c>x</c> argument.</returns>
/// <remarks>
/// <para>The outgoing message is a distribution matching the moments of <c>x</c> as the random arguments are varied. The formula is <c>proj[p(x) sum_(isPositive) p(isPositive) factor(isPositive,x)]/p(x)</c>.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="isPositive" /> is not a proper distribution.</exception>
/// <exception cref="ImproperMessageException">
/// <paramref name="x" /> is not a proper distribution.</exception>
public static Gaussian XAverageConditional([SkipIfUniform] Bernoulli isPositive, [SkipIfUniform, Proper] Gaussian x)
{
return(IsPositiveOp.XAverageConditional_Helper(isPositive, x, forceProper: true));
}