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)"
});
}
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)"
});
}
/// <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)\")"
});
}