public void GPClassificationTest2()
{
bool[] yData = new bool[] { false, true, false };
double[] xData = new double[]
{
-1.555555555555556, -0.2222222222222223, 1.555555555555555
};
Vector[] xVec = Array.ConvertAll(xData, v => Vector.Constant(1, v));
Vector[] basis = new Vector[] { Vector.Zero(1) };
IKernelFunction kf = new SquaredExponential(0.0);
SparseGPFixed sgpf = new SparseGPFixed(kf, basis);
Variable <bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
Variable <IFunction> f = Variable.Random <IFunction>(new SparseGP(sgpf)).Named("f");
Range item = new Range(xVec.Length).Named("item");
VariableArray <Vector> x = Variable.Array <Vector>(item).Named("x");
x.ObservedValue = xVec;
VariableArray <bool> y = Variable.Array <bool>(item).Named("y");
y.ObservedValue = yData;
VariableArray <double> h = Variable.Array <double>(item).Named("h");
h[item] = Variable.FunctionEvaluate(f, x[item]);
y[item] = (h[item] > 0);
block.CloseBlock();
InferenceEngine engine = new InferenceEngine();
SparseGP sgp = engine.Infer <SparseGP>(f);
Vector alphaExpected = Vector.FromArray(new double[] { 0.573337393823702 });
Console.WriteLine("alpha = {0} should be {1}", sgp.Alpha, alphaExpected);
double[] xTest = new double[]
{
-2, -1, 0.0
};
Vector[] xTestVec = Array.ConvertAll(xTest, v => Vector.Constant(1, v));
double[] yMeanTest = new double[]
{
0.077592778583272, 0.347746707713812, 0.573337393823702
};
double[] yVarTest = new double[]
{
0.986784459962251, 0.734558782611933, 0.278455962249970
};
for (int i = 0; i < xTestVec.Length; i++)
{
Gaussian pred = sgp.Marginal(xTestVec[i]);
Gaussian predExpected = new Gaussian(yMeanTest[i], yVarTest[i]);
Console.WriteLine("f({0}) = {1} should be {2}", xTest[i], pred, predExpected);
Assert.True(predExpected.MaxDiff(pred) < 1e-4);
}
double evExpected = -2.463679892165236;
double evActual = engine.Infer <Bernoulli>(evidence).LogOdds;
Console.WriteLine("evidence = {0} should be {1}", evActual, evExpected);
Assert.True(MMath.AbsDiff(evExpected, evActual, 1e-6) < 1e-4);
}
public void GPClassificationTest1()
{
bool[] yData = new bool[] { true };
double[] xData = new double[] { -0.2222222222222223 };
Vector[] xVec = Array.ConvertAll(xData, v => Vector.Constant(1, v));
Vector[] basis = new Vector[] { Vector.Zero(1) };
IKernelFunction kf = new SquaredExponential(0.0);
SparseGPFixed sgpf = new SparseGPFixed(kf, basis);
Variable <bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
Variable <IFunction> f = Variable.Random <IFunction>(new SparseGP(sgpf)).Named("f");
Range item = new Range(xVec.Length).Named("item");
VariableArray <Vector> x = Variable.Array <Vector>(item).Named("x");
x.ObservedValue = xVec;
VariableArray <bool> y = Variable.Array <bool>(item).Named("y");
y.ObservedValue = yData;
VariableArray <double> h = Variable.Array <double>(item).Named("h");
h[item] = Variable.FunctionEvaluate(f, x[item]);
y[item] = (h[item] > 0);
block.CloseBlock();
InferenceEngine engine = new InferenceEngine();
SparseGP sgp = engine.Infer <SparseGP>(f);
Vector alphaExpected = Vector.FromArray(new double[] { 0.778424938343491 });
Console.WriteLine("alpha = {0} should be {1}", sgp.Alpha, alphaExpected);
double[] xTest = new double[]
{
-2, -1, 0.0
};
Vector[] xTestVec = Array.ConvertAll(xTest, v => Vector.Constant(1, v));
double[] yMeanTest = new double[]
{
0.105348359509159, 0.472138591390244, 0.778424938343491
};
double[] yVarTest = new double[]
{
0.988901723148729, 0.777085150520037, 0.394054615364932
};
for (int i = 0; i < xTestVec.Length; i++)
{
Gaussian pred = sgp.Marginal(xTestVec[i]);
Gaussian predExpected = new Gaussian(yMeanTest[i], yVarTest[i]);
Console.WriteLine("f({0}) = {1} should be {2}", xTest[i], pred, predExpected);
Assert.True(predExpected.MaxDiff(pred) < 1e-4);
}
double evExpected = -0.693147180559945;
double evActual = engine.Infer <Bernoulli>(evidence).LogOdds;
Console.WriteLine("evidence = {0} should be {1}", evActual, evExpected);
Assert.True(MMath.AbsDiff(evExpected, evActual, 1e-6) < 1e-4);
}
/// <summary>EP message to <c>y</c>.</summary>
/// <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>
/// <returns>The outgoing EP message to the <c>y</c> argument.</returns>
/// <remarks>
/// <para>The outgoing message is a distribution matching the moments of <c>y</c> as the random arguments are varied. The formula is <c>proj[p(y) sum_(func) p(func) factor(y,func,x)]/p(y)</c>.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="func" /> is not a proper distribution.</exception>
public static Gaussian YAverageConditional([SkipIfUniform] SparseGP func, Vector x)
{
return(func.Marginal(x));
}
internal void HeteroscedasticGPR()
{
// This model is based on the paper "Most Likely Heteroscedastic Gaussian Process Regression" by Kersting et al, ICML 2007
// Silverman's motorcycle benchmark dataset
double[] inputs = new double[]
{
2.4, 2.6, 3.2, 3.6, 4, 6.2, 6.6, 6.8, 7.8, 8.199999999999999, 8.800000000000001, 8.800000000000001,
9.6, 10, 10.2, 10.6, 11, 11.4, 13.2, 13.6, 13.8, 14.6, 14.6, 14.6, 14.6, 14.6, 14.6, 14.8, 15.4, 15.4,
15.4, 15.4, 15.6, 15.6, 15.8, 15.8, 16, 16, 16.2, 16.2, 16.2, 16.4, 16.4, 16.6, 16.8, 16.8, 16.8, 17.6,
17.6, 17.6, 17.6, 17.8, 17.8, 18.6, 18.6, 19.2, 19.4, 19.4, 19.6, 20.2, 20.4, 21.2, 21.4, 21.8, 22, 23.2,
23.4, 24, 24.2, 24.2, 24.6, 25, 25, 25.4, 25.4, 25.6, 26, 26.2, 26.2, 26.4, 27, 27.2, 27.2, 27.2, 27.6,
28.2, 28.4, 28.4, 28.6, 29.4, 30.2, 31, 31.2, 32, 32, 32.8, 33.4, 33.8, 34.4, 34.8, 35.2, 35.2, 35.4, 35.6,
35.6, 36.2, 36.2, 38, 38, 39.2, 39.4, 40, 40.4, 41.6, 41.6, 42.4, 42.8, 42.8, 43, 44, 44.4, 45, 46.6, 47.8,
47.8, 48.8, 50.6, 52, 53.2, 55, 55, 55.4, 57.6
};
double[] outputs = new double[]
{
0, -1.3, -2.7, 0, -2.7, -2.7, -2.7, -1.3, -2.7, -2.7, -1.3, -2.7, -2.7, -2.7, -5.4,
-2.7, -5.4, 0, -2.7, -2.7, 0, -13.3, -5.4, -5.4, -9.300000000000001, -16, -22.8, -2.7, -22.8, -32.1, -53.5,
-54.9, -40.2, -21.5, -21.5, -50.8, -42.9, -26.8, -21.5, -50.8, -61.7, -5.4, -80.40000000000001, -59, -71,
-91.09999999999999, -77.7, -37.5, -85.59999999999999, -123.1, -101.9, -99.09999999999999, -104.4, -112.5,
-50.8, -123.1, -85.59999999999999, -72.3, -127.2, -123.1, -117.9, -134, -101.9, -108.4, -123.1, -123.1, -128.5,
-112.5, -95.09999999999999, -81.8, -53.5, -64.40000000000001, -57.6, -72.3, -44.3, -26.8, -5.4, -107.1, -21.5,
-65.59999999999999, -16, -45.6, -24.2, 9.5, 4, 12, -21.5, 37.5, 46.9, -17.4, 36.2, 75, 8.1, 54.9, 48.2, 46.9,
16, 45.6, 1.3, 75, -16, -54.9, 69.59999999999999, 34.8, 32.1, -37.5, 22.8, 46.9, 10.7, 5.4, -1.3, -21.5, -13.3,
30.8, -10.7, 29.4, 0, -10.7, 14.7, -1.3, 0, 10.7, 10.7, -26.8, -14.7, -13.3, 0, 10.7, -14.7, -2.7, 10.7, -2.7, 10.7
};
Range j = new Range(inputs.Length);
Vector[] inputsVec = Util.ArrayInit(inputs.Length, i => Vector.FromArray(inputs[i]));
VariableArray <Vector> x = Variable.Observed(inputsVec, j).Named("x");
VariableArray <double> y = Variable.Observed(outputs, j).Named("y");
// Set up the GP prior, which will be filled in later
Variable <SparseGP> prior = Variable.New <SparseGP>().Named("prior");
Variable <SparseGP> prior2 = Variable.New <SparseGP>().Named("prior2");
// The sparse GP variable - a distribution over functions
Variable <IFunction> f = Variable <IFunction> .Random(prior).Named("f");
Variable <IFunction> r = Variable <IFunction> .Random(prior2).Named("r");
Variable <double> mean = Variable.FunctionEvaluate(f, x[j]).Named("mean");
Variable <double> logVariance = Variable.FunctionEvaluate(r, x[j]).Named("logVariance");
Variable <double> variance = Variable.Exp(logVariance);
y[j] = Variable.GaussianFromMeanAndVariance(mean, variance);
InferenceEngine engine = new InferenceEngine();
GaussianProcess gp = new GaussianProcess(new ConstantFunction(0), new SquaredExponential(0));
GaussianProcess gp2 = new GaussianProcess(new ConstantFunction(0), new SquaredExponential(0));
// Fill in the sparse GP prior
//Vector[] basis = Util.ArrayInit(120, i => Vector.FromArray(0.5*i));
Vector[] basis = Util.ArrayInit(60, i => Vector.FromArray(1.0 * i));
prior.ObservedValue = new SparseGP(new SparseGPFixed(gp, basis));
prior2.ObservedValue = new SparseGP(new SparseGPFixed(gp2, basis));
// Infer the posterior Sparse GP
SparseGP sgp = engine.Infer <SparseGP>(f);
// Check that training set is classified correctly
Console.WriteLine();
Console.WriteLine("Predictions on training set:");
for (int i = 0; i < outputs.Length; i++)
{
Gaussian post = sgp.Marginal(inputsVec[i]);
//double postMean = post.GetMean();
Console.WriteLine("f({0}) = {1}", inputs[i], post);
}
//TODO: change path for cross platform using
using (MatlabWriter writer = new MatlabWriter(@"..\..\HGPR.mat"))
{
int n = outputs.Length;
double[] m = new double[n];
double[] s = new double[n];
for (int i = 0; i < n; i++)
{
Gaussian post = sgp.Marginal(inputsVec[i]);
double mi, vi;
post.GetMeanAndVariance(out mi, out vi);
m[i] = mi;
s[i] = System.Math.Sqrt(vi);
}
writer.Write("mean", m);
writer.Write("std", s);
}
}
public void GPClassificationTest()
{
bool[] yData = new bool[] { false, false, false, true, true, true, true, false, false, false };
double[] xData = new double[]
{
-2, -1.555555555555556, -1.111111111111111, -0.6666666666666667, -0.2222222222222223, 0.2222222222222223, 0.6666666666666665, 1.111111111111111,
1.555555555555555, 2
};
Vector[] xVec = Array.ConvertAll(xData, v => Vector.Constant(1, v));
Vector[] basis = new Vector[] { xVec[1], xVec[4], xVec[8] };
//basis = xVec;
IKernelFunction kf = new SquaredExponential(0.0);
SparseGPFixed sgpf = new SparseGPFixed(kf, basis);
Variable <bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
Variable <IFunction> f = Variable.Random <IFunction>(new SparseGP(sgpf)).Named("f");
Range item = new Range(xVec.Length).Named("item");
VariableArray <Vector> x = Variable.Array <Vector>(item).Named("x");
x.ObservedValue = xVec;
VariableArray <bool> y = Variable.Array <bool>(item).Named("y");
y.ObservedValue = yData;
VariableArray <double> h = Variable.Array <double>(item).Named("h");
h[item] = Variable.FunctionEvaluate(f, x[item]);
y[item] = (h[item] > 0);
block.CloseBlock();
InferenceEngine engine = new InferenceEngine();
SparseGP sgp = engine.Infer <SparseGP>(f);
Vector alphaExpected = Vector.FromArray(new double[] { -1.410457563120709, 1.521306076273262, -1.008600221619413 });
Console.WriteLine("alpha = {0} should be {1}", sgp.Alpha, alphaExpected);
double[] xTest = new double[]
{
-2, -1, 0.0
};
Vector[] xTestVec = Array.ConvertAll(xTest, v => Vector.Constant(1, v));
// computed by matlab/MNT/GP/test_gpc.m
double[] yMeanTest = new double[]
{
-0.966351175090184, -0.123034591744284, 0.762757400008960
};
double[] yVarTest = new double[]
{
0.323871157983366, 0.164009511251333, 0.162068482365962
};
for (int i = 0; i < xTestVec.Length; i++)
{
Gaussian pred = sgp.Marginal(xTestVec[i]);
Gaussian predExpected = new Gaussian(yMeanTest[i], yVarTest[i]);
Console.WriteLine("f({0}) = {1} should be {2}", xTest[i], pred, predExpected);
Assert.True(predExpected.MaxDiff(pred) < 1e-4);
}
double evExpected = -4.907121241357144;
double evActual = engine.Infer <Bernoulli>(evidence).LogOdds;
Console.WriteLine("evidence = {0} should be {1}", evActual, evExpected);
Assert.True(MMath.AbsDiff(evExpected, evActual, 1e-6) < 1e-4);
}
public void GPClassificationExample()
{
// The data
bool[] ydata = { true, true, false, true, false, false };
Vector[] xdata = new Vector[]
{
Vector.FromArray(new double[2] {
0, 0
}),
Vector.FromArray(new double[2] {
0, 1
}),
Vector.FromArray(new double[2] {
1, 0
}),
Vector.FromArray(new double[2] {
0, 0.5
}),
Vector.FromArray(new double[2] {
1.5, 0
}),
Vector.FromArray(new double[2] {
0.5, 1.0
})
};
// Open an evidence block to allow model scoring
Variable <bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
// Set up the GP prior, which will be filled in later
Variable <SparseGP> prior = Variable.New <SparseGP>().Named("prior");
// The sparse GP variable - a distribution over functions
Variable <IFunction> f = Variable <IFunction> .Random(prior).Named("f");
// The locations to evaluate the function
VariableArray <Vector> x = Variable.Constant(xdata).Named("x");
Range j = x.Range.Named("j");
// The observation model
VariableArray <bool> y = Variable.Array <bool>(j).Named("y");
y[j] = (Variable.GaussianFromMeanAndVariance(Variable.FunctionEvaluate(f, x[j]), 0.1) > 0);
// Attach the observations
y.ObservedValue = ydata;
// Close the evidence block
block.CloseBlock();
InferenceEngine engine = new InferenceEngine();
// The basis
Vector[] basis = new Vector[]
{
Vector.FromArray(new double[2] {
0.2, 0.2
}),
Vector.FromArray(new double[2] {
0.2, 0.8
}),
Vector.FromArray(new double[2] {
0.8, 0.2
}),
Vector.FromArray(new double[2] {
0.8, 0.8
})
};
for (int trial = 0; trial < 3; trial++)
{
// The kernel
IKernelFunction kf;
if (trial == 0)
{
kf = new SquaredExponential(-0.0);
//kf = new LinearKernel(new double[] { 0.0, 0.0 });
}
else if (trial == 1)
{
kf = new SquaredExponential(-0.5);
}
else
{
kf = new NNKernel(new double[] { 0.0, 0.0 }, -1.0);
}
// Fill in the sparse GP prior
prior.ObservedValue = new SparseGP(new SparseGPFixed(kf, basis));
// Model score
double NNscore = engine.Infer <Bernoulli>(evidence).LogOdds;
Console.WriteLine("{0} evidence = {1}", kf, NNscore.ToString("g4"));
}
// Infer the posterior Sparse GP
SparseGP sgp = engine.Infer <SparseGP>(f);
// Check that training set is classified correctly
Console.WriteLine();
Console.WriteLine("Predictions on training set:");
for (int i = 0; i < ydata.Length; i++)
{
Gaussian post = sgp.Marginal(xdata[i]);
double postMean = post.GetMean();
string comment = (ydata[i] == (postMean > 0.0)) ? "correct" : "incorrect";
Console.WriteLine("f({0}) = {1} ({2})", xdata[i], post, comment);
Assert.True(ydata[i] == (postMean > 0.0));
}
}
public void GPRegressionTest()
{
double[] yData = new double[]
{
-0.06416828853982412, -0.6799959810206935, -0.4541652863622044, 0.155770359928991, 1.036659040456137, 0.7353821980830825, 0.8996680933259047,
-0.05368704705684217, -0.7905775695015919, -0.1436284683992815
};
double[] xData = new double[]
{
-2, -1.555555555555556, -1.111111111111111, -0.6666666666666667, -0.2222222222222223, 0.2222222222222223, 0.6666666666666665, 1.111111111111111,
1.555555555555555, 2
};
Vector[] xVec = Array.ConvertAll(xData, v => Vector.Constant(1, v));
Vector[] basis = new Vector[] { xVec[1], xVec[4], xVec[8] };
IKernelFunction kf = new SquaredExponential(System.Math.Log(2.0));
SparseGPFixed sgpf = new SparseGPFixed(kf, basis);
Variable <bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
Variable <IFunction> f = Variable.Random <IFunction>(new SparseGP(sgpf)).Named("f");
Range item = new Range(xVec.Length).Named("item");
VariableArray <Vector> x = Variable.Array <Vector>(item).Named("x");
x.ObservedValue = xVec;
VariableArray <double> y = Variable.Array <double>(item).Named("y");
y.ObservedValue = yData;
VariableArray <double> h = Variable.Array <double>(item).Named("h");
h[item] = Variable.FunctionEvaluate(f, x[item]);
y[item] = Variable.GaussianFromMeanAndVariance(h[item], 0.1);
block.CloseBlock();
InferenceEngine engine = new InferenceEngine();
SparseGP sgp = engine.Infer <SparseGP>(f);
Vector alphaExpected = Vector.FromArray(new double[] { -3.250044160725389, 4.579296091435270, -2.227005562666341 });
PositiveDefiniteMatrix betaExpected = new PositiveDefiniteMatrix(new double[, ]
{
{ 3.187555652658986, -3.301824438047169, 1.227566907279797 },
{ -3.30182443804717, 5.115027119603418, -2.373085083966294 },
{ 1.227566907279797, -2.373085083966294, 2.156308696222915 }
});
Console.WriteLine("alpha = {0} should be {1}", sgp.Alpha, alphaExpected);
Console.WriteLine(StringUtil.JoinColumns("beta = ", sgp.Beta, " should be ", betaExpected));
double[] xTest = new double[]
{
-2, -1, 0.0
};
Vector[] xTestVec = Array.ConvertAll(xTest, v => Vector.Constant(1, v));
// computed by matlab/MNT/GP/test_gpr.m
double[] yMeanTest = new double[]
{
-0.544583265595561, 0.134323399801302, 0.503623822120711
};
double[] yVarTest = new double[]
{
0.058569682375201, 0.022695532903985, 0.024439582002951
};
for (int i = 0; i < xTestVec.Length; i++)
{
Gaussian pred = sgp.Marginal(xTestVec[i]);
Gaussian predExpected = new Gaussian(yMeanTest[i], yVarTest[i]);
Console.WriteLine("f({0}) = {1} should be {2}", xTest[i], pred, predExpected);
Assert.True(predExpected.MaxDiff(pred) < 1e-4);
}
double evExpected = -13.201173794945003;
double evActual = engine.Infer <Bernoulli>(evidence).LogOdds;
Console.WriteLine("evidence = {0} should be {1}", evActual, evExpected);
Assert.True(MMath.AbsDiff(evExpected, evActual, 1e-6) < 1e-4);
}
public void Run()
{
InferenceEngine engine = new InferenceEngine();
if (!(engine.Algorithm is Algorithms.ExpectationPropagation))
{
Console.WriteLine("This example only runs with Expectation Propagation");
return;
}
// The data
Vector[] inputs = new Vector[]
{
Vector.FromArray(new double[2] {
0, 0
}),
Vector.FromArray(new double[2] {
0, 1
}),
Vector.FromArray(new double[2] {
1, 0
}),
Vector.FromArray(new double[2] {
0, 0.5
}),
Vector.FromArray(new double[2] {
1.5, 0
}),
Vector.FromArray(new double[2] {
0.5, 1.0
})
};
bool[] outputs = { true, true, false, true, false, false };
// Open an evidence block to allow model scoring
Variable <bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
// Set up the GP prior, a distribution over functions, which will be filled in later
Variable <SparseGP> prior = Variable.New <SparseGP>().Named("prior");
// The sparse GP variable - a random function
Variable <IFunction> f = Variable <IFunction> .Random(prior).Named("f");
// The locations to evaluate the function
VariableArray <Vector> x = Variable.Observed(inputs).Named("x");
Range j = x.Range.Named("j");
// The observation model
VariableArray <bool> y = Variable.Observed(outputs, j).Named("y");
Variable <double> score = Variable.FunctionEvaluate(f, x[j]).Named("score");
y[j] = (Variable.GaussianFromMeanAndVariance(score, 0.1) > 0);
// Close the evidence block
block.CloseBlock();
// The basis
Vector[] basis = new Vector[]
{
Vector.FromArray(new double[2] {
0.2, 0.2
}),
Vector.FromArray(new double[2] {
0.2, 0.8
}),
Vector.FromArray(new double[2] {
0.8, 0.2
}),
Vector.FromArray(new double[2] {
0.8, 0.8
})
};
for (int trial = 0; trial < 3; trial++)
{
// The kernel
IKernelFunction kf;
if (trial == 0)
{
kf = new SquaredExponential(-0.0);
}
else if (trial == 1)
{
kf = new SquaredExponential(-0.5);
}
else
{
kf = new NNKernel(new double[] { 0.0, 0.0 }, -1.0);
}
// Fill in the sparse GP prior
GaussianProcess gp = new GaussianProcess(new ConstantFunction(0), kf);
prior.ObservedValue = new SparseGP(new SparseGPFixed(gp, basis));
// Model score
double NNscore = engine.Infer <Bernoulli>(evidence).LogOdds;
Console.WriteLine("{0} evidence = {1}", kf, NNscore.ToString("g4"));
}
// Infer the posterior Sparse GP
SparseGP sgp = engine.Infer <SparseGP>(f);
// Check that training set is classified correctly
Console.WriteLine("");
Console.WriteLine("Predictions on training set:");
for (int i = 0; i < outputs.Length; i++)
{
Gaussian post = sgp.Marginal(inputs[i]);
double postMean = post.GetMean();
string comment = (outputs[i] == (postMean > 0.0)) ? "correct" : "incorrect";
Console.WriteLine("f({0}) = {1} ({2})", inputs[i], post, comment);
}
}