Пример #1
0
        public static void TestWithNoise(Vector[] inputs, double[] data)
        {
            var n = new Range(data.Length);
            //var kf = new SummationKernel(new ARD(new double[]{ 0 }, 0))+new WhiteNoise();
            var kf = new SummationKernel(new SquaredExponential()) + new WhiteNoise(-3);
            var y  = Variable <Vector> .Factor <double, Vector[], int[], KernelFunction>(MyFactors.GP, 1.0 /*Variable.GammaFromShapeAndRate(1,1)*/, inputs, new int[] { 0, 1 },
                                                                                         kf);

            GPFactor.settings = new Settings
            {
                solverMethod = Settings.SolverMethod.GradientDescent,
            };

            var kf_noise      = new SummationKernel(new SquaredExponential()) + new WhiteNoise(-3);
            var noiseFunction = Variable <Vector> .Factor <double, Vector[], int[], KernelFunction>(MyFactors.GP, 1.0 /*Variable.GammaFromShapeAndRate(1,1)*/, inputs, new int[] { 0, 1 },
                                                                                                    kf_noise);

            GPFactor.settings = new Settings
            {
                solverMethod = Settings.SolverMethod.GradientDescent,
            };
            noiseFunction.AddAttribute(new MarginalPrototype(new VectorGaussian(n.SizeAsInt)));
            var noiseFunctionValues  = Variable.ArrayFromVector(noiseFunction, n);
            var noisePrecisionValues = Variable.Array <double>(n);

            //noisePrecisionValues[n] = Variable.Exp(noiseFunctionValues[n] + 2.0);
            noisePrecisionValues[n] = Variable.Exp(noiseFunctionValues[n] + Variable.GaussianFromMeanAndPrecision(0, 1));

            y.AddAttribute(new MarginalPrototype(new VectorGaussian(n.SizeAsInt)));
            var y2noiseless = Variable.ArrayFromVector(y, n);
            var y2          = Variable.Array <double>(n);

            y2[n]            = Variable.GaussianFromMeanAndPrecision(y2noiseless[n], noisePrecisionValues[n]);
            y2.ObservedValue = data;
            var ypredictiveNoiseless = Variable.ArrayFromVector(y, n);
            var ypredictive          = Variable.Array <double>(n);

            ypredictive[n] = Variable.GaussianFromMeanAndPrecision(ypredictiveNoiseless[n], noisePrecisionValues[n]);
            var ie   = new InferenceEngine(new VariationalMessagePassing());
            var post = ie.Infer <Gaussian[]>(ypredictive);

            var mplWrapper = new MatplotlibWrapper();

            mplWrapper.AddArray("x", inputs.Select(j => j[0]).ToArray());
            mplWrapper.AddArray("y", data);
            var f = post.Select(i => i.GetMean()).ToArray();
            var e = post.Select(i => 2.0 * Math.Sqrt(i.GetVariance())).ToArray();

            mplWrapper.AddArray("f", f);
            mplWrapper.AddArray("e", e);

            mplWrapper.Plot(new string[] {
                "fill_between(x,f-e,f+e,color=\"gray\")",
                "plot(x,f,'k')",
                "scatter(x,y)"
            });
        }
Пример #2
0
        public static void Test()
        {
            var inputs = Enumerable.Range(0, 50).Select(i => Vector.Constant(1, i)).ToArray();
            var data   = inputs.Select(j => Math.Cos(2 * j[0] / 10.0)).ToArray();
            var n      = new Range(data.Length);
            //var kf = new SummationKernel(new ARD(new double[]{ 0 }, 0))+new WhiteNoise();
            var kf = new SummationKernel(new SquaredExponential()) + new WhiteNoise();
            var y  = Variable <Vector> .Factor <double, Vector[], int[], KernelFunction>(MyFactors.GP, 1.0 /*Variable.GammaFromShapeAndRate(1,1)*/, inputs, new int[] { 0, 1 },
                                                                                         kf);

            GPFactor.settings = new Settings
            {
                solverMethod = Settings.SolverMethod.GradientDescent,
            };
            y.AddAttribute(new MarginalPrototype(new VectorGaussian(n.SizeAsInt)));
            var y2 = Variable.ArrayFromVector(y, n);

            y2.ObservedValue = data;
            var ypredictive = Variable.ArrayFromVector(y, n);
            var ie          = new InferenceEngine(new VariationalMessagePassing());
            var post        = ie.Infer <Gaussian[]>(ypredictive);

            var mplWrapper = new MatplotlibWrapper();

            mplWrapper.AddArray("x", inputs.Select(j => j[0]).ToArray());
            mplWrapper.AddArray("y", data);
            var f = post.Select(i => i.GetMean()).ToArray();
            var e = post.Select(i => Math.Sqrt(i.GetVariance())).ToArray();

            mplWrapper.AddArray("f", f);
            mplWrapper.AddArray("e", e);

            mplWrapper.Plot(new string[] {
                "fill_between(x,f-e,f+e,color=\"gray\")",
                "scatter(x,y)"
            });
        }
Пример #3
0
        /// <summary>
        /// Infer.NET definition of the Semi Parametric Latent Factor Model of
        /// Teh, Y., Seeger, M., and Jordan, M. (AISTATS 2005).
        /// </summary>
        /// <param name="inputs">Covariates X</param>
        /// <param name="data">Outputs Y</param>
        /// <param name="Q">Number of latent functions</param>
        /// <param name="missing">Which elements of Y are missing</param>
        /// <param name="nodeFunctionNoise">Whether to include node noise</param>
        public void SPLFM(
            Vector[] inputs,
            double[,] data,
            int Q,
            bool[,] missing        = null,
            bool nodeFunctionNoise = false)
        {
            var             toInfer = new List <IVariable>();
            SummationKernel kf_node = new SummationKernel(new SquaredExponential(0));
            var             K_node  = Utils.GramMatrix(kf_node, inputs);

            var D    = Variable.Observed <int>(data.GetLength(0)).Named("D");
            var d    = new Range(D).Named("d");
            var Qvar = Variable.Observed <int>(Q).Named("Q");
            var q    = new Range(Qvar).Named("q");
            var N    = Variable.Observed <int>(data.GetLength(1)).Named("N");
            var n    = new Range(N).Named("n");

            if (missing == null)
            {
                missing = new bool[D.ObservedValue, N.ObservedValue]; // check this is all false
            }
            var ev         = Variable.Bernoulli(.5).Named("ev");
            var modelBlock = Variable.If(ev);

            var nodeSignalPrecisions = Variable.Array <double>(q).Named("nodeSignalPrecisions");
            // set this to 1 if not learning signal variance
            var nodeSignalPrecisionsPrior = Variable.Observed(Enumerable.Range(0, Q).Select(_ => Gamma.FromShapeAndRate(.1, .1)).ToArray(), q).Named("nodeSignalPrecisionsPrior");

            nodeSignalPrecisions[q] = Variable.Random <double, Gamma>(nodeSignalPrecisionsPrior[q]);

            var nodeFunctions  = Variable.Array <Vector>(q).Named("nodeFunctions");
            var K_node_inverse = Variable.Observed(K_node.Inverse()).Named("K_node_inverse");

            nodeFunctions[q] = Variable <Vector> .Factor(MyFactors.VectorGaussianScaled, nodeSignalPrecisions[q], K_node_inverse);

            nodeFunctions.AddAttribute(new MarginalPrototype(new VectorGaussian(N.ObservedValue)));
            var nodeFunctionValues           = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValues");
            var nodeFunctionValuesPredictive = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValuesPredictive");

            VariableArray <double> nodeNoisePrecisions = null;

            if (nodeFunctionNoise)
            {
                var nodeFunctionValuesClean = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValuesClean");
                nodeFunctionValuesClean[q] = Variable.ArrayFromVector(nodeFunctions[q], n);
                nodeNoisePrecisions        = Variable.Array <double>(q).Named("nodeNoisePrecisions");
                var nodeNoisePrecisionPrior = Variable.Observed(Enumerable.Range(0, Q).Select(_ => Gamma.FromShapeAndRate(.1, .01)).ToArray(), q).Named("nodeNoisePrecisionPrior");
                nodeNoisePrecisions[q] = Variable.Random <double, Gamma>(nodeNoisePrecisionPrior[q]);
                toInfer.Add(nodeNoisePrecisions);
                nodeFunctionValues[q][n] = Variable.GaussianFromMeanAndPrecision(nodeFunctionValuesClean[q][n], nodeNoisePrecisions[q]);

                nodeFunctionValuesPredictive[q][n] = Variable.GaussianFromMeanAndPrecision(nodeFunctionValuesClean[q][n], nodeNoisePrecisions[q]);
            }
            else
            {
                nodeFunctionValues[q]           = Variable.ArrayFromVector(nodeFunctions[q], n);
                nodeFunctionValuesPredictive[q] = Variable.ArrayFromVector(nodeFunctions[q], n);
            }

            var weights = Variable.Array <double>(d, q).Named("weights");

            weights[d, q] = Variable.GaussianFromMeanAndPrecision(0, 1).ForEach(d, q);
            var observedData        = Variable.Array <double>(d, n).Named("observedData");
            var noisePrecisionPrior = Variable.Observed(Gamma.FromShapeAndRate(1, .1)).Named("noisePrecisionPrior");
            var noisePrecision      = Variable.Random <double, Gamma>(noisePrecisionPrior).Named("noisePrecision");

            var isMissing = Variable.Array <bool>(d, n).Named("isMissing");

            isMissing.ObservedValue = missing;

            var noiseLessY = Variable.Array <double>(d, n).Named("noiseLessY");

            using (Variable.ForEach(n))
                using (Variable.ForEach(d))
                {
                    var temp = Variable.Array <double>(q).Named("temp");
                    temp[q]          = weights[d, q] * nodeFunctionValues[q][n];
                    noiseLessY[d, n] = Variable.Sum(temp);
                    using (Variable.IfNot(isMissing[d, n]))
                        observedData[d, n] = Variable.GaussianFromMeanAndPrecision(noiseLessY[d, n], noisePrecision);
                    using (Variable.If(isMissing[d, n]))
                        observedData[d, n] = Variable.GaussianFromMeanAndPrecision(0, 1);
                }
            observedData.ObservedValue = data;
            var nodeFunctionsInit = Enumerable.Range(0, Q).Select(i =>
                                                                  VectorGaussian.FromMeanAndVariance(
                                                                      VectorGaussian.Sample(Vector.Zero(N.ObservedValue), PositiveDefiniteMatrix.IdentityScaledBy(N.ObservedValue, 100)),
                                                                      PositiveDefiniteMatrix.IdentityScaledBy(N.ObservedValue, 100))).ToArray(); // should put this manually in generated code

            var distArray = Distribution <Vector> .Array(nodeFunctionsInit);

            var nodeFunctionsInitVar = Variable.Observed(distArray).Named("nodeFunctionsInitVar");

            nodeFunctions.InitialiseTo(nodeFunctionsInitVar);

            modelBlock.CloseBlock();

            toInfer.AddRange(new List <IVariable>()
            {
                ev, noiseLessY, noisePrecision, nodeFunctionValues, nodeSignalPrecisions, nodeFunctionValuesPredictive, weights
            });

            var ie = new InferenceEngine(new VariationalMessagePassing());

            ie.ModelName = "SPLFM";
            var ca = ie.GetCompiledInferenceAlgorithm(toInfer.ToArray());

            ca.Execute(100);
            var fvals      = ca.Marginal <Gaussian[][]>(nodeFunctionValues.NameInGeneratedCode)[0]; // [q][n]
            var x          = inputs.Select(i => i[0]).ToArray();
            var mplWrapper = new MatplotlibWrapper();

            mplWrapper.AddArray("x", x);
            mplWrapper.AddArray("y", fvals.Select(i => i.GetMean()).ToArray());
            mplWrapper.AddArray("s", fvals.Select(i => Math.Sqrt(i.GetVariance())).ToArray());

            mplWrapper.Plot(new string[] {
                "fill_between(x,y-s,y+s,color=\"gray\")",
                "ylabel(\"node (fitted)\")"
            });
        }