public static Gaussian FindxF4(double[] xs, double[] logTrue, Gaussian xF)
{
double[] logApprox = new double[xs.Length];
Func <Vector, double> func = delegate(Vector x2)
{
Gaussian xFt = Gaussian.FromMeanAndPrecision(x2[0], System.Math.Exp(x2[1]));
for (int i = 0; i < xs.Length; i++)
{
logApprox[i] = xFt.GetLogProb(xs[i]);
}
Normalize(logApprox);
double sum = 0;
for (int i = 0; i < xs.Length; i++)
{
sum += System.Math.Abs(System.Math.Exp(logApprox[i]) - System.Math.Exp(logTrue[i]));
//sum += Math.Pow(Math.Exp(logApprox[i]) - Math.Exp(logTrue[i]), 2);
//sum += Math.Pow(Math.Exp(logApprox[i]/2) - Math.Exp(logTrue[i]/2), 2);
//sum += Math.Exp(logApprox[i])*(logApprox[i] - logTrue[i]);
//sum += Math.Exp(logTrue[i])*(logTrue[i] - logApprox[i]);
}
return(sum);
};
double m = xF.GetMean();
double p = xF.Precision;
Vector x = Vector.FromArray(m, System.Math.Log(p));
Minimize2(func, x);
return(Gaussian.FromMeanAndPrecision(x[0], System.Math.Exp(x[1])));
}
public void JaggedSetValues2()
{
Array jaggedGaussian = JaggedArray.ConvertToNew(
jagged, typeof(int), typeof(Gaussian),
delegate(object elt) { return(new Gaussian(1.0, 1.0)); });
Assert.Equal(
JaggedArray.GetLength(jaggedGaussian, typeof(Gaussian)),
JaggedArray.GetLength(jagged, typeof(int)));
JaggedArray.ConvertElements2(
jaggedGaussian, jagged, typeof(Gaussian),
delegate(object elt1, object elt2)
{
Gaussian g = (Gaussian)elt1;
double d = (int)elt2;
return(Gaussian.FromMeanAndPrecision(d + g.GetMean(), 2.0));
});
int i = 0;
foreach (Gaussian g in JaggedArray.ElementIterator(jaggedGaussian, typeof(Gaussian)))
{
Assert.Equal(g.GetMean(), 1.0 + arrExpected[i++]);
}
}
public static Discrete RunMultipleCyclistInference(Dictionary <int, double[]> trainingData)
{
ModelData initPriors = new ModelData(
Gaussian.FromMeanAndPrecision(29.5, 0.01),
Gamma.FromShapeAndScale(1.0, 0.5));
//Train the model
MultipleCyclistsTraining cyclistsTraining = new MultipleCyclistsTraining();
cyclistsTraining.CreateModel();
cyclistsTraining.SetModelData(initPriors);
ModelData[] posteriors1 = cyclistsTraining.InferModelData(trainingData[0], trainingData[1], trainingData[2], trainingData[3], trainingData[4], trainingData[5]);
Console.WriteLine("Cyclist 1 average travel time: {0}", posteriors1[0].AverageTimeDist);
Console.WriteLine("Cyclist 1 traffic noise: {0}", posteriors1[0].TrafficNoiseDist);
//Make predictions based on the trained model
MultipleCyclistsPrediction cyclistsPrediction = new MultipleCyclistsPrediction();
cyclistsPrediction.CreateModel();
cyclistsPrediction.SetModelData(posteriors1);
Gaussian[] posteriors2 = cyclistsPrediction.InferTomorrowsTime();
return(cyclistsPrediction.InferWinner());
}
private void IsPositiveModel()
{
double a = Factor.Random(Gaussian.FromMeanAndPrecision(1.2, 2.3));
bool c = Factor.IsPositive(a);
InferNet.Infer(c, nameof(c));
}
public static void RunCyclingTime4()
{
double[] trainingData = new double[] { 13, 17, 16, 12, 13, 12, 14, 18, 16, 16, 27, 32 };
ModelData initPriors = new ModelData(
Gaussian.FromMeanAndPrecision(15.0, 0.01),
Gamma.FromShapeAndScale(2.0, 0.5));
CyclistWithEvidence cyclistWithEvidence = new CyclistWithEvidence();
cyclistWithEvidence.CreateModel();
cyclistWithEvidence.SetModelData(initPriors);
double logEvidence = cyclistWithEvidence.InferEvidence(trainingData);
ModelDataMixed initPriorsMixed;
initPriorsMixed.AverageTimeDist = new Gaussian[] { new Gaussian(15.0, 100), new Gaussian(30.0, 100) };
initPriorsMixed.TrafficNoiseDist = new Gamma[] { new Gamma(2.0, 0.5), new Gamma(2.0, 0.5) };
initPriorsMixed.MixingDist = new Dirichlet(1, 1);
CyclistMixedWithEvidence cyclistMixedWithEvidence = new CyclistMixedWithEvidence();
cyclistMixedWithEvidence.CreateModel();
cyclistMixedWithEvidence.SetModelData(initPriorsMixed);
double logEvidenceMixed = cyclistMixedWithEvidence.InferEvidence(trainingData);
Console.WriteLine("Log evidence for single Gaussian: {0:f2}", logEvidence);
Console.WriteLine("Log evidence for mixture of two Gaussians: {0:f2}", logEvidenceMixed);
}
private void Max_APointMass(Gaussian max, Gaussian b)
{
double point = 3;
Gaussian toPoint = MaxGaussianOp.AAverageConditional(max, Gaussian.PointMass(point), b);
//Console.WriteLine($"{point} {toPoint} {toPoint.MeanTimesPrecision:g17} {toPoint.Precision:g17}");
if (max.IsPointMass && b.IsPointMass)
{
Gaussian toUniform = MaxGaussianOp.AAverageConditional(max, Gaussian.Uniform(), b);
if (max.Point > b.Point)
{
Assert.Equal(toUniform, max);
}
else
{
Assert.Equal(toUniform, Gaussian.Uniform());
}
}
double oldDiff = double.PositiveInfinity;
for (int i = 3; i < 100; i++)
{
Gaussian a = Gaussian.FromMeanAndPrecision(point, System.Math.Pow(10, i));
Gaussian to_a = MaxGaussianOp.AAverageConditional(max, a, b);
double diff = toPoint.MaxDiff(to_a);
//Console.WriteLine($"{a} {to_a} {to_a.MeanTimesPrecision:g17} {to_a.Precision:g17} {diff:g17}");
if (diff < 1e-14)
{
diff = 0;
}
Assert.True(diff <= oldDiff);
oldDiff = diff;
}
}
public void GaussianOpPrecision_IsMonotonicInSampleVariance()
{
using (TestUtils.TemporarilyAllowGaussianImproperMessages)
{
Gaussian mean = Gaussian.PointMass(0);
for (int logRate = 0; logRate < 310; logRate++)
{
Gamma precision = Gamma.FromShapeAndRate(300, System.Math.Pow(10, logRate));
double previousRate = double.PositiveInfinity;
for (int i = 0; i < 310; i++)
{
Gaussian sample = Gaussian.FromMeanAndPrecision(0, System.Math.Pow(10, -i));
Gamma precMsg = GaussianOp.PrecisionAverageConditional(sample, mean, precision);
//precMsg = GaussianOp_Laplace.PrecisionAverageConditional_slow(sample, mean, precision);
//Gamma precMsg2 = GaussianOp_Slow.PrecisionAverageConditional(sample, mean, precision);
//Console.WriteLine("{0}: {1} should be {2}", sample, precMsg, precMsg2);
Gamma post = precMsg * precision;
//Trace.WriteLine($"{sample}: {precMsg.Rate} post = {post.Rate}");
if (i >= logRate)
{
Assert.True(precMsg.Rate <= previousRate);
}
previousRate = precMsg.Rate;
}
}
}
}
public static Gaussian FindxB(Gaussian xB, Gaussian meanPrior, Gamma precPrior, Gaussian xF)
{
Gaussian xB3 = IsPositiveOp.XAverageConditional(true, xF);
Func <Vector, double> func = delegate(Vector x2)
{
Gaussian xB2 = Gaussian.FromMeanAndPrecision(x2[0], System.Math.Exp(x2[1]));
//Gaussian xF2 = GaussianOp.SampleAverageConditional_slow(xB2, meanPrior, precPrior);
Gaussian xF2 = GaussianOp_Slow.SampleAverageConditional(xB2, meanPrior, precPrior);
//Assert.True(xF2.MaxDiff(xF3) < 1e-10);
//return Math.Pow((xF*xB2).GetMean() - (xF2*xB2).GetMean(), 2) + Math.Pow((xF*xB2).GetVariance() - (xF2*xB2).GetVariance(), 2);
//return KlDiv(xF2*xB2, xF*xB2) + KlDiv(xF*xB3, xF*xB2);
//return KlDiv(xF2*xB2, xF*xB2) + Math.Pow((xF*xB3).GetMean() - (xF*xB2).GetMean(),2);
return(MeanError(xF2 * xB2, xF * xB2) + KlDiv(xF * xB3, xF * xB2));
//return xF.MaxDiff(xF2);
//Gaussian q = new Gaussian(0, 0.1);
//return Math.Pow((xF*q).GetMean() - (xF2*q).GetMean(), 2) + Math.Pow((xF*q).GetVariance() - (xF2*q).GetVariance(), 2);
};
double m = xB.GetMean();
double p = xB.Precision;
Vector x = Vector.FromArray(m, System.Math.Log(p));
Minimize2(func, x);
return(Gaussian.FromMeanAndPrecision(x[0], System.Math.Exp(x[1])));
}
public static Gaussian FindxF3(Gaussian xExpected, double evExpected, Gaussian meanPrior, Gamma precPrior, Gaussian xF)
{
Func <Vector, double> func = delegate(Vector x2)
{
Gaussian xFt = Gaussian.FromMeanAndPrecision(x2[0], System.Math.Exp(x2[1]));
Gaussian xB = IsPositiveOp.XAverageConditional(true, xFt);
Gaussian xM = xFt * xB;
//return KlDiv(xExpected, xM);
return(KlDiv(xM, xExpected));
//Gaussian xF2 = GaussianOp.SampleAverageConditional_slow(xB, meanPrior, precPrior);
//Gaussian xF2 = GaussianOp_Slow.SampleAverageConditional(xB, meanPrior, precPrior);
//Gaussian xM2 = xF2*xB;
//double ev1 = IsPositiveOp.LogAverageFactor(true, xFt);
//double ev2 = GaussianOp.LogAverageFactor_slow(xB, meanPrior, precPrior) - xFt.GetLogAverageOf(xB);
//double ev = ev1 + ev2;
//return xExpected.MaxDiff(xM);
//return Math.Pow(xExpected.GetMean() - xM.GetMean(), 2) + Math.Pow(ev - Math.Log(evExpected), 2);
//return 100*Math.Pow(xM.GetMean() - xM2.GetMean(), 2) -ev;
//return 100*Math.Pow(ev2, 2) + Math.Pow(ev - Math.Log(evExpected), 2);
//return 100*Math.Pow(ev2, 2) + Math.Pow(xM2.GetMean() - xM.GetMean(), 2);
};
double m = xF.GetMean();
double p = xF.Precision;
Vector x = Vector.FromArray(m, System.Math.Log(p));
Minimize2(func, x);
return(Gaussian.FromMeanAndPrecision(x[0], System.Math.Exp(x[1])));
}
public static WrappedGaussian AngleAverageLogarithm([SkipIfUniform] VectorGaussian rotate, double x, double y)
{
if (rotate.Dimension != 2)
{
throw new ArgumentException("rotate.Dimension (" + rotate.Dimension + ") != 2");
}
double rPrec = rotate.Precision[0, 0];
if (rotate.Precision[0, 1] != 0)
{
throw new ArgumentException("rotate.Precision is not diagonal");
}
if (rotate.Precision[1, 1] != rPrec)
{
throw new ArgumentException("rotate.Precision is not spherical");
}
#if false
Vector rotateMean = rotate.GetMean();
double a = x * rotateMean[0] + y * rotateMean[1];
double b = x * rotateMean[1] - y * rotateMean[0];
#else
double rotateMean0 = rotate.MeanTimesPrecision[0] / rotate.Precision[0, 0];
double rotateMean1 = rotate.MeanTimesPrecision[1] / rotate.Precision[1, 1];
double a = x * rotateMean0 + y * rotateMean1;
double b = x * rotateMean1 - y * rotateMean0;
#endif
double c = Math.Sqrt(a * a + b * b) * rPrec;
double angle0 = Math.Atan2(b, a);
// the exact conditional is exp(c*cos(angle - angle0)) which is a von Mises distribution.
// we will approximate this with a Gaussian lower bound that makes contact at the mode.
WrappedGaussian result = WrappedGaussian.Uniform();
result.Gaussian = Gaussian.FromMeanAndPrecision(angle0, c);
return(result);
}
private void IsBetweenModel()
{
double a = Factor.Random(Gaussian.FromMeanAndPrecision(0.1, 0.2));
double b = Factor.Random(Gaussian.FromMeanAndPrecision(0.3, 0.4));
double x = Factor.Random(Gaussian.FromMeanAndPrecision(0.2, 0.5));
bool c = Factor.IsBetween(x, a, b);
InferNet.Infer(c, nameof(c));
}
public static void RunCyclingTime2()
{
double[] trainingData = new double[] { 13, 17, 16, 12, 13, 12, 14, 18, 16, 16 };
ModelData initPriors = new ModelData(
Gaussian.FromMeanAndPrecision(1.0, 0.01),
Gamma.FromShapeAndScale(2.0, 0.5));
// Train the model
CyclistTraining cyclistTraining = new CyclistTraining();
cyclistTraining.CreateModel();
cyclistTraining.SetModelData(initPriors);
ModelData posteriors1 = cyclistTraining.InferModelData(trainingData);
Console.WriteLine("Average travel time = " + posteriors1.AverageTimeDist);
Console.WriteLine("Traffic noise = " + posteriors1.TrafficNoiseDist);
// Make predictions based on the trained model
CyclistPrediction cyclistPrediction = new CyclistPrediction();
cyclistPrediction.CreateModel();
cyclistPrediction.SetModelData(posteriors1);
Gaussian tomorrowsTimeDist = cyclistPrediction.InferTomorrowsTime();
double tomorrowsMean = tomorrowsTimeDist.GetMean();
double tomorrowsStdDev = Math.Sqrt(tomorrowsTimeDist.GetVariance());
Console.WriteLine("Tomorrows average time: {0:f2}", tomorrowsMean);
Console.WriteLine("Tomorrows standard deviation: {0:f2}", tomorrowsStdDev);
Console.WriteLine("Probability that tomorrow's time is < 18 min: {0}",
cyclistPrediction.InferProbabilityTimeLessThan(18.0));
// Second round of training
double[] trainingData2 = new double[] { 17, 19, 18, 21, 15 };
cyclistTraining.SetModelData(posteriors1);
ModelData posteriors2 = cyclistTraining.InferModelData(trainingData2);
Console.WriteLine("\n2nd training pass");
Console.WriteLine("Average travel time = " + posteriors2.AverageTimeDist);
Console.WriteLine("Traffic noise = " + posteriors2.TrafficNoiseDist);
// Predictions based on two rounds of training
cyclistPrediction.SetModelData(posteriors2);
tomorrowsTimeDist = cyclistPrediction.InferTomorrowsTime();
tomorrowsMean = tomorrowsTimeDist.GetMean();
tomorrowsStdDev = Math.Sqrt(tomorrowsTimeDist.GetVariance());
Console.WriteLine("Tomorrows average time: {0:f2}", tomorrowsMean);
Console.WriteLine("Tomorrows standard deviation: {0:f2}", tomorrowsStdDev);
Console.WriteLine("Probability that tomorrow's time is < 18 min: {0}",
cyclistPrediction.InferProbabilityTimeLessThan(18));
}
internal void StudentIsPositiveTest4()
{
double shape = 1;
Gamma precPrior = Gamma.FromShapeAndRate(shape, shape);
// mean=-1 causes improper messages
double mean = -1;
Gaussian meanPrior = Gaussian.PointMass(mean);
double evExpected;
Gaussian xExpected = StudentIsPositiveExact(mean, precPrior, out evExpected);
GaussianOp.ForceProper = false;
GaussianOp_Laplace.modified = true;
GaussianOp_Laplace.modified2 = true;
Gaussian xF = Gaussian.Uniform();
Gaussian xB = Gaussian.Uniform();
Gamma q = GaussianOp_Laplace.QInit();
double r0 = 0.38;
r0 = 0.1;
for (int iter = 0; iter < 20; iter++)
{
q = GaussianOp_Laplace.Q(xB, meanPrior, precPrior, q);
//xF = GaussianOp_Laplace.SampleAverageConditional(xB, meanPrior, precPrior, q);
xF = Gaussian.FromMeanAndPrecision(mean, r0);
xB = IsPositiveOp.XAverageConditional(true, xF);
Console.WriteLine("xF = {0} xB = {1}", xF, xB);
}
Console.WriteLine("x = {0} should be {1}", xF * xB, xExpected);
double[] precs = EpTests.linspace(1e-3, 5, 100);
double[] evTrue = new double[precs.Length];
double[] evApprox = new double[precs.Length];
double[] evApprox2 = new double[precs.Length];
//r0 = q.GetMean();
double sum = 0, sum2 = 0;
for (int i = 0; i < precs.Length; i++)
{
double r = precs[i];
Gaussian xFt = Gaussian.FromMeanAndPrecision(mean, r);
evTrue[i] = IsPositiveOp.LogAverageFactor(true, xFt) + precPrior.GetLogProb(r);
evApprox[i] = IsPositiveOp.LogAverageFactor(true, xF) + precPrior.GetLogProb(r) + xB.GetLogAverageOf(xFt) - xB.GetLogAverageOf(xF);
evApprox2[i] = IsPositiveOp.LogAverageFactor(true, xF) + precPrior.GetLogProb(r0) + q.GetLogProb(r) - q.GetLogProb(r0);
sum += System.Math.Exp(evApprox[i]);
sum2 += System.Math.Exp(evApprox2[i]);
}
Console.WriteLine("r0 = {0}: {1} {2} {3}", r0, sum, sum2, q.GetVariance() + System.Math.Pow(r0 - q.GetMean(), 2));
//TODO: change path for cross platform using
using (var writer = new MatlabWriter(@"..\..\..\Tests\student.mat"))
{
writer.Write("z", evTrue);
writer.Write("z2", evApprox);
writer.Write("z3", evApprox2);
writer.Write("precs", precs);
}
}
/// <summary>
/// Find the Laplace approximation for Beta(Logistic(x)) * Gaussian(x))
/// </summary>
/// <param name="beta">Beta distribution</param>
/// <param name="gauss">Gaussian distribution</param>
/// <returns>A proposal distribution</returns>
public static Gaussian LogisticProposalDistribution(Beta beta, Gaussian gauss)
{
if (beta.IsUniform())
{
return(new Gaussian(gauss));
}
// if gauss is uniform, m,p = 0 below, and the following code will just ignore the Gaussian
// and do a Laplace approximation for Beta(Logistic(x))
double c = beta.TrueCount - 1;
double d = beta.FalseCount - 1;
double m = gauss.GetMean();
double p = gauss.Precision;
// We want to find the mode of
// ln(g(x)) = c.ln(f(x)) + d.ln(1 - f(x)) - 0.5p((x - m)^2) + constant
// First deriv:
// h(x) = (ln(g(x))' = c.(1 - f(x)) - d.f(x) - p(x-m)
// Second deriv:
// h'(x) = (ln(g(x))' = -(c+d).f'(x) - p
// Use Newton-Raphson to find unique root of h(x).
// g(x) is log-concave so Newton-Raphson should converge quickly.
// Set the initial point by projecting beta
// to a Gaussian and taking the mean of the product:
double bMean, bVar;
beta.GetMeanAndVariance(out bMean, out bVar);
Gaussian prod = new Gaussian();
double invLogisticMean = Math.Log(bMean) - Math.Log(1.0 - bMean);
prod.SetToProduct(Gaussian.FromMeanAndVariance(invLogisticMean, bVar), gauss);
double xnew = prod.GetMean();
double x = 0, fx, dfx, hx, dhx = 0;
int maxIters = 100; // Should only need a handful of iters
int cnt = 0;
do
{
x = xnew;
fx = MMath.Logistic(x);
dfx = fx * (1.0 - fx);
// Find the root of h(x)
hx = c * (1.0 - fx) - d * fx - p * (x - m);
dhx = -(c + d) * dfx - p;
xnew = x - (hx / dhx); // The Newton step
if (Math.Abs(x - xnew) < 0.00001)
{
break;
}
} while (++cnt < maxIters);
if (cnt >= maxIters)
{
throw new InferRuntimeException("Unable to find proposal distribution mode");
}
return(Gaussian.FromMeanAndPrecision(x, -dhx));
}
public void MP_Sum()
{
InferenceEngine engine = new InferenceEngine();
engine.Compiler.DeclarationProvider = Microsoft.ML.Probabilistic.Compiler.RoslynDeclarationProvider.Instance;
Gaussian[] aPrior = new Gaussian[2];
aPrior[0] = Gaussian.FromMeanAndPrecision(0.1, 0.2);
aPrior[1] = Gaussian.FromMeanAndPrecision(0.3, 0.4);
var ca = engine.Compiler.Compile(SumModel, aPrior);
ca.Execute(1);
Gaussian cMarg = ca.Marginal <Gaussian>("c");
}
public void Run()
{
BayesianPCAModel bpca = new BayesianPCAModel();
if (!(bpca.engine.Algorithm is Algorithms.VariationalMessagePassing))
{
Console.WriteLine("This example only runs with Variational Message Passing");
return;
}
// Set a stable random number seed for repeatable runs
Rand.Restart(12347);
double[,] data = generateData(1000);
// Set the data
bpca.vData.ObservedValue = data;
// Set the dimensions
bpca.vN.ObservedValue = data.GetLength(0);
bpca.vD.ObservedValue = data.GetLength(1);
bpca.vM.ObservedValue = 6;
// Set the priors
bpca.priorMu.ObservedValue = Gaussian.FromMeanAndPrecision(0.0, 0.01);
bpca.priorPi.ObservedValue = Gamma.FromShapeAndRate(2.0, 2.0);
bpca.priorAlpha.ObservedValue = Gamma.FromShapeAndRate(2.0, 2.0);
// Initialize the W marginal to break symmetry
bpca.vW.InitialiseTo(randomGaussianArray(bpca.vM.ObservedValue, bpca.vD.ObservedValue));
// Infer the marginals
bpca.engine.NumberOfIterations = 200;
Gaussian[,] inferredW = bpca.engine.Infer <Gaussian[, ]>(bpca.vW);
Gaussian[] inferredMu = bpca.engine.Infer <Gaussian[]>(bpca.vMu);
Gamma[] inferredPi = bpca.engine.Infer <Gamma[]>(bpca.vPi);
// Print out the results
Console.WriteLine("Inferred W:");
printMatrixToConsole(inferredW);
Console.Write("Mean absolute means of rows in W: ");
printVectorToConsole(meanAbsoluteRowMeans(inferredW));
Console.Write(" True bias: ");
printVectorToConsole(trueMu);
Console.Write("Inferred bias: ");
printVectorToConsole(inferredMu);
Console.Write(" True noise:");
printVectorToConsole(truePi);
Console.Write("Inferred noise:");
printVectorToConsole(inferredPi);
Console.WriteLine();
}
public void Run()
{
BayesianPCAModel bpca = new BayesianPCAModel();
if (!(bpca.engine.Algorithm is Algorithms.VariationalMessagePassing))
{
Console.WriteLine("This example only runs with Variational Message Passing");
return;
}
// Set a stable random number seed for repeatable runs
Rand.Restart(12347);
double[,] data = generateData(1000);
// Set the data
bpca.data.ObservedValue = data;
// Set the dimensions
bpca.observationCount.ObservedValue = data.GetLength(0);
bpca.featureCount.ObservedValue = data.GetLength(1);
bpca.componentCount.ObservedValue = 6;
// Set the priors
bpca.priorMu.ObservedValue = Gaussian.FromMeanAndPrecision(0.0, 0.01);
bpca.priorPi.ObservedValue = Gamma.FromShapeAndRate(2.0, 2.0);
bpca.priorAlpha.ObservedValue = Gamma.FromShapeAndRate(2.0, 2.0);
// Set the initialization
bpca.initW.ObservedValue = randomGaussianArray(bpca.componentCount.ObservedValue, bpca.featureCount.ObservedValue);
// Infer the marginals
bpca.engine.NumberOfIterations = 200;
var inferredW = bpca.engine.Infer <IArray2D <Gaussian> >(bpca.W);
var inferredMu = bpca.engine.Infer <IReadOnlyList <Gaussian> >(bpca.mu);
var inferredPi = bpca.engine.Infer <IReadOnlyList <Gamma> >(bpca.pi);
// Print out the results
Console.WriteLine("Inferred W:");
printMatrixToConsole(inferredW);
Console.Write("Mean absolute means of rows in W: ");
printVectorToConsole(meanAbsoluteRowMeans(inferredW));
Console.Write(" True bias: ");
printVectorToConsole(trueMu);
Console.Write("Inferred bias: ");
printVectorToConsole(inferredMu.Select(d => d.GetMean()));
Console.Write(" True noise:");
printVectorToConsole(truePi);
Console.Write("Inferred noise:");
printVectorToConsole(inferredPi.Select(d => d.GetMean()));
Console.WriteLine();
}
private void MatrixMultiplyModel()
{
double[,] a = new double[3, 2];
double[,] b = new double[2, 3];
double[,] c = new double[3, 3];
for (int i = 0; i < 3; i++)
{
for (int j = 0; j < 2; j++)
{
a[i, j] = Factor.Random(Gaussian.FromMeanAndPrecision(1.2, 3.4));
b[j, i] = Factor.Random(Gaussian.FromMeanAndPrecision(4.3, 2.1));
}
}
c = Factor.MatrixMultiply(a, b);
InferNet.Infer(c, nameof(c));
}
private static Gaussian GetConstrainedMessage1(Gaussian sample, Gaussian mean, Gamma precision, Gaussian to_sample)
{
Gaussian sampleMarginal = sample * to_sample;
double m1, v1;
to_sample.GetMeanAndVariance(out m1, out v1);
double m, v;
sampleMarginal.GetMeanAndVariance(out m, out v);
double moment2 = m * m + v;
// vq < moment2 implies 1/vq > 1/moment2
// implies 1/v2 > 1/moment2 - to_sample.Precision
double v2max = 1 / (1 / moment2 - to_sample.Precision);
double v2min = 1e-2;
double[] v2s = EpTests.linspace(v2min, v2max, 100);
double p2min = 1 / moment2 - to_sample.Precision;
if (p2min < 0.0)
{
return(to_sample);
}
double p2max = sample.Precision * 10;
double[] p2s = EpTests.linspace(p2min, p2max, 100);
Gaussian bestResult = to_sample;
double bestScore = double.PositiveInfinity;
for (int i = 0; i < p2s.Length; i++)
{
double p2 = p2s[i];
double vq = 1 / (to_sample.Precision + p2);
double m2 = (System.Math.Sqrt(moment2 - vq) / vq - to_sample.MeanTimesPrecision) / p2;
// check
double mq = vq * (to_sample.MeanTimesPrecision + m2 * p2);
Assert.True(MMath.AbsDiff(mq * mq + vq, moment2) < 1e-10);
Gaussian sample2 = Gaussian.FromMeanAndPrecision(m2, p2);
Gaussian result = GaussianOp.SampleAverageConditional_slow(sample2, mean, precision);
double score = System.Math.Abs(result.MeanTimesPrecision);
if (score < bestScore)
{
bestScore = score;
bestResult = result;
}
}
return(bestResult);
}
public static Gaussian FindxF2(Gaussian meanPrior, Gamma precPrior, Gaussian xF)
{
Func <Vector, double> func = delegate(Vector x2)
{
Gaussian xFt = Gaussian.FromMeanAndPrecision(x2[0], System.Math.Exp(x2[1]));
Gaussian xB = IsPositiveOp.XAverageConditional(true, xFt);
Gaussian xF2 = GaussianOp_Slow.SampleAverageConditional(xB, meanPrior, precPrior);
return(xFt.MaxDiff(xF2));
};
double m = xF.GetMean();
double p = xF.Precision;
Vector x = Vector.FromArray(m, System.Math.Log(p));
Minimize2(func, x);
return(Gaussian.FromMeanAndPrecision(x[0], System.Math.Exp(x[1])));
}
public void GenData(int n, int seed, out double[] data,
out double trueR2, out double truePrec)
{
Rand.Restart(seed);
Gamma r2Dist = Gamma.FromShapeAndRate(Shape1, Rate1);
trueR2 = r2Dist.Sample();
Gamma precDist = Gamma.FromShapeAndRate(Shape2, trueR2);
truePrec = precDist.Sample();
data = new double[n];
for (int i = 0; i < n; i++)
{
Gaussian xDist = Gaussian.FromMeanAndPrecision(GaussMean, truePrec);
data[i] = xDist.Sample();
}
}
/// <summary>
/// Priors from the community posteriors, using the means of the weight mean and weight precision posteriors.
/// </summary>
/// <param name="posteriors">The posteriors.</param>
/// <param name="featureSet">The feature set.</param>
/// <param name="thresholdAndNoiseVariance">The threshold and noise variance.</param>
/// <returns>The <see cref="Priors" /></returns>
internal static Priors FromCommunityPosteriors(CommunityPosteriors posteriors, FeatureSet featureSet, double thresholdAndNoiseVariance)
{
return(new Priors
{
Weights =
featureSet.FeatureBuckets.ToDictionary(
ia => ia,
ia =>
posteriors.WeightMeans.ContainsKey(ia) && posteriors.WeightPrecisions.ContainsKey(ia)
? Gaussian.FromMeanAndPrecision(
posteriors.WeightMeans[ia].GetMean(),
posteriors.WeightPrecisions[ia].GetMean())
: Gaussian.FromMeanAndVariance(0.0, thresholdAndNoiseVariance)),
Threshold = Gaussian.FromMeanAndVariance(0.0, thresholdAndNoiseVariance),
NoiseVariance = thresholdAndNoiseVariance
});
}
internal void GaussianOpPrecision3()
{
using (TestUtils.TemporarilyAllowGaussianImproperMessages)
{
Gaussian mean = Gaussian.PointMass(0);
Gamma precision = Gamma.FromShapeAndRate(2, 10);
for (int i = -10; i < 10; i++)
{
Gaussian sample = Gaussian.FromMeanAndPrecision(0, System.Math.Pow(10, -i));
Gamma precMsg = GaussianOp.PrecisionAverageConditional(sample, mean, precision);
//precMsg = GaussianOp_Laplace.PrecisionAverageConditional_slow(sample, mean, precision);
//Gamma precMsg2 = GaussianOp_Slow.PrecisionAverageConditional(sample, mean, precision);
//Console.WriteLine("{0}: {1} should be {2}", sample, precMsg, precMsg2);
Gamma post = precMsg * precision;
Console.WriteLine("{0}: {1} post = {2}", sample, precMsg.Rate, post.Rate);
}
}
}
public static Gaussian XAverageLogarithm([SkipIfUniform] VectorGaussian rotate, [Proper] WrappedGaussian angle)
{
// for x ~ N(m,v):
// E[cos(x)] = cos(m)*exp(-v/2)
// E[sin(x)] = sin(m)*exp(-v/2)
if (angle.Period != 2 * Math.PI)
{
throw new ArgumentException("angle.Period (" + angle.Period + ") != 2*PI (" + 2 * Math.PI + ")");
}
double angleMean, angleVar;
angle.Gaussian.GetMeanAndVariance(out angleMean, out angleVar);
double expVar = Math.Exp(-0.5 * angleVar);
double mCos = Math.Cos(angleMean) * expVar;
double mSin = Math.Sin(angleMean) * expVar;
if (rotate.Dimension != 2)
{
throw new ArgumentException("rotate.Dimension (" + rotate.Dimension + ") != 2");
}
double prec = rotate.Precision[0, 0];
if (rotate.Precision[0, 1] != 0)
{
throw new ArgumentException("rotate.Precision is not diagonal");
}
if (rotate.Precision[1, 1] != prec)
{
throw new ArgumentException("rotate.Precision is not spherical");
}
#if false
Vector rotateMean = rotate.GetMean();
double mean = mCos * rotateMean[0] + mSin * rotateMean[1];
#else
double rotateMean0 = rotate.MeanTimesPrecision[0] / rotate.Precision[0, 0];
double rotateMean1 = rotate.MeanTimesPrecision[1] / rotate.Precision[1, 1];
double mean = mCos * rotateMean0 + mSin * rotateMean1;
#endif
if (double.IsNaN(mean))
{
throw new ApplicationException("result is nan");
}
return(Gaussian.FromMeanAndPrecision(mean, prec));
}
public void JaggedSetValues()
{
Array jaggedGaussian = JaggedArray.ConvertToNew(
jagged, typeof(int), typeof(Gaussian),
delegate(object elt) { return(new Gaussian(0.0, 1.0)); });
Assert.Equal(
JaggedArray.GetLength(jaggedGaussian, typeof(Gaussian)),
JaggedArray.GetLength(jagged, typeof(int)));
JaggedArray.ConvertElements(
jaggedGaussian, typeof(Gaussian),
delegate(object elt) { return(Gaussian.FromMeanAndPrecision(1.0, 2.0)); });
foreach (Gaussian g in JaggedArray.ElementIterator(jaggedGaussian, typeof(Gaussian)))
{
Assert.Equal(1.0, g.GetMean());
}
}
public static Gaussian FindxF(Gaussian xB, Gaussian meanPrior, Gamma precPrior, Gaussian xF)
{
Gaussian xF3 = GaussianOp_Slow.SampleAverageConditional(xB, meanPrior, precPrior);
Func <Vector, double> func = delegate(Vector x2)
{
Gaussian xF2 = Gaussian.FromMeanAndPrecision(x2[0], System.Math.Exp(x2[1]));
Gaussian xB2 = IsPositiveOp.XAverageConditional(true, xF2);
//return (xF2*xB2).MaxDiff(xF2*xB) + (xF3*xB).MaxDiff(xF2*xB);
//return KlDiv(xF2*xB2, xF2*xB) + KlDiv(xF3*xB, xF2*xB);
//return KlDiv(xF3*xB, xF2*xB) + Math.Pow((xF2*xB2).GetMean() - (xF2*xB).GetMean(),2);
return(KlDiv(xF2 * xB2, xF2 * xB) + MeanError(xF3 * xB, xF2 * xB));
};
double m = xF.GetMean();
double p = xF.Precision;
Vector x = Vector.FromArray(m, System.Math.Log(p));
Minimize2(func, x);
//MinimizePowell(func, x);
return(Gaussian.FromMeanAndPrecision(x[0], System.Math.Exp(x[1])));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="DoublePlusOp"]/message_doc[@name="SumAverageConditional(double, Gaussian)"]/*'/>
public static Gaussian SumAverageConditional(double a, [SkipIfUniform] Gaussian b)
{
if (b.IsPointMass)
{
return(SumAverageConditional(a, b.Point));
}
if (b.IsUniform())
{
return(b);
}
double meanTimesPrecision = b.MeanTimesPrecision + a * b.Precision;
if (Math.Abs(meanTimesPrecision) > double.MaxValue)
{
return(Gaussian.FromMeanAndPrecision(b.GetMean() + a, b.Precision));
}
else
{
return(Gaussian.FromNatural(meanTimesPrecision, b.Precision));
}
}
private void Max_MaxPointMass(Gaussian a, Gaussian b)
{
double point = 3;
Gaussian toPoint = MaxGaussianOp.MaxAverageConditional(Gaussian.PointMass(point), a, b);
//Console.WriteLine($"{point} {toPoint} {toPoint.MeanTimesPrecision} {toPoint.Precision}");
double oldDiff = double.PositiveInfinity;
for (int i = 5; i < 100; i++)
{
Gaussian max = Gaussian.FromMeanAndPrecision(point, System.Math.Pow(10, i));
Gaussian to_max = MaxGaussianOp.MaxAverageConditional(max, a, b);
double diff = toPoint.MaxDiff(to_max);
//Console.WriteLine($"{max} {to_max} {to_max.MeanTimesPrecision} {to_max.Precision} {diff}");
if (diff < 1e-14)
{
diff = 0;
}
Assert.True(diff <= oldDiff);
oldDiff = diff;
}
}
private Gaussian StudentIsPositiveExact(double mean, Gamma precPrior, out double evidence)
{
// importance sampling for true answer
GaussianEstimator est = new GaussianEstimator();
int nSamples = 1000000;
evidence = 0;
for (int iter = 0; iter < nSamples; iter++)
{
double precSample = precPrior.Sample();
Gaussian xPrior = Gaussian.FromMeanAndPrecision(mean, precSample);
double logWeight = IsPositiveOp.LogAverageFactor(true, xPrior);
evidence += System.Math.Exp(logWeight);
double xSample = xPrior.Sample();
if (xSample > 0)
{
est.Add(xSample);
}
}
evidence /= nSamples;
return(est.GetDistribution(new Gaussian()));
}
public EstimatorTest()
{
// Create distribution jagged 2D array, and create
// the parallel jagged 2D array of distributions
dim1 = 2;
dim2 = 3;
ga2aDistArray = new GaussianArray2DArray(dim1, dim2);
ga2aArrayOfDist = new Gaussian[dim1, dim2][];
for (int i = 0; i < dim1; i++)
{
for (int j = 0; j < dim2; j++)
{
ga2aDistArray[i, j] = new GaussianArray(i + j + 1);
ga2aArrayOfDist[i, j] = new Gaussian[i + j + 1];
for (int k = 0; k < ga2aDistArray[i, j].Count; k++)
{
ga2aDistArray[i, j][k] = Gaussian.FromMeanAndPrecision((double)k, (double)((k + 1) * (k + 1)));
ga2aArrayOfDist[i, j][k] = new Gaussian(ga2aDistArray[i, j][k]);
}
}
}
}
