/// <summary>
/// VMP message to 'a'
/// </summary>
/// <param name="Product">Incoming message from 'product'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="B">Incoming message from 'b'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <returns>The outgoing VMP message to the 'a' argument</returns>
/// <remarks><para>
/// The outgoing message is the exponential of the average log-factor value, where the average is over all arguments except 'a'.
/// Because the factor is deterministic, 'product' is integrated out before taking the logarithm.
/// The formula is <c>exp(sum_(b) p(b) log(sum_product p(product) factor(product,a,b)))</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="Product"/> is not a proper distribution</exception>
/// <exception cref="ImproperMessageException"><paramref name="B"/> is not a proper distribution</exception>
public static Gaussian AAverageLogarithm([SkipIfUniform] Gaussian Product, [Proper] Gamma B)
{
if (B.IsPointMass)
{
return(GaussianProductVmpOp.AAverageLogarithm(Product, B.Point));
}
if (Product.IsPointMass)
{
return(AAverageLogarithm(Product.Point, B));
}
if (!B.IsProper())
{
throw new ImproperMessageException(B);
}
double mb, vb;
B.GetMeanAndVariance(out mb, out vb);
// catch uniform case to avoid 0*Inf
if (Product.IsUniform())
{
return(Product);
}
Gaussian result = new Gaussian();
result.Precision = Product.Precision * (vb + mb * mb);
result.MeanTimesPrecision = Product.MeanTimesPrecision * mb;
return(result);
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="ProductGaussianBetaVmpOp"]/message_doc[@name="AAverageLogarithm(Gaussian, Beta)"]/*'/>
public static Gaussian AAverageLogarithm([SkipIfUniform] Gaussian Product, [Proper] Beta B)
{
if (B.IsPointMass)
{
return(GaussianProductVmpOp.AAverageLogarithm(Product, B.Point));
}
if (Product.IsPointMass)
{
return(AAverageLogarithm(Product.Point, B));
}
double mb, vb;
B.GetMeanAndVariance(out mb, out vb);
Gaussian result = new Gaussian();
result.Precision = Product.Precision * (vb + mb * mb);
result.MeanTimesPrecision = Product.MeanTimesPrecision * mb;
return(result);
}
public void ProductOpTest()
{
Assert.True(GaussianProductVmpOp.ProductAverageLogarithm(
2.0,
Gaussian.FromMeanAndVariance(3.0, 5.0)).MaxDiff(Gaussian.FromMeanAndVariance(2 * 3, 4 * 5)) < 1e-8);
Assert.True(GaussianProductOp.ProductAverageConditional(
2.0,
Gaussian.FromMeanAndVariance(3.0, 5.0)).MaxDiff(Gaussian.FromMeanAndVariance(2 * 3, 4 * 5)) < 1e-8);
Assert.True(GaussianProductOp.ProductAverageConditional(new Gaussian(0, 1),
Gaussian.PointMass(2.0),
Gaussian.FromMeanAndVariance(3.0, 5.0)).MaxDiff(Gaussian.FromMeanAndVariance(2 * 3, 4 * 5)) < 1e-8);
Assert.True(GaussianProductVmpOp.ProductAverageLogarithm(
0.0,
Gaussian.FromMeanAndVariance(3.0, 5.0)).MaxDiff(Gaussian.PointMass(0.0)) < 1e-8);
Assert.True(GaussianProductOp.ProductAverageConditional(
0.0,
Gaussian.FromMeanAndVariance(3.0, 5.0)).MaxDiff(Gaussian.PointMass(0.0)) < 1e-8);
Assert.True(GaussianProductOp.ProductAverageConditional(new Gaussian(0, 1),
Gaussian.PointMass(0.0),
Gaussian.FromMeanAndVariance(3.0, 5.0)).MaxDiff(Gaussian.PointMass(0.0)) < 1e-8);
Assert.True(GaussianProductVmpOp.ProductAverageLogarithm(
Gaussian.FromMeanAndVariance(2, 4),
Gaussian.FromMeanAndVariance(3, 5)).MaxDiff(Gaussian.FromMeanAndVariance(2 * 3, 4 * 5 + 3 * 3 * 4 + 2 * 2 * 5)) < 1e-8);
Assert.True(GaussianProductOp.ProductAverageConditional(Gaussian.Uniform(),
Gaussian.FromMeanAndVariance(2, 4),
Gaussian.FromMeanAndVariance(3, 5)).MaxDiff(Gaussian.FromMeanAndVariance(2 * 3, 4 * 5 + 3 * 3 * 4 + 2 * 2 * 5)) <
1e-8);
Assert.True(GaussianProductOp.ProductAverageConditional(Gaussian.FromMeanAndVariance(0, 1e16),
Gaussian.FromMeanAndVariance(2, 4),
Gaussian.FromMeanAndVariance(3, 5)).MaxDiff(Gaussian.FromMeanAndVariance(2 * 3, 4 * 5 + 3 * 3 * 4 + 2 * 2 * 5)) <
1e-4);
Assert.True(GaussianProductOp.AAverageConditional(6.0, 2.0)
.MaxDiff(Gaussian.PointMass(6.0 / 2.0)) < 1e-8);
Assert.True(GaussianProductOp.AAverageConditional(6.0, new Gaussian(1, 3), Gaussian.PointMass(2.0))
.MaxDiff(Gaussian.PointMass(6.0 / 2.0)) < 1e-8);
Assert.True(GaussianProductOp.AAverageConditional(0.0, 0.0).IsUniform());
Assert.True(GaussianProductOp.AAverageConditional(Gaussian.Uniform(), 2.0).IsUniform());
Assert.True(GaussianProductOp.AAverageConditional(Gaussian.Uniform(), new Gaussian(1, 3), Gaussian.PointMass(2.0)).IsUniform());
Assert.True(GaussianProductOp.AAverageConditional(Gaussian.Uniform(), new Gaussian(1, 3), new Gaussian(2, 4)).IsUniform());
Gaussian aPrior = Gaussian.FromMeanAndVariance(0.0, 1000.0);
Assert.True((GaussianProductOp.AAverageConditional(
Gaussian.FromMeanAndVariance(10.0, 1.0),
aPrior,
Gaussian.FromMeanAndVariance(5.0, 1.0)) * aPrior).MaxDiff(
Gaussian.FromMeanAndVariance(2.208041421368822, 0.424566765678152)) < 1e-4);
Gaussian g = new Gaussian(0, 1);
Assert.True(GaussianProductOp.AAverageConditional(g, 0.0).IsUniform());
Assert.True(GaussianProductOp.AAverageConditional(0.0, 0.0).IsUniform());
Assert.True(GaussianProductVmpOp.AAverageLogarithm(g, 0.0).IsUniform());
Assert.True(Gaussian.PointMass(3.0).MaxDiff(GaussianProductVmpOp.AAverageLogarithm(6.0, 2.0)) < 1e-10);
Assert.True(GaussianProductVmpOp.AAverageLogarithm(0.0, 0.0).IsUniform());
try
{
Assert.True(GaussianProductVmpOp.AAverageLogarithm(6.0, g).IsUniform());
Assert.True(false, "Did not throw NotSupportedException");
}
catch (NotSupportedException)
{
}
try
{
g = GaussianProductOp.AAverageConditional(12.0, 0.0);
Assert.True(false, "Did not throw AllZeroException");
}
catch (AllZeroException)
{
}
try
{
g = GaussianProductVmpOp.AAverageLogarithm(12.0, 0.0);
Assert.True(false, "Did not throw AllZeroException");
}
catch (AllZeroException)
{
}
}
