/// <summary>EP message to <c>func</c>.</summary>
/// <param name="y">Incoming message from <c>y</c>. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="func">Incoming message from <c>func</c>. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="x">Constant value for <c>x</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>func</c> as the random arguments are varied. The formula is <c>proj[p(func) sum_(y) p(y) factor(y,func,x)]/p(func)</c>.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="y" /> is not a proper distribution.</exception>
/// <exception cref="ImproperMessageException">
/// <paramref name="func" /> is not a proper distribution.</exception>
public static SparseGP FuncAverageConditional([SkipIfUniform] Gaussian y, [SkipIfUniform] SparseGP func, Vector x, SparseGP result)
{
if (y.IsUniform() || func.IsUniform())
{
result.SetToUniform();
return(result);
}
result.FixedParameters = func.FixedParameters;
result.IncludePrior = false;
double vf = func.Variance(x);
double my, vy;
y.GetMeanAndVariance(out my, out vy);
Vector kbx = func.FixedParameters.KernelOf_X_B(x);
Vector proj = func.FixedParameters.InvKernelOf_B_B * kbx;
double prec = 1.0 / (vy + vf - func.Var_B_B.QuadraticForm(proj));
result.InducingDist.Precision.SetToOuter(proj, proj);
result.InducingDist.Precision.Scale(prec);
result.InducingDist.MeanTimesPrecision.SetTo(proj);
result.InducingDist.MeanTimesPrecision.Scale(prec * my);
result.ClearCachedValues();
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="SparseGPOp"]/message_doc[@name="FuncAverageConditional(Gaussian, SparseGP, Vector, SparseGP)"]/*'/>
public static SparseGP FuncAverageConditional([SkipIfUniform] Gaussian y, [SkipIfUniform] SparseGP func, Vector x, SparseGP result)
{
if (y.IsUniform() || func.IsUniform())
{
result.SetToUniform();
return(result);
}
result.FixedParameters = func.FixedParameters;
result.IncludePrior = false;
Vector kbx = func.FixedParameters.KernelOf_X_B(x);
Vector proj = func.FixedParameters.InvKernelOf_B_B * kbx;
// To avoid computing Var_B_B:
// vf - func.Var_B_B.QuadraticForm(proj) = kxx - kbx'*beta*kbx - kbx'*inv(K)*Var_B_B*inv(K)*kbx
// = kxx - kbx'*(beta + inv(K)*Var_B_B*inv(K))*kbx
// = kxx - kbx'*(beta + inv(K)*(K - K*Beta*K)*inv(K))*kbx
// = kxx - kbx'*inv(K)*kbx
// Since Var_B_B = K - K*Beta*K
double kxx = func.FixedParameters.Prior.Variance(x);
if (y.Precision == 0)
{
result.InducingDist.Precision.SetAllElementsTo(0);
result.InducingDist.MeanTimesPrecision.SetTo(proj);
result.InducingDist.MeanTimesPrecision.Scale(y.MeanTimesPrecision);
}
else
{
double my, vy;
y.GetMeanAndVariance(out my, out vy);
double prec = 1.0 / (vy + kxx - kbx.Inner(proj));
//Console.WriteLine($"{vf - func.Var_B_B.QuadraticForm(proj)} {func.FixedParameters.Prior.Variance(x) - func.FixedParameters.InvKernelOf_B_B.QuadraticForm(kbx)}");
if (prec > double.MaxValue || prec < 0)
{
int i = proj.IndexOfMaximum();
result.InducingDist.Precision.SetAllElementsTo(0);
result.InducingDist.Precision[i, i] = double.PositiveInfinity;
result.InducingDist.MeanTimesPrecision.SetAllElementsTo(0);
result.InducingDist.MeanTimesPrecision[i] = my;
}
else
{
result.InducingDist.Precision.SetToOuter(proj, proj);
result.InducingDist.Precision.Scale(prec);
result.InducingDist.MeanTimesPrecision.SetTo(proj);
result.InducingDist.MeanTimesPrecision.Scale(prec * my);
}
}
result.ClearCachedValues();
return(result);
}