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); }
public void TestSEReadWrite() { double log_length = System.Math.Log(1.234); double log_sig_sd = System.Math.Log(2.345); SquaredExponential sekf = new SquaredExponential(log_length, log_sig_sd); TestReadWrite(sekf); }
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); }
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); }
public void TestSEKernelDerivs() { double log_length = System.Math.Log(1.234); double log_sig_sd = System.Math.Log(2.345); SquaredExponential sekf = new SquaredExponential(log_length, log_sig_sd); double[] x1 = { 0.1, 0.2, 0.3 }; double[] x2 = { 0.9, 0.7, 0.5 }; Vector x1Vec = Vector.FromArray(x1); Vector x2Vec = Vector.FromArray(x2); TestDerivatives(sekf, x1Vec, x1Vec); TestDerivatives(sekf, x1Vec, x2Vec); }
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); } }