public static VectorGaussianWishart CombinationAverageConditional(
[Proper] Gaussian positionX, [Proper] Gaussian positionY, [Proper] Wishart orientation, VectorGaussianWishart combination, VectorGaussianWishart result)
{
VectorGaussian position = VectorGaussian.FromMeanAndPrecision(
Vector.FromArray(positionX.GetMean(), positionY.GetMean()),
new PositiveDefiniteMatrix(new[,] { { positionX.Precision, 0 }, { 0, positionY.Precision } }));
return CombineOps.Combine(position, orientation, result);
}
public static VectorGaussianWishart Combine(VectorGaussian position, Wishart orientation, VectorGaussianWishart result)
{
if (orientation.IsUniform())
{
result.SetToUniform();
}
else if (position.IsUniform())
{
result.SetTo(orientation.Shape, orientation.Rate, Vector.Zero(2), 0);
}
else
{
PositiveDefiniteMatrix rateTimesPrecision = new PositiveDefiniteMatrix(2, 2);
rateTimesPrecision.SetToProduct(orientation.Rate, position.Precision);
double trace = MathHelpers.Invert(rateTimesPrecision).Trace();
Vector positionMean = position.MeanTimesPrecision * MathHelpers.Invert(position.Precision);
result.SetTo(orientation.Shape, orientation.Rate, positionMean, orientation.Dimension / (orientation.Shape * trace));
}
return result;
}
public static VectorGaussian ExtractVectorPart(VectorGaussianWishart gaussianWishart, VectorGaussian result)
{
if (gaussianWishart.IsVectorMarginalUniform())
{
return VectorGaussian.Uniform(2);
}
double firstShape, secondPrecisionScale;
PositiveDefiniteMatrix firstRate;
Vector secondLocation;
gaussianWishart.ExtractParameters(out firstShape, out firstRate, out secondLocation, out secondPrecisionScale);
result.SetMeanAndPrecision(secondLocation, MathHelpers.Invert(firstRate) * (firstShape * secondPrecisionScale));
return result;
}
public static Wishart ExtractMatrixPart(VectorGaussianWishart gaussianWishart, Wishart result)
{
result.SetTo(gaussianWishart.GetMatrixMarginal());
return result;
}
public static VectorGaussianWishart CombinationAverageConditional(
VectorGaussian position, Wishart orientation, VectorGaussianWishart combination, VectorGaussianWishart result)
{
return Combine(position, orientation, result);
}
private static VectorGaussianWishart DistributionTimesFactor(Vector point, VectorGaussianWishart shapeParamsDistr)
{
var factorAsDistr = VectorGaussianWishart.FromNaturalParameters(0, new PositiveDefiniteMatrix(point.Outer(point) * (-0.5)), point, -0.5);
VectorGaussianWishart result = new VectorGaussianWishart(2);
result.SetToProduct(factorAsDistr, shapeParamsDistr);
return result;
}
public static VectorGaussianWishart ShapeParamsAverageConditional(
Vector point, Bernoulli label, [Proper] VectorGaussianWishart shapeParams, VectorGaussianWishart result)
{
VectorGaussianWishart shapeParamsTimesFactor = DistributionTimesFactor(point, shapeParams);
double labelProbFalse = label.GetProbFalse();
double shapeParamsWeight = labelProbFalse;
double shapeParamsTimesFactorWeight =
Math.Exp(shapeParamsTimesFactor.GetLogNormalizer() - shapeParams.GetLogNormalizer()) *
(1 - 2 * labelProbFalse);
var projectionOfSum = new VectorGaussianWishart(2);
projectionOfSum.SetToSum(shapeParamsWeight, shapeParams, shapeParamsTimesFactorWeight, shapeParamsTimesFactor);
Debug.Assert(projectionOfSum.IsProper()); // TODO: remove me
result.SetToRatio(projectionOfSum, shapeParams);
return result;
}
