Convergence problem in simple regression with learning noise


  • Hi,

    I am trying to run a simple regression model based on:

    if a make the noise (noise=0.1) a fixed value it works great, also making noise with a gamma prior (see code below) works great for very small data set (intNumObservaciones=10) but if I increase a little bit the dataset (intNumObservaciones=25) I have convergence problems-> System.Exception: 'Not converging for n=0,x=NaN'. I have tried differente setting of the Gamma without luck also other algorithm but with out luck.

    Any help with that error?

    Anyhow basically I wanted not to have a fixed noise since I wanted a probability distribution for y when I predicted a new value instead of a point estimated. Maybe there is another option to have y predicted as a distribution?.




    // This is based on:
                // Create synthetic data Y=B+10X1+20X2+error (uniform(0,20)), X1 and X2 Uniform[1,10]
                Vector[] xdata;
                double[] distress;
                List<double> lstEcuacion = new List<double>();
                Int32 intErrorMax = 20;
                Int32 intNumObservaciones = 25;
                xdata = new Vector[intNumObservaciones];
                distress = new double[intNumObservaciones];
                Int32 intNumFactores = lstEcuacion.Count;
                Random rnd = new Random();
                for (Int32 intI = 0; intI < intNumObservaciones; intI++)
                    double dblYtmp = 0;
                    double[] dblXTmp = new double[lstEcuacion.Count + 1];
                    dblXTmp[0] = 1;
                    for (Int32 intFactor = 0; intFactor < lstEcuacion.Count; intFactor++)
                        Int32 intFlag = rnd.Next(1, 10);
                        dblYtmp = dblYtmp + lstEcuacion[intFactor] * intFlag;
                        dblXTmp[intFactor + 1] = intFlag;
                    dblYtmp = dblYtmp + rnd.Next(0, intErrorMax);
                    distress[intI] = dblYtmp;
                    xdata[intI] = Vector.FromArray(dblXTmp.ToArray());

                // define a prior distribution and attach that to "w" random variable
                VectorGaussian wPrior = new VectorGaussian(Vector.Zero(intNumFactores + 1), PositiveDefiniteMatrix.Identity(intNumFactores + 1));
                Variable<Vector> w = Variable.Random(wPrior);

                //Noise distribution mean of a Gamma distribution is shape * scale, and its variance is shape * scale * scale
                double shape = 1000;
                double scale = 0.0001;
                Gamma noiseDist = new Gamma(shape, scale);
                Variable<double> noise = Variable.Random(noiseDist);

                // set features "x" and observations "y" as observed in the model
                VariableArray<double> y = Variable.Observed(distress);
                Range n = y.Range;
                VariableArray<Vector> x = Variable.Observed(xdata, n);

                // define "y" statistically: Gaussian RV array. Mean is defined by dot-product of param vector "w" and the feature vector x[n]
                y[n] = Variable.GaussianFromMeanAndVariance(Variable.InnerProduct(w, x[n]), noise);

                // Training
                InferenceEngine engine = new InferenceEngine();
                engine.ModelName = "Regression";
                engine.Algorithm = new ExpectationPropagation();
                // engine.Algorithm = new VariationalMessagePassing();
                //engine.Algorithm = new GibbsSampling();

                // infer "w" posterior as a distribution
                VectorGaussian wPosterior = engine.Infer<VectorGaussian>(w);
                Gamma noisePosterior = engine.Infer<Gamma>(noise);
                Console.WriteLine("Distribution over w = \n" + wPosterior);
                Console.WriteLine("Distribution over noise = \n" + noisePosterior);

    Sunday, July 8, 2018 9:55 AM


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