public void GPClassificationTest4() { bool[] yData = new bool[] { false, false, true, false }; double[] xData = new double[] { -1.555555555555556, -1.111111111111111, -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[] { 0.409693797629808 }); Console.WriteLine("alpha = {0} should be {1}", sgp.Alpha, alphaExpected); }
private void SparseGPModel() { // Basis Vector 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 }) }; // The kernel double[] kp = new double[2]; kp[0] = 0.0; kp[1] = 0.0; IKernelFunction kf = new NNKernel(kp, 0.0); // The fixed parameters SparseGPFixed sgpf = new SparseGPFixed(kf, basis); SparseGP agp = new SparseGP(sgpf); IFunction a = Factor.Random(agp); Vector b = Vector.FromArray(0.1, 0.2); double c = Factor.FunctionEvaluate(a, b); InferNet.Infer(c, nameof(c)); }
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> /// Construct a sparse GP, given basis etc /// </summary> /// <param name="spgf"></param> public LowRankSparseGP(SparseGPFixed spgf) : base(spgf) { int numBasis = spgf.NumberBasisPoints; xi = new Vector(numBasis); yi = 0.0; lambInv = 1.0; kBx = null; pvec = null; kxx = double.NaN; }
public void SparseGPTest() { // 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 }) }; // The kernel IKernelFunction kf = new NNKernel(new double[] { 0.0, 0.0 }, 0.0); // The fixed parameters SparseGPFixed sgpf = new SparseGPFixed(kf, basis); // Alpha and beta Vector alpha = Vector.Zero(basis.Length); PositiveDefiniteMatrix beta = new PositiveDefiniteMatrix(basis.Length, basis.Length); for (int i = 0; i < alpha.Count; i++) { alpha[i] = i; for (int j = 0; j < alpha.Count; j++) { beta[i, j] = alpha.Count - System.Math.Abs(i - j); } } SparseGP a = new SparseGP(sgpf); #if false Rank1Pot r1p = new Rank1Pot(); r1p.Xi = basis[0]; // must be a basis point for this test r1p.Yi = 2.2; r1p.LambdaInv = 0.7; SparseGP b = new SparseGP(sgpf, r1p); DistributionTests.SettableToRatioTest(a, b); #endif DistributionTests.ProductWithUniformTest(a); DistributionTests.RatioWithUniformTest(a); DistributionTests.SettableToTest(a); }
public void GPRegressionTest1() { double[] yData = new double[] { 1.036659040456137 }; double[] xData = new double[] { -0.2222222222222223 }; Vector[] xVec = Array.ConvertAll(xData, v => Vector.Constant(1, v)); Vector[] basis = new Vector[] { xVec[0] }; 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[] { 0.942417309505579 }); 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_gpr.m double[] yTest = new double[] { 0.634848540665472, 0.873781982196160, 0.936617836728720 }; for (int i = 0; i < xTestVec.Length; i++) { double pred = sgp.Mean(xTestVec[i]); Console.WriteLine("Ef({0}) = {1} should be {2}", xTest[i], pred, yTest[i]); Assert.True(MMath.AbsDiff(pred, yTest[i], 1e-6) < 1e-4); } double evExpected = -1.455076334997490; 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); }
private void GetItemSparseGPModel() { // Basis Vector 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 }) }; // The kernel double[] kp = new double[2]; kp[0] = 0.0; kp[1] = 0.0; IKernelFunction kf = new NNKernel(kp, 0.0); // The fixed parameters SparseGPFixed sgpf = new SparseGPFixed(kf, basis); SparseGP sgp = new SparseGP(sgpf); IFunction[] array = new IFunction[3]; for (int i = 0; i < 3; i++) { array[i] = Factor.Random(sgp); } IFunction c = Factor.GetItem(array, 1); IFunction[] d = new IFunction[2]; if (true) // preserve the previous assignment { d = Factor.GetItems(array, new int[] { 0, 2 }); } InferNet.Infer(c, nameof(c)); InferNet.Infer(d, nameof(d)); }
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 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); }