/// <summary>
/// Computes the sum of a geometric series <c>1 + w + w^2 + w^3 + ...</c>,
/// where <c>w</c> is a given weight.
/// </summary>
/// <param name="weight">The weight.</param>
/// <returns>The computed sum, or <see cref="Infinity"/> if the sum diverges.</returns>
public static Weight Closure(Weight weight)
{
const double Eps = 1e-20;
if (weight.LogValue < -Eps)
{
// The series converges
return(new Weight(-MMath.Log1MinusExp(weight.logValue)));
}
// The series diverges
return(Weight.Infinity);
}
/// <summary>
/// Computes the sum of a geometric series <c>1 + w + w^2 + w^3 + ...</c>,
/// where <c>w</c> is a given weight.
/// If the sum diverges, replaces the infinite sum by a finite sum with a lot of terms.
/// </summary>
/// <param name="weight">The weight.</param>
/// <returns>The computed sum.</returns>
public static Weight ApproximateClosure(Weight weight)
{
const double Eps = 1e-20;
const double TermCount = 10000;
if (weight.LogValue < -Eps)
{
// The series converges
return(new Weight(-MMath.Log1MinusExp(weight.LogValue)));
}
if (weight.LogValue < Eps)
{
// The series diverges, geometric progression formula does not apply
return(new Weight(Math.Log(TermCount)));
}
// Compute geometric progression with a lot of terms
return(new Weight(MMath.LogExpMinus1(weight.LogValue * TermCount) - MMath.LogExpMinus1(weight.LogValue)));
}
/// <summary>EP message to <c>value</c>.</summary>
/// <param name="enterOne">Incoming message from <c>enterOne</c>. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="selector">Incoming message from <c>selector</c>.</param>
/// <param name="value">Incoming message from <c>value</c>.</param>
/// <param name="index">Constant value for <c>index</c>.</param>
/// <param name="result">Modified to contain the outgoing message.</param>
/// <returns>
/// <paramref name="result" />
/// </returns>
/// <remarks>
/// <para>The outgoing message is a distribution matching the moments of <c>value</c> as the random arguments are varied. The formula is <c>proj[p(value) sum_(enterOne,selector) p(enterOne,selector) factor(enterOne,selector,value,index)]/p(value)</c>.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="enterOne" /> is not a proper distribution.</exception>
/// <typeparam name="TDist">The type of the distribution over the variable entering the gate.</typeparam>
public static TDist ValueAverageConditional <TDist>([SkipIfAllUniform] TDist enterOne, Discrete selector, TDist value, int index, TDist result)
where TDist : ICloneable, SettableToUniform, SettableToWeightedSum <TDist>, SettableTo <TDist>, CanGetLogAverageOf <TDist>, CanGetLogNormalizer
{
if (selector == null)
{
throw new ArgumentNullException("selector");
}
double logProbSum = selector.GetLogProb(index);
if (logProbSum == 0.0)
{
result.SetTo(enterOne);
}
else if (double.IsNegativeInfinity(logProbSum))
{
result.SetToUniform();
}
else
{
double logProb = MMath.Log1MinusExp(logProbSum);
double shift = Math.Max(logProbSum, logProb);
// Avoid (-Infinity) - (-Infinity)
if (double.IsNegativeInfinity(shift))
{
throw new AllZeroException();
}
TDist uniform = (TDist)result.Clone();
uniform.SetToUniform();
result.SetToSum(Math.Exp(logProbSum - shift - enterOne.GetLogAverageOf(value)), enterOne, Math.Exp(logProb - shift + uniform.GetLogNormalizer()), uniform);
}
return(result);
}
/// <summary>EP message to <c>value</c>.</summary>
/// <param name="enterPartial">Incoming message from <c>enterPartial</c>. Must be a proper distribution. If any element is uniform, the result will be uniform.</param>
/// <param name="selector">Incoming message from <c>selector</c>. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="value">Incoming message from <c>value</c>.</param>
/// <param name="indices">Constant value for <c>indices</c>.</param>
/// <param name="result">Modified to contain the outgoing message.</param>
/// <returns>
/// <paramref name="result" />
/// </returns>
/// <remarks>
/// <para>The outgoing message is a distribution matching the moments of <c>value</c> as the random arguments are varied. The formula is <c>proj[p(value) sum_(enterPartial,selector) p(enterPartial,selector) factor(enterPartial,selector,value,indices)]/p(value)</c>.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="enterPartial" /> is not a proper distribution.</exception>
/// <exception cref="ImproperMessageException">
/// <paramref name="selector" /> is not a proper distribution.</exception>
/// <typeparam name="TDist">The type of the distribution over the variable entering the gate.</typeparam>
public static TDist ValueAverageConditional <TDist>(
[SkipIfUniform] IList <TDist> enterPartial, [SkipIfUniform] Bernoulli selector, TDist value, int[] indices, TDist result)
where TDist : ICloneable, SettableToUniform, SettableTo <TDist>, SettableToWeightedSum <TDist>, CanGetLogAverageOf <TDist>, CanGetLogNormalizer
{
if (enterPartial == null)
{
throw new ArgumentNullException("enterPartial");
}
if (indices == null)
{
throw new ArgumentNullException("indices");
}
if (indices.Length != enterPartial.Count)
{
throw new ArgumentException("indices.Length != enterPartial.Count");
}
if (2 < enterPartial.Count)
{
throw new ArgumentException("enterPartial.Count should be 2 or 1");
}
if (indices.Length == 0)
{
throw new ArgumentException("indices.Length == 0");
}
// TODO: use pre-allocated buffers
double logProbSum = (indices[0] == 0) ? selector.GetLogProbTrue() : selector.GetLogProbFalse();
double logWeightSum = logProbSum;
if (!double.IsNegativeInfinity(logProbSum))
{
logWeightSum -= enterPartial[0].GetLogAverageOf(value);
result.SetTo(enterPartial[0]);
}
if (indices.Length > 1)
{
for (int i = 1; i < indices.Length; i++)
{
double logProb = (indices[i] == 0) ? selector.GetLogProbTrue() : selector.GetLogProbFalse();
logProbSum += logProb;
double shift = Math.Max(logWeightSum, logProb);
// Avoid (-Infinity) - (-Infinity)
if (double.IsNegativeInfinity(shift))
{
if (i == 1)
{
throw new AllZeroException();
}
// Do nothing
}
else
{
double logWeightShifted = logProb - shift;
if (!double.IsNegativeInfinity(logWeightShifted))
{
logWeightShifted -= enterPartial[i].GetLogAverageOf(value);
result.SetToSum(Math.Exp(logWeightSum - shift), result, Math.Exp(logWeightShifted), enterPartial[i]);
logWeightSum = MMath.LogSumExp(logWeightSum, logWeightShifted + shift);
}
}
}
}
if (indices.Length < 2)
{
double logProb = MMath.Log1MinusExp(logProbSum);
double shift = Math.Max(logWeightSum, logProb);
if (double.IsNegativeInfinity(shift))
{
throw new AllZeroException();
}
var uniform = (TDist)result.Clone();
uniform.SetToUniform();
double logWeight = logProb + uniform.GetLogNormalizer();
result.SetToSum(Math.Exp(logWeightSum - shift), result, Math.Exp(logWeight - shift), uniform);
}
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="BeliefPropagationGateEnterPartialOp"]/message_doc[@name="ValueAverageConditional{TDist}(IList{TDist}, Discrete, TDist, int[], TDist)"]/*'/>
/// <typeparam name="TDist">The type of the distribution over the variable entering the gate.</typeparam>
public static TDist ValueAverageConditional <TDist>(
[SkipIfUniform] IList <TDist> enterPartial, [SkipIfUniform] Discrete selector, TDist value, int[] indices, TDist result)
where TDist : ICloneable, SettableToUniform, SettableTo <TDist>, SettableToWeightedSum <TDist>, CanGetLogAverageOf <TDist>, CanGetLogNormalizer
{
if (enterPartial == null)
{
throw new ArgumentNullException(nameof(enterPartial));
}
if (selector == null)
{
throw new ArgumentNullException(nameof(selector));
}
if (indices == null)
{
throw new ArgumentNullException(nameof(indices));
}
if (indices.Length != enterPartial.Count)
{
throw new ArgumentException("indices.Length != enterPartial.Count");
}
if (selector.Dimension < enterPartial.Count)
{
throw new ArgumentException("selector.Dimension < enterPartial.Count");
}
if (indices.Length == 0)
{
throw new ArgumentException("indices.Length == 0");
}
// TODO: use pre-allocated buffers
double logProbSum = selector.GetLogProb(indices[0]);
double logWeightSum = logProbSum;
if (!double.IsNegativeInfinity(logWeightSum))
{
// Subtract to avoid double-counting since selector already contains this quantity
// See IntCasesOp.IAverageConditional
double logAverage = enterPartial[0].GetLogAverageOf(value);
if (!double.IsNegativeInfinity(logAverage))
{
logWeightSum -= logAverage;
result.SetTo(enterPartial[0]);
}
}
if (indices.Length > 1)
{
for (int i = 1; i < indices.Length; i++)
{
double logProb = selector.GetLogProb(indices[i]);
logProbSum = MMath.LogSumExp(logProbSum, logProb);
double shift = Math.Max(logWeightSum, logProb);
// Avoid (-Infinity) - (-Infinity)
if (double.IsNegativeInfinity(shift))
{
if (i == selector.Dimension - 1)
{
throw new AllZeroException();
}
// Do nothing
}
else
{
double logWeightShifted = logProb - shift;
if (!double.IsNegativeInfinity(logWeightShifted))
{
double logAverage = enterPartial[i].GetLogAverageOf(value);
if (!double.IsNegativeInfinity(logAverage))
{
logWeightShifted -= logAverage;
result.SetToSum(Math.Exp(logWeightSum - shift), result, Math.Exp(logWeightShifted), enterPartial[i]);
logWeightSum = MMath.LogSumExp(logWeightSum, logWeightShifted + shift);
}
}
}
}
}
if (indices.Length < selector.Dimension)
{
double logProb = MMath.Log1MinusExp(logProbSum);
double shift = Math.Max(logWeightSum, logProb);
if (double.IsNegativeInfinity(shift))
{
throw new AllZeroException();
}
var uniform = (TDist)result.Clone();
uniform.SetToUniform();
double logWeight = logProb + uniform.GetLogNormalizer();
result.SetToSum(Math.Exp(logWeightSum - shift), result, Math.Exp(logWeight - shift), uniform);
}
return(result);
}
