public static void NoiseTest(double noiseVariance)
{
int d = 2;
int n = 1000;
// generate data
var N0I = new VectorGaussian(Vector.Zero(d), PositiveDefiniteMatrix.Identity(d));
var wTrue = N0I.Sample();
Normalize(wTrue);
Vector[] x = new Vector[n];
bool[] y = new bool[n];
for (int i = 0; i < n; i++)
{
x[i] = N0I.Sample();
y[i] = (x[i].Inner(wTrue) + Gaussian.Sample(0, 1.0 / noiseVariance)) > 0.0;
}
// evaluate models
var fixedNoise = new BPM_FixedNoise(d, n);
var noiseRange = new double[] { 1, 2, 10, 20, 30, 100, 1000, 1e4 };
foreach (double noiseTrain in noiseRange)
{
Vector wTrain = fixedNoise.Train(x, y, noiseTrain);
Normalize(wTrain);
double err = System.Math.Acos(wTrain.Inner(wTrue)) / System.Math.PI;
//double err = Math.Sqrt(wTrue.Inner(wTrue) -2*wTrue.Inner(wTrain) + wTrain.Inner(wTrain));
Console.WriteLine("noiseTrain = {0}, error = {1}", noiseTrain, err);
}
}
/// <summary>
/// Generates a data set from a particular true model.
/// </summary>
public Vector[] GenerateData(int nData)
{
Vector trueM1 = Vector.FromArray(2.0, 3.0);
Vector trueM2 = Vector.FromArray(7.0, 5.0);
PositiveDefiniteMatrix trueP1 = new PositiveDefiniteMatrix(
new double[, ] {
{ 3.0, 0.2 }, { 0.2, 2.0 }
});
PositiveDefiniteMatrix trueP2 = new PositiveDefiniteMatrix(
new double[, ] {
{ 2.0, 0.4 }, { 0.4, 4.0 }
});
VectorGaussian trueVG1 = VectorGaussian.FromMeanAndPrecision(trueM1, trueP1);
VectorGaussian trueVG2 = VectorGaussian.FromMeanAndPrecision(trueM2, trueP2);
double truePi = 0.6;
Bernoulli trueB = new Bernoulli(truePi);
// Restart the infer.NET random number generator
Rand.Restart(12347);
Vector[] data = new Vector[nData];
for (int j = 0; j < nData; j++)
{
bool bSamp = trueB.Sample();
data[j] = bSamp ? trueVG1.Sample() : trueVG2.Sample();
}
return(data);
}
/// <summary>
/// For the multinomial regression model: generate synthetic data,
/// infer the model parameters and calculate the RMSE between the true
/// and mean inferred coefficients.
/// </summary>
/// <param name="numSamples">Number of samples</param>
/// <param name="numFeatures">Number of input features</param>
/// <param name="numClasses">Number of classes</param>
/// <param name="countPerSample">Total count per sample</param>
/// <returns>RMSE between the true and mean inferred coefficients</returns>
public double MultinomialRegressionSynthetic(
int numSamples, int numFeatures, int numClasses, int countPerSample, double noiseVar = 0.0)
{
var features = new Vector[numSamples];
var counts = new int[numSamples][];
var coefficients = new Vector[numClasses];
var bias = Vector.Zero(numClasses);
Rand.Restart(1);
for (int i = 0; i < numClasses - 1; i++)
{
bias[i] = Rand.Normal();
coefficients[i] = Vector.Zero(numFeatures);
Rand.Normal(Vector.Zero(numFeatures), PositiveDefiniteMatrix.Identity(numFeatures), coefficients[i]);
}
bias[numClasses - 1] = 0;
coefficients[numClasses - 1] = Vector.Zero(numFeatures);
var noiseDistribution = new VectorGaussian(Vector.Zero(numClasses), PositiveDefiniteMatrix.IdentityScaledBy(numClasses, noiseVar));
for (int i = 0; i < numSamples; i++)
{
features[i] = Vector.Zero(numFeatures);
Rand.Normal(Vector.Zero(numFeatures), PositiveDefiniteMatrix.Identity(numFeatures), features[i]);
var temp = Vector.FromArray(coefficients.Select(o => o.Inner(features[i])).ToArray());
if (noiseVar != 0.0)
{
temp += noiseDistribution.Sample();
}
var p = MMath.Softmax(temp + bias);
counts[i] = Rand.Multinomial(countPerSample, p);
}
IList <VectorGaussian> weightsPost;
IList <Gaussian> biasPost;
bool trackLowerBound = true;
double ev = MultinomialRegression(features, counts, out weightsPost, out biasPost, trackLowerBound);
if (trackLowerBound)
{
Console.WriteLine("Log lower bound= " + ev);
}
double error = 0;
Console.WriteLine("Weights -------------- ");
for (int i = 0; i < numClasses; i++)
{
var bMean = weightsPost[i].GetMean();
error += (bMean - coefficients[i]).Sum(o => o * o);
Console.WriteLine("Class " + i + " True " + coefficients[i]);
Console.WriteLine("Class " + i + " Inferred " + bMean);
}
error = System.Math.Sqrt(error / (numClasses * numFeatures));
Console.WriteLine("RMSE " + error);
Console.WriteLine("Bias -------------- ");
Console.WriteLine("True " + bias);
Console.WriteLine("Inferred " + Vector.FromArray(biasPost.Select(o => o.GetMean()).ToArray()));
return(error);
}
public double MulticlassRegressionSynthetic(int numSamples, object softmaxOperator, out int iterations, out double lowerBound, double noiseVar = 0.0)
{
int numFeatures = 6;
int numClasses = 4;
var features = new Vector[numSamples];
var counts = new int[numSamples];
var coefficients = new Vector[numClasses];
var mean = Vector.Zero(numClasses);
for (int i = 0; i < numClasses - 1; i++)
{
mean[i] = Rand.Normal();
coefficients[i] = Vector.Zero(numFeatures);
Rand.Normal(Vector.Zero(numFeatures), PositiveDefiniteMatrix.Identity(numFeatures), coefficients[i]);
}
mean[numClasses - 1] = 0;
coefficients[numClasses - 1] = Vector.Zero(numFeatures);
var noiseDistribution = new VectorGaussian(Vector.Zero(numClasses), PositiveDefiniteMatrix.IdentityScaledBy(numClasses, noiseVar));
for (int i = 0; i < numSamples; i++)
{
features[i] = Vector.Zero(numFeatures);
Rand.Normal(Vector.Zero(numFeatures), PositiveDefiniteMatrix.Identity(numFeatures), features[i]);
var temp = Vector.FromArray(coefficients.Select(o => o.Inner(features[i])).ToArray());
if (noiseVar != 0.0)
{
temp += noiseDistribution.Sample();
}
var p = MMath.Softmax(temp + mean);
counts[i] = Rand.Sample(p);
}
Rand.Restart(DateTime.Now.Millisecond);
VectorGaussian[] bPost;
Gaussian[] meanPost;
iterations = MulticlassRegression(features, counts, numClasses, out bPost, out meanPost, out lowerBound, softmaxOperator, true);
var bMeans = bPost.Select(o => o.GetMean()).ToArray();
var bVars = bPost.Select(o => o.GetVariance()).ToArray();
double error = 0;
Console.WriteLine("Coefficients -------------- ");
for (int i = 0; i < numClasses; i++)
{
error += (bMeans[i] - coefficients[i]).Sum(o => o * o);
Console.WriteLine("True " + coefficients[i]);
Console.WriteLine("Inferred " + bMeans[i]);
}
Console.WriteLine("Mean -------------- ");
Console.WriteLine("True " + mean);
Console.WriteLine("Inferred " + Vector.FromArray(meanPost.Select(o => o.GetMean()).ToArray()));
error = System.Math.Sqrt(error / (numClasses * numFeatures));
Console.WriteLine(numSamples + " " + error);
return(error);
}
public IFunction Sample()
{
if (this.FixedParameters.NumberFeatures > 1)
{
throw new Exception("Sampling of a Sparse Gaussian Process is not supported for input spaces of dimension > 1.");
}
if (this.FixedParameters.NumberBasisPoints <= 0)
{
return(((Sampleable <IFunction>) this.FixedParameters.Prior).Sample());
}
// Try to find a reasonable range to sample from
int numSamplePoints = 51;
double maxabs = 1.0;
for (int i = 0; i < this.FixedParameters.NumberBasisPoints; i++)
{
double absb = Math.Abs(this.FixedParameters.Basis[i][0]);
if (maxabs < absb)
{
maxabs = absb;
}
}
maxabs *= 1.5; // Go beyond the basis points
List <Vector> x = new List <Vector>(numSamplePoints);
double increm = (2.0 * maxabs) / ((double)(numSamplePoints - 1));
double start = -maxabs;
double currx = start;
for (int i = 0; i < numSamplePoints; i++)
{
Vector xv = Vector.Zero(1);
xv[0] = currx;
x.Add(xv);
currx += increm;
}
// x now contains the set of input points at which we'll sample the
// posterior function distribution
VectorGaussian vg = VectorGaussian.FromMeanAndVariance(Mean(x), Covariance(x));
// Sample to get the outputs
Vector y = vg.Sample();
// Build the spline
LinearSpline ls = new LinearSpline();
ls.KnotStart = start;
ls.KnotIncrem = increm;
ls.YPoints = y;
return(ls as IFunction);
}
public int SyntheticData(int D, int N, int Ntest, double noiseVariance)
{
xtrain = new Vector[N];
xtest = new Vector[Ntest];
ytrain = new bool[N];
ytest = new bool[Ntest];
var N0I = new VectorGaussian(Vector.Zero(D), PositiveDefiniteMatrix.Identity(D));
var trueW = N0I.Sample();
for (int i = 0; i < N; i++)
{
xtrain[i] = N0I.Sample();
ytrain[i] = (xtrain[i].Inner(trueW) + Gaussian.Sample(0, 1.0 / noiseVariance)) > 0.0;
}
for (int i = 0; i < Ntest; i++)
{
xtest[i] = N0I.Sample();
ytest[i] = (xtest[i].Inner(trueW) + Gaussian.Sample(0, 1.0 / noiseVariance)) > 0.0;
}
return(0);
}
/// <summary>
/// Run our VB implementation of the Semi Parametric Latent Factor Model of
/// Teh, Y., Seeger, M., and Jordan, M. (AISTATS 2005).
/// </summary>
public SPLFM_VMP RunSPLFM_VMP(Vector[] inputs,
double[,] data,
bool[,] isMissing,
Settings settings,
string[] errorMeasureNames = null,
Converter <IPredictionSPLFMModel, double[]> modelAssessor = null,
string swfn = null)
{
var model = new SPLFM_VMP();
var nodeOptimiser = new KernelOptimiser(settings);
nodeOptimiser.xData = inputs;
nodeOptimiser.kernel = ObjectCloner.Clone(settings.node_kernel);
nodeOptimiser.hypersToOptimise = settings.nodeHypersToOptimise;
var nodeFunctionsInit = Enumerable.Range(0, settings.Q).Select(i =>
VectorGaussian.FromMeanAndVariance(
VectorGaussian.Sample(Vector.Zero(data.GetLength(1)), PositiveDefiniteMatrix.IdentityScaledBy(data.GetLength(1), 100)),
PositiveDefiniteMatrix.IdentityScaledBy(data.GetLength(1), settings.init_precision))).ToArray(); // should put this manually in generated code
var distArray = Distribution <Vector> .Array(nodeFunctionsInit);
double inputsRange
= inputs.Select(i => i[0]).Max() - inputs.Select(i => i[0]).Min();
Console.WriteLine("Init node kernel {0}", settings.node_kernel);
model.SetObservedValue("D", data.GetLength(0));
model.SetObservedValue("Q", settings.Q);
model.SetObservedValue("N", data.GetLength(1));
model.SetObservedValue("observedData", data);
model.SetObservedValue("nodeFunctionsInitVar", distArray);
model.SetObservedValue("K_node_inverse", Utils.GramMatrix(nodeOptimiser.kernel, inputs).Inverse());
model.SetObservedValue("noisePrecisionPrior", settings.noisePrecisionPrior);
//model.SetObservedValue("nodeNoisePrecisionPrior", settings.nodeNoisePrecisionPrior);
model.SetObservedValue("nodeSignalPrecisionsPrior", Enumerable.Range(0, settings.Q).Select(o => settings.nodeSignalPrecisionsPrior).ToArray());
model.SetObservedValue("isMissing", isMissing);
model.nodeKernelOptimiser = nodeOptimiser;
model.Reset();
var start = DateTime.Now;
if (swfn != null)
{
using (var sw = new StreamWriter(swfn, true))
{
sw.Write("{0} {1} {2}", "it", "time", "ml");
if (errorMeasureNames != null)
{
sw.Write(" " + errorMeasureNames.Aggregate((p, q) => p + " " + q));
}
sw.Write(" " + Utils.KernelHyperNames(nodeOptimiser.kernel).Select(o => "node_" + o).Aggregate((p, q) => p + " " + q));
sw.Write(" noise");
for (int i = 0; i < settings.Q; i++)
{
sw.Write(" signal" + i);
}
sw.WriteLine();
}
}
double oldML = double.NegativeInfinity;
double ml = 0;
int it = 0;
for (; it < settings.max_iterations; it++)
{
model.Update(1);
ml = model.Marginal <Bernoulli>("ev").LogOdds;
var noisePrecisionPost = model.Marginal <Gamma>("noisePrecision");
var assessment = (modelAssessor != null) ? modelAssessor(model).Select(o => o.ToString()).Aggregate((p, q) => p + " " + q) : "";
Console.WriteLine("It " + it + " node " + nodeOptimiser.kernel + " ml " + ml + " err " + assessment);
if (Math.Abs(oldML - ml) < settings.ml_tolerance)
{
break;
}
oldML = ml;
if (swfn != null)
{
using (var sw = new StreamWriter(swfn, true))
{
var nodeSignalPrecisionsPost = model.Marginal <Gamma[]>("nodeSignalPrecisions");
sw.Write("{0} {1} {2}", it, (DateTime.Now - start).TotalMilliseconds, ml);
if (modelAssessor != null)
{
sw.Write(" " + assessment);
}
sw.Write(" " + Utils.KernelToArray(nodeOptimiser.kernel).Select(o => o.ToString()).Aggregate((p, q) => p + " " + q));
sw.Write(" " + noisePrecisionPost.GetMeanInverse());
for (int i = 0; i < settings.Q; i++)
{
sw.Write(" " + nodeSignalPrecisionsPost[i].GetMeanInverse());
}
sw.WriteLine();
}
}
}
Console.WriteLine("Finished after " + it);
return(model);
}
/// <summary>
/// Run GPRN without node noise
/// </summary>
/// <param name="inputs">Covariates X</param>
/// <param name="data">Outputs Y</param>
/// <param name="settings">Algorithm settings</param>
/// <param name="swfn">Filename for logging</param>
/// <returns>Fitted model</returns>
public GPRN_VMP NetworkModelCA(Vector[] inputs,
double[,] data,
Settings settings,
string swfn = null)
{
bool anyIsMissing = false; // AnyIsMissing(isMissing);
var model = new GPRN_VMP();
var nodeOptimiser = new KernelOptimiser(settings);
var weightOptimiser = new KernelOptimiser(settings);
nodeOptimiser.xData = inputs;
weightOptimiser.xData = inputs;
nodeOptimiser.kernel = ObjectCloner.Clone(settings.node_kernel);
nodeOptimiser.hypersToOptimise = settings.nodeHypersToOptimise;
weightOptimiser.kernel = ObjectCloner.Clone(settings.weight_kernel);
weightOptimiser.hypersToOptimise = settings.weightHypersToOptimise;
var nodeFunctionsInit = Enumerable.Range(0, settings.Q).Select(i =>
VectorGaussian.FromMeanAndVariance(
VectorGaussian.Sample(Vector.Zero(data.GetLength(1)), PositiveDefiniteMatrix.IdentityScaledBy(data.GetLength(1), 100)),
PositiveDefiniteMatrix.IdentityScaledBy(data.GetLength(1), settings.init_precision))).ToArray(); // should put this manually in generated code
var distArray = Distribution <Vector> .Array(nodeFunctionsInit);
double inputsRange
= inputs.Select(i => i[0]).Max() - inputs.Select(i => i[0]).Min();
Console.WriteLine("Init node kernel {0}\ninit weight kernel {1}", settings.node_kernel, settings.weight_kernel);
model.SetObservedValue("D", data.GetLength(0));
model.SetObservedValue("Q", settings.Q);
model.SetObservedValue("N", data.GetLength(1));
model.SetObservedValue("observedData", data);
model.SetObservedValue("nodeFunctionsInitVar", distArray);
model.SetObservedValue("K_node_inverse", Utils.GramMatrix(nodeOptimiser.kernel, inputs).Inverse());
model.SetObservedValue("K_weights_inverse", Utils.GramMatrix(weightOptimiser.kernel, inputs).Inverse());
model.SetObservedValue("noisePrecisionPrior", settings.noisePrecisionPrior);
//model.SetObservedValue("nodeNoisePrecisionPrior", settings.nodeNoisePrecisionPrior);
model.SetObservedValue("nodeSignalPrecisionsPrior", settings.nodeSignalPrecisionsPrior);
//model.SetObservedValue("isMissing", isMissing);
model.nodeKernelOptimiser = nodeOptimiser;
model.weightKernelOptimiser = weightOptimiser;
model.Reset();
var start = DateTime.Now;
if (swfn != null)
{
using (var sw = new StreamWriter(swfn, true))
{
sw.Write("{0} {1} {2}", "it", "time", "ml");
if (anyIsMissing)
{
sw.Write(" {0} {1}", "logProb", "error");
}
sw.Write(" " + Utils.KernelHyperNames(nodeOptimiser.kernel).Select(o => "node_" + o).Aggregate((p, q) => p + " " + q));
sw.Write(" " + Utils.KernelHyperNames(weightOptimiser.kernel).Select(o => "weight_" + o).Aggregate((p, q) => p + " " + q));
sw.Write(" noise");
for (int i = 0; i < settings.Q; i++)
{
sw.Write(" signal" + i);
}
sw.WriteLine();
}
}
double oldML = double.NegativeInfinity;
double ml = 0;
int it = 0;
for (; it < settings.max_iterations; it++)
{
model.Update(1);
ml = model.Marginal <Bernoulli>("ev").LogOdds;
var noisePrecisionPost = model.Marginal <Gamma>("noisePrecision");
double logProb = 0, error = 0, MSLL = 0, SMSE = 0;
Console.WriteLine("It {9} Time: {8:G3} Node ls=exp({0:G3})={1:G3} Weight ls=exp({2:G3})={3:G3} ml={4:G3} error={5:G3} msll={6:G3} smse={7:G3}", nodeOptimiser.kernel[0], Math.Exp(nodeOptimiser.kernel[0]),
weightOptimiser.kernel[0], Math.Exp(weightOptimiser.kernel[0]), ml, error, MSLL, SMSE, (DateTime.Now - start).TotalMilliseconds, it);
if (Math.Abs(oldML - ml) < settings.ml_tolerance)
{
break;
}
oldML = ml;
if (swfn != null)
{
using (var sw = new StreamWriter(swfn, true))
{
var nodeSignalPrecisionsPost = model.Marginal <Gamma[]>("nodeSignalPrecisions");
sw.Write("{0} {1} {2}", it, (DateTime.Now - start).TotalMilliseconds, ml);
if (anyIsMissing)
{
sw.Write(" {0} {1}", logProb, error);
}
sw.Write(" " + Utils.KernelToArray(nodeOptimiser.kernel).Select(o => o.ToString()).Aggregate((p, q) => p + " " + q));
sw.Write(" " + Utils.KernelToArray(weightOptimiser.kernel).Select(o => o.ToString()).Aggregate((p, q) => p + " " + q));
sw.Write(" " + noisePrecisionPost.GetMeanInverse());
for (int i = 0; i < settings.Q; i++)
{
sw.Write(" " + nodeSignalPrecisionsPost[i].GetMeanInverse());
}
sw.WriteLine();
}
}
}
Console.WriteLine("Finished after " + it);
return(model);
}
static IEnumerable<double[]> Samples(VectorGaussian distribution)
{
while (true)
{
yield return distribution.Sample().ToArray();
}
}
/// <summary>
/// Primary definition of the GPRN model as an Infer.NET model.
/// </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>
/// <param name="constrainWpositive">Whether to constrain W to be positive [experimental]</param>
/// <param name="isotropicNoise">Whether to use isotropic observation noise</param>
/// <param name="meanFunctions">Whether to include a per output mean function</param>
/// <param name="initLoglengthscales">Initial values for the length scales of the kernels</param>
/// <param name="sw">An output file for logging</param>
public void GPRN_InferNET_model(Vector[] inputs,
double[,] data,
int Q,
bool grid = false,
bool[,] missing = null,
bool nodeFunctionNoise = false,
bool constrainWpositive = false,
bool isotropicNoise = true,
bool meanFunctions = false,
double[] initLoglengthscales = null,
StreamWriter sw = null)
{
var toInfer = new List <IVariable>();
SummationKernel kf_node = new SummationKernel(new SquaredExponential(0)) + new WhiteNoise(-3);
var K_node = Utils.GramMatrix(kf_node, inputs);
SummationKernel kf_weights = new SummationKernel(new SquaredExponential(1)) + new WhiteNoise(-3);
var K_weights = Utils.GramMatrix(kf_weights, 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 weightFunctions = Variable.Array <Vector>(d, q).Named("weightFunctions");
var K_weights_inverse = Variable.Observed(K_weights.Inverse()).Named("K_weights_inverse");
weightFunctions[d, q] = Variable <Vector> .Factor(MyFactors.VectorGaussianScaled, Variable.Constant <double>(1), K_weights_inverse).ForEach(d, q);
weightFunctions.AddAttribute(new MarginalPrototype(new VectorGaussian(N.ObservedValue)));
var weightFunctionValues = Variable.Array(Variable.Array <double>(n), d, q).Named("weightFunctionValues");
var weightFunctionValues2 = Variable.Array(Variable.Array <double>(n), d, q).Named("weightFunctionValuesPredictive");
weightFunctionValues[d, q] = Variable.ArrayFromVector(weightFunctions[d, q], n);
if (constrainWpositive)
{
var weightFunctionValuesCopy = Variable.Array(Variable.Array <double>(n), d, q).Named("weightFunctionValuesCopy");
weightFunctionValuesCopy[d, q][n] = Variable.GaussianFromMeanAndPrecision(weightFunctionValues[d, q][n], 100);
Variable.ConstrainPositive(weightFunctionValuesCopy[d, q][n]);
}
weightFunctionValues2[d, q] = Variable.ArrayFromVector(weightFunctions[d, q], n);
var observedData = Variable.Array <double>(d, n).Named("observedData");
var noisePrecisionPrior = Variable.Observed(Gamma.FromShapeAndRate(1, .1)).Named("noisePrecisionPrior");
Variable <double> noisePrecision = null;
VariableArray <double> noisePrecisionArray = null;
if (isotropicNoise)
{
noisePrecision = Variable.Random <double, Gamma>(noisePrecisionPrior).Named("noisePrecision");
toInfer.Add(noisePrecision);
}
else
{
noisePrecisionArray = Variable.Array <double>(d).Named("noisePrecision");
noisePrecisionArray[d] = Variable.Random <double, Gamma>(noisePrecisionPrior).ForEach(d);
toInfer.Add(noisePrecisionArray);
}
var isMissing = Variable.Array <bool>(d, n).Named("isMissing");
isMissing.ObservedValue = missing;
var noiseLessY = Variable.Array <double>(d, n).Named("noiseLessY");
VariableArray <VariableArray <double>, double[][]> meanFunctionValues = null;
if (meanFunctions)
{
GPFactor.settings = new Settings
{
solverMethod = Settings.SolverMethod.GradientDescent,
};
VariableArray <KernelFunction> kf = Variable.Array <KernelFunction>(d);
kf.ObservedValue = Enumerable.Range(0, D.ObservedValue).Select(
o => new SummationKernel(new SquaredExponential()) + new WhiteNoise(-3)).ToArray();
var mf = Variable.Array <Vector>(d).Named("meanFunctions");
mf[d] = Variable <Vector> .Factor <double, Vector[], int[], KernelFunction>(MyFactors.GP, 1.0 /*Variable.GammaFromShapeAndRate(1,1)*/, inputs, new int[] { 0 },
kf[d]);
mf.AddAttribute(new MarginalPrototype(new VectorGaussian(N.ObservedValue)));
meanFunctionValues = Variable.Array(Variable.Array <double>(n), d).Named("meanFunctionValues");
meanFunctionValues[d] = Variable.ArrayFromVector(mf[d], n);
toInfer.Add(meanFunctionValues);
}
using (Variable.ForEach(n))
using (Variable.ForEach(d))
{
var temp = Variable.Array <double>(q).Named("temp");
temp[q] = weightFunctionValues[d, q][n] * nodeFunctionValues[q][n];
if (meanFunctions)
{
noiseLessY[d, n] = Variable.Sum(temp) + meanFunctionValues[d][n];
}
else
{
noiseLessY[d, n] = Variable.Sum(temp);
}
using (Variable.IfNot(isMissing[d, n]))
if (isotropicNoise)
{
observedData[d, n] = Variable.GaussianFromMeanAndPrecision(noiseLessY[d, n], noisePrecision);
}
else
{
observedData[d, n] = Variable.GaussianFromMeanAndPrecision(noiseLessY[d, n], noisePrecisionArray[d]);
}
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, nodeFunctionValues, nodeSignalPrecisions, nodeFunctionValuesPredictive, weightFunctionValues, weightFunctionValues2
});
var infer = new InferenceEngine(new VariationalMessagePassing());
infer.ModelName = "MeanFunction";
var ca = infer.GetCompiledInferenceAlgorithm(toInfer.ToArray());
var kernel = new SummationKernel(new SquaredExponential(initLoglengthscales[0]));
kernel += new WhiteNoise(-3);
ca.SetObservedValue(K_node_inverse.NameInGeneratedCode, Utils.GramMatrix(kernel, inputs).Inverse());
kernel = new SummationKernel(new SquaredExponential(initLoglengthscales[1]));
kernel += new WhiteNoise(-3);
ca.SetObservedValue(K_weights_inverse.NameInGeneratedCode, Utils.GramMatrix(kernel, inputs).Inverse());
ca.Reset();
double oldML = double.NegativeInfinity;
double ml = 0;
int it = 0;
for (; it < 100; it++)
{
ca.Update(1);
ml = ca.Marginal <Bernoulli>(ev.NameInGeneratedCode).LogOdds;
Console.WriteLine(ml);
if (Math.Abs(oldML - ml) < .1)
{
break;
}
oldML = ml;
}
Console.WriteLine("Finished after " + it);
}
/// <summary>
/// An implementation of GPRN specialised for one step look ahead multivariate volatility experiments
/// </summary>
/// <param name="inputs">Covariates X</param>
/// <param name="data">Outputs Y</param>
/// <returns>Predicted covariance for the next time point</returns>
public VectorGaussian GPRN_MultivariateVolatility(
Vector[] inputs,
double[,] data,
double[] nodeSignalPrecs,
double[] nodeNoisePrecs,
double obsNoisePrec,
ref VectorGaussian[] finit,
ref VectorGaussian[,] winit,
KernelFunction nodeKernel,
KernelFunction weightKernel)
{
var missing = new bool[data.GetLength(0), data.GetLength(1)];
for (int i = 0; i < data.GetLength(0); i++)
{
missing[i, data.GetLength(1) - 1] = true; // last data point is missing
}
int Q = nodeSignalPrecs.Length;
var toInfer = new List <IVariable>();
var K_node = Utils.GramMatrix(nodeKernel, inputs);
var K_weights = Utils.GramMatrix(weightKernel, 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");
var ev = Variable.Bernoulli(.5).Named("ev");
var modelBlock = Variable.If(ev);
var nodeSignalPrecisions = Variable.Array <double>(q).Named("nodeSignalPrecisions");
nodeSignalPrecisions.ObservedValue = nodeSignalPrecs;
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");
var nodeFunctionValuesClean = Variable.Array(Variable.Array <double>(n), q).Named("nodeFunctionValuesClean");
nodeFunctionValuesClean[q] = Variable.ArrayFromVector(nodeFunctions[q], n);
var nodeNoisePrecisions = Variable.Array <double>(q).Named("nodeNoisePrecisions");
nodeNoisePrecisions.ObservedValue = nodeNoisePrecs;
nodeFunctionValues[q][n] = Variable.GaussianFromMeanAndPrecision(nodeFunctionValuesClean[q][n], nodeNoisePrecisions[q]);
nodeFunctionValuesPredictive[q][n] = Variable.GaussianFromMeanAndPrecision(nodeFunctionValuesClean[q][n], nodeNoisePrecisions[q]);
var weightFunctions = Variable.Array <Vector>(d, q).Named("weightFunctions");
var K_weights_inverse = Variable.Observed(K_weights.Inverse()).Named("K_weights_inverse");
weightFunctions[d, q] = Variable <Vector> .Factor(MyFactors.VectorGaussianScaled, Variable.Constant <double>(1), K_weights_inverse).ForEach(d, q);
weightFunctions.AddAttribute(new MarginalPrototype(new VectorGaussian(N.ObservedValue)));
var weightFunctionValues = Variable.Array(Variable.Array <double>(n), d, q).Named("weightFunctionValues");
var weightFunctionValuesPredictive = Variable.Array(Variable.Array <double>(n), d, q).Named("weightFunctionValuesPredictive");
weightFunctionValues[d, q] = Variable.ArrayFromVector(weightFunctions[d, q], n);
weightFunctionValuesPredictive[d, q] = Variable.ArrayFromVector(weightFunctions[d, q], n);
var observedData = Variable.Array <double>(d, n).Named("observedData");
var noisePrecision = Variable.Observed(obsNoisePrec).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] = weightFunctionValues[d, q][n] * 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);
var finitNew = finit.Select(i => Utils.extendByOneDimension(i, Gaussian.FromMeanAndVariance(0, 1))).ToArray();
nodeFunctions.InitialiseTo(Distribution <Vector> .Array(finitNew));
var winitNew = new VectorGaussian[data.GetLength(0), Q];
for (int i = 0; i < data.GetLength(0); i++)
{
for (int j = 0; j < Q; j++)
{
winitNew[i, j] = Utils.extendByOneDimension(winit[i, j], Gaussian.FromMeanAndVariance(0, 1));
}
}
weightFunctions.InitialiseTo(Distribution <Vector> .Array(winitNew));
modelBlock.CloseBlock();
toInfer.AddRange(new List <IVariable>()
{
ev, noiseLessY, nodeFunctions, weightFunctions, nodeFunctionValuesPredictive, weightFunctionValues, weightFunctionValuesPredictive /* is this redundant? */
});
var ie = new InferenceEngine(new VariationalMessagePassing());
var ca = ie.GetCompiledInferenceAlgorithm(toInfer.ToArray());
ca.SetObservedValue(K_node_inverse.NameInGeneratedCode, Utils.GramMatrix(nodeKernel, inputs).Inverse());
ca.SetObservedValue(K_weights_inverse.NameInGeneratedCode, Utils.GramMatrix(weightKernel, inputs).Inverse());
ca.Reset();
double oldML = double.NegativeInfinity;
double ml = 0;
int it = 0;
for (; it < 30; it++)
{
ca.Update(1);
ml = ca.Marginal <Bernoulli>(ev.NameInGeneratedCode).LogOdds;
Console.WriteLine(ml);
if (Math.Abs(oldML - ml) < .1)
{
break;
}
oldML = ml;
}
var f = ca.Marginal <Gaussian[][]>("nodeFunctionValuesPredictive");
var W = ca.Marginal <Gaussian[, ][]>("weightFunctionValuesPredictive");
finit = ca.Marginal <VectorGaussian[]>(nodeFunctions.NameInGeneratedCode);
winit = ca.Marginal <VectorGaussian[, ]>(weightFunctions.NameInGeneratedCode);
return(Utils.CorrelatedPredictionsHelper(f, W, Gamma.PointMass(obsNoisePrec), Q, data.GetLength(0), data.GetLength(1) - 1));
}
/// <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)\")"
});
}