/// <summary>EP message to <c>list</c>.</summary>
/// <param name="Buffer">Buffer <c>Buffer</c>.</param>
/// <param name="to_list">Previous outgoing message to <c>list</c>.</param>
/// <param name="IndexOfMaximumDouble">Constant value for <c>indexOfMaximumDouble</c>.</param>
/// <returns>The outgoing EP message to the <c>list</c> argument.</returns>
/// <remarks>
/// <para>The outgoing message is the factor viewed as a function of <c>list</c> conditioned on the given values.</para>
/// </remarks>
/// <typeparam name="GaussianList">The type of an incoming message from <c>list</c>.</typeparam>
public static GaussianList listAverageConditional <GaussianList>(
IndexOfMaximumBuffer Buffer, GaussianList to_list, int IndexOfMaximumDouble)
where GaussianList : IList <Gaussian>
{
to_list.SetTo(Buffer.to_list);
return(to_list);
}
/// <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);
}
public static double LogAverageFactor <GaussianList>([SkipIfUniform] GaussianList list, GaussianList to_list, IndexOfMaximumBuffer[] Buffers, Discrete IndexOfMaximumDouble)
where GaussianList : DistributionStructArray <Gaussian, double>
{
var evidences = new double[list.Count];
var tempBuffer = new IndexOfMaximumBuffer();
for (int i = 0; i < list.Count; i++)
{
tempBuffer.to_list = new DistributionStructArray <Gaussian, double>(list.Select(o => Gaussian.Uniform()).ToArray());
tempBuffer.to_list[i] = Buffers[i].MessagesToMax.Aggregate((p, q) => p * q);
tempBuffer.MessagesToMax = new DistributionStructArray <Gaussian, double>(Buffers[i].MessagesToMax.Select(o => (Gaussian)o.Clone()).ToArray());
evidences[i] = IndexOfMaximumOp.LogAverageFactor(tempBuffer, list, i) + IndexOfMaximumDouble.GetLogProb(i);;
}
return(MMath.LogSumExp(evidences));
}
// 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>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 contribution the EP model evidence.</returns>
/// <remarks>
/// <para>The formula for the result is <c>log(sum_(list) p(list) factor(indexOfMaximumDouble,list))</c>. Adding up these values across all factors and variables gives the log-evidence estimate for EP.</para>
/// </remarks>
/// <typeparam name="GaussianList">The type of an incoming message from <c>list</c>.</typeparam>
public static double LogEvidenceRatio <GaussianList>(IndexOfMaximumBuffer Buffer, GaussianList list, int IndexOfMaximumDouble)
where GaussianList : IList <Gaussian>
{
return(LogAverageFactor(Buffer, list, IndexOfMaximumDouble));
}