public void GaussianOpLogAverageFactor()
{
Gaussian uniform = new Gaussian();
Gaussian X0 = Gaussian.FromMeanAndVariance(3, 0.5);
Gaussian Mean0 = Gaussian.FromMeanAndVariance(7, 1.0 / 3);
Gamma Precision0 = Gamma.FromShapeAndScale(3, 3);
// Fixed precision
Gamma Precision = Gamma.PointMass(3);
Gaussian X = X0;
Gaussian Mean = uniform;
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor_slow(X, Mean, Precision), 0, 1e-4) < 1e-4);
Assert.True(MMath.AbsDiff(GaussianOp_Slow.LogAverageFactor(X, Mean, Precision), 0, 1e-4) < 1e-4);
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor(X, Mean, Precision.Point), 0, 1e-4) < 1e-4);
Mean = Mean0;
// in matlab: normpdfln(3,7,[],0.5+1/3+1/3)
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor_slow(X, Mean, Precision), -7.8532, 1e-4) < 1e-4);
Assert.True(MMath.AbsDiff(GaussianOp_Slow.LogAverageFactor(X, Mean, Precision), -7.8532, 1e-4) < 1e-4);
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor(X, Mean, Precision.Point), -7.8532, 1e-4) < 1e-4);
Mean = Gaussian.PointMass(Mean0.GetMean());
// in matlab: normpdfln(3,7,[],0.5+1/3)
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor_slow(X, Mean, Precision), -10.42777775, 1e-4) < 1e-4);
Assert.True(MMath.AbsDiff(GaussianOp_Slow.LogAverageFactor(X, Mean, Precision), -10.42777775, 1e-4) < 1e-4);
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor(X, Mean, Precision.Point), -10.42777775, 1e-4) < 1e-4);
X = uniform;
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor_slow(X, Mean, Precision), 0, 1e-4) < 1e-4);
Assert.True(MMath.AbsDiff(GaussianOp_Slow.LogAverageFactor(X, Mean, Precision), 0, 1e-4) < 1e-4);
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor(X, Mean, Precision.Point), 0, 1e-4) < 1e-4);
// Unknown precision
Precision = Precision0;
X = X0;
Mean = Mean0;
// converge the precision message. (only matters if KeepLastMessage is set).
//for (int i = 0; i < 10; i++) PrecisionAverageConditional(precisionMessage);
// in matlab: log(t_normal_exact(mx-my,vx+vy,a+1,b))
// log(t_normal_exact(3-7,0.5+1/3,3,1/3))
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor_slow(X, Mean, Precision), -8.4363, 1e-4) < 1e-4);
Assert.True(MMath.AbsDiff(GaussianOp_Slow.LogAverageFactor(X, Mean, Precision), -8.4363, 1e-4) < 1e-4);
Mean = Gaussian.PointMass(Mean0.GetMean());
// converge the precision message. (only matters if KeepLastMessage is set).
//for (int i = 0; i < 10; i++) PrecisionAverageConditional(precisionMessage);
// in matlab: log(t_normal_exact(3-7,0.5,3,1/3))
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor_slow(X, Mean, Precision), -9.9890, 1e-4) < 1e-4);
X = Gaussian.PointMass(X0.GetMean());
Mean = Mean0;
// converge the precision message. (only matters if KeepLastMessage is set).
//for (int i = 0; i < 10; i++) PrecisionAverageConditional(precisionMessage);
// in matlab: log(t_normal_exact(3-7,1/3,3,1/3))
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor_slow(X, Mean, Precision), -10.478382, 1e-4) < 1e-4);
X = Gaussian.PointMass(X0.GetMean());
Mean = Gaussian.PointMass(Mean0.GetMean());
// in matlab: log(t_normal_exact(3-7,1e-4,3,1/3)) or tpdfln(3-7,0,2*1/3,2*3+1)
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor_slow(X, Mean, Precision), -11.1278713, 1e-4) < 1e-4);
X = uniform;
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor_slow(X, Mean, Precision), 0, 1e-4) < 1e-4);
// uniform precision
// the answer should always be Double.PositiveInfinity
Precision = Gamma.Uniform();
X = X0;
Mean = Mean0;
Assert.True(MMath.AbsDiff(GaussianOp.LogAverageFactor_slow(X, Mean, Precision), Double.PositiveInfinity, 1e-4) < 1e-4);
Assert.True(MMath.AbsDiff(GaussianOp_Slow.LogAverageFactor(new Gaussian(-0.641, 9.617e-22), Gaussian.PointMass(-1), new Gamma(1, 1)), -1.133394734344457, 1e-8) <
1e-4);
GaussianOp_Slow.LogAverageFactor(new Gaussian(8.156, 9.653), Gaussian.PointMass(-1), new Gamma(1, 1));
}
internal void StudentIsPositiveTest2()
{
GaussianOp.ForceProper = false;
double shape = 1;
double mean = -1;
Gamma precPrior = Gamma.FromShapeAndRate(shape, shape);
Gaussian meanPrior = Gaussian.PointMass(mean);
double evExpected;
Gaussian xExpected = StudentIsPositiveExact(mean, precPrior, out evExpected);
Gaussian xF2 = Gaussian.FromMeanAndVariance(-1, 1);
// the energy has a stationary point here (min in both dimensions), even though xF0 is improper
Gaussian xB0 = new Gaussian(2, 1);
xF2 = Gaussian.FromMeanAndVariance(-4.552, 6.484);
//xB0 = new Gaussian(1.832, 0.9502);
//xB0 = new Gaussian(1.792, 1.558);
//xB0 = new Gaussian(1.71, 1.558);
//xB0 = new Gaussian(1.792, 1.5);
Gaussian xF0 = GaussianOp_Slow.SampleAverageConditional(xB0, meanPrior, precPrior);
//Console.WriteLine("xB0 = {0} xF0 = {1}", xB0, xF0);
//Console.WriteLine(xF0*xB0);
//Console.WriteLine(xF2*xB0);
xF2 = new Gaussian(0.8651, 1.173);
xB0 = new Gaussian(-4, 2);
xB0 = new Gaussian(7, 7);
if (false)
{
xF2 = new Gaussian(mean, 1);
double[] xs = EpTests.linspace(0, 100, 1000);
double[] logTrue = Util.ArrayInit(xs.Length, i => GaussianOp.LogAverageFactor(xs[i], mean, precPrior));
Normalize(logTrue);
xF2 = FindxF4(xs, logTrue, xF2);
xF2 = Gaussian.FromNatural(-0.85, 0);
xB0 = IsPositiveOp.XAverageConditional(true, xF2);
Console.WriteLine("xF = {0} xB = {1}", xF2, xB0);
Console.WriteLine("x = {0} should be {1}", xF2 * xB0, xExpected);
Console.WriteLine("proj[T*xB] = {0}", GaussianOp_Slow.SampleAverageConditional(xB0, meanPrior, precPrior) * xB0);
double ev = System.Math.Exp(IsPositiveOp.LogAverageFactor(true, xF2) + GaussianOp_Slow.LogAverageFactor(xB0, meanPrior, precPrior) - xF2.GetLogAverageOf(xB0));
Console.WriteLine("evidence = {0} should be {1}", ev, evExpected);
return;
}
if (false)
{
xF2 = new Gaussian(mean, 1);
xF2 = FindxF3(xExpected, evExpected, meanPrior, precPrior, xF2);
xB0 = IsPositiveOp.XAverageConditional(true, xF2);
Console.WriteLine("xF = {0} xB = {1}", xF2, xB0);
Console.WriteLine("x = {0} should be {1}", xF2 * xB0, xExpected);
//double ev = Math.Exp(IsPositiveOp.LogAverageFactor(true, xF2) + GaussianOp.LogAverageFactor_slow(xB0, meanPrior, precPrior) - xF2.GetLogAverageOf(xB0));
//Console.WriteLine("evidence = {0} should be {1}", ev, evExpected);
return;
}
if (false)
{
xF2 = new Gaussian(-2, 10);
xF2 = FindxF2(meanPrior, precPrior, xF2);
xB0 = IsPositiveOp.XAverageConditional(true, xF2);
xF0 = GaussianOp_Slow.SampleAverageConditional(xB0, meanPrior, precPrior);
Console.WriteLine("xB = {0}", xB0);
Console.WriteLine("xF = {0} should be {1}", xF0, xF2);
return;
}
if (false)
{
xF2 = new Gaussian(-3998, 4000);
xF2 = new Gaussian(0.8651, 1.173);
xB0 = new Gaussian(-4, 2);
xB0 = new Gaussian(2000, 1e-5);
xB0 = FindxB(xB0, meanPrior, precPrior, xF2);
xF0 = GaussianOp_Slow.SampleAverageConditional(xB0, meanPrior, precPrior);
Console.WriteLine("xB = {0}", xB0);
Console.WriteLine("xF = {0} should be {1}", xF0, xF2);
return;
}
if (false)
{
//xF2 = new Gaussian(-7, 10);
//xF2 = new Gaussian(-50, 52);
xB0 = new Gaussian(-1.966, 5.506e-08);
//xF2 = new Gaussian(-3998, 4000);
xF0 = FindxF(xB0, meanPrior, precPrior, xF2);
Gaussian xB2 = IsPositiveOp.XAverageConditional(true, xF0);
Console.WriteLine("xF = {0}", xF0);
Console.WriteLine("xB = {0} should be {1}", xB2, xB0);
return;
}
if (true)
{
xF0 = new Gaussian(-3.397e+08, 5.64e+08);
xF0 = new Gaussian(-2.373e+04, 2.8e+04);
xB0 = new Gaussian(2.359, 1.392);
xF0 = Gaussian.FromNatural(-0.84, 0);
//xF0 = Gaussian.FromNatural(-0.7, 0);
for (int iter = 0; iter < 10; iter++)
{
xB0 = FindxB(xB0, meanPrior, precPrior, xF0);
Gaussian xFt = GaussianOp_Slow.SampleAverageConditional(xB0, meanPrior, precPrior);
Console.WriteLine("xB = {0}", xB0);
Console.WriteLine("xF = {0} should be {1}", xFt, xF0);
xF0 = FindxF0(xB0, meanPrior, precPrior, xF0);
Gaussian xBt = IsPositiveOp.XAverageConditional(true, xF0);
Console.WriteLine("xF = {0}", xF0);
Console.WriteLine("xB = {0} should be {1}", xBt, xB0);
}
Console.WriteLine("x = {0} should be {1}", xF0 * xB0, xExpected);
double ev = System.Math.Exp(IsPositiveOp.LogAverageFactor(true, xF0) + GaussianOp_Slow.LogAverageFactor(xB0, meanPrior, precPrior) - xF0.GetLogAverageOf(xB0));
Console.WriteLine("evidence = {0} should be {1}", ev, evExpected);
return;
}
//var precs = EpTests.linspace(1e-6, 1e-5, 200);
var precs = EpTests.linspace(xB0.Precision / 11, xB0.Precision, 100);
//var precs = EpTests.linspace(xF0.Precision/20, xF0.Precision/3, 100);
precs = EpTests.linspace(1e-9, 1e-5, 100);
//precs = new double[] { xB0.Precision };
var ms = EpTests.linspace(xB0.GetMean() - 1, xB0.GetMean() + 1, 100);
//var ms = EpTests.linspace(xF0.GetMean()-1, xF0.GetMean()+1, 100);
//precs = EpTests.linspace(1.0/10, 1.0/8, 200);
ms = EpTests.linspace(2000, 4000, 100);
//ms = new double[] { xB0.GetMean() };
Matrix result = new Matrix(precs.Length, ms.Length);
Matrix result2 = new Matrix(precs.Length, ms.Length);
//ms = new double[] { 0.7 };
for (int j = 0; j < ms.Length; j++)
{
double maxZ = double.NegativeInfinity;
double minZ = double.PositiveInfinity;
Gaussian maxxF = Gaussian.Uniform();
Gaussian minxF = Gaussian.Uniform();
Gaussian maxxB = Gaussian.Uniform();
Gaussian minxB = Gaussian.Uniform();
Vector v = Vector.Zero(3);
for (int i = 0; i < precs.Length; i++)
{
Gaussian xF = Gaussian.FromMeanAndPrecision(ms[j], precs[i]);
xF = xF2;
Gaussian xB = IsPositiveOp.XAverageConditional(true, xF);
xB = Gaussian.FromMeanAndPrecision(ms[j], precs[i]);
//xB = xB0;
v[0] = IsPositiveOp.LogAverageFactor(true, xF);
v[1] = GaussianOp.LogAverageFactor_slow(xB, meanPrior, precPrior);
//v[1] = GaussianOp_Slow.LogAverageFactor(xB, meanPrior, precPrior);
v[2] = -xF.GetLogAverageOf(xB);
double logZ = v.Sum();
double Z = logZ;
if (Z > maxZ)
{
maxZ = Z;
maxxF = xF;
maxxB = xB;
}
if (Z < minZ)
{
minZ = Z;
minxF = xF;
minxB = xB;
}
result[i, j] = Z;
result2[i, j] = IsPositiveOp.LogAverageFactor(true, xF) + xF0.GetLogAverageOf(xB) - xF.GetLogAverageOf(xB);
//Gaussian xF3 = GaussianOp.SampleAverageConditional_slower(xB, meanPrior, precPrior);
//result[i, j] = Math.Pow(xF3.Precision - xF.Precision, 2);
//result2[i, j] = Math.Pow((xF2*xB).Precision - (xF*xB).Precision, 2);
//result2[i, j] = -xF.GetLogAverageOf(xB);
//Gaussian xF2 = GaussianOp.SampleAverageConditional_slow(xB, Gaussian.PointMass(0), precPrior);
Gaussian xMarginal = xF * xB;
//Console.WriteLine("xF = {0} Z = {1} x = {2}", xF, Z.ToString("g4"), xMarginal);
}
double delta = v[1] - v[2];
//Console.WriteLine("xF = {0} xB = {1} maxZ = {2} x = {3}", maxxF, maxxB, maxZ.ToString("g4"), maxxF*maxxB);
//Console.WriteLine("xF = {0} maxZ = {1} delta = {2}", maxxF, maxZ.ToString("g4"), delta.ToString("g4"));
Console.WriteLine("xF = {0} xB = {1} minZ = {2} x = {3}", minxF, minxB, minZ.ToString("g4"), minxF * minxB);
}
//TODO: change path for cross platform using
using (var writer = new MatlabWriter(@"..\..\..\Tests\student.mat"))
{
writer.Write("z", result);
writer.Write("z2", result2);
writer.Write("precs", precs);
writer.Write("ms", ms);
}
}