public static (Vector[] dataX, double[] dataY) GenerateRandomData(int numData, double proportionCorrupt)
{
int randomSeed = 9876;
Random rng = new Random(randomSeed);
Rand.Restart(randomSeed);
InferenceEngine engine = Utilities.GetInferenceEngine();
// The points to evaluate
Vector[] randomInputs = Utilities.VectorRange(0, 1, numData, null);
var gaussianProcessGenerator = new GaussianProcessRegressor(randomInputs);
// The basis
Vector[] basis = Utilities.VectorRange(0, 1, 6, rng);
// The kernel
var kf = new SummationKernel(new SquaredExponential(-1)) + new WhiteNoise();
// Fill in the sparse GP prior
GaussianProcess gp = new GaussianProcess(new ConstantFunction(0), kf);
gaussianProcessGenerator.Prior.ObservedValue = new SparseGP(new SparseGPFixed(gp, basis));
// Infer the posterior Sparse GP, and sample a random function from it
SparseGP sgp = engine.Infer <SparseGP>(gaussianProcessGenerator.F);
var randomFunc = sgp.Sample();
double[] randomOutputs = new double[randomInputs.Length];
int numCorrupted = (int)Math.Ceiling(numData * proportionCorrupt);
var subset = Enumerable.Range(0, randomInputs.Length + 1).OrderBy(x => rng.Next()).Take(numCorrupted);
// get random data
for (int i = 0; i < randomInputs.Length; i++)
{
double post = randomFunc.Evaluate(randomInputs[i]);
// corrupt data point if it we haven't exceed the proportion we wish to corrupt
if (subset.Contains(i))
{
double sign = rng.NextDouble() > 0.5 ? 1 : -1;
double distance = rng.NextDouble() * 1;
post = (sign * distance) + post;
}
randomOutputs[i] = post;
}
Console.WriteLine("Model complete: Generated {0} points with {1} corrupted", numData, numCorrupted);
return(randomInputs, randomOutputs);
}
static void FitDataset(bool useSynthetic)
{
Vector[] trainingInputs;
double[] trainingOutputs;
if (!useSynthetic)
{
var trainingData = Utilities.LoadAISDataset();
trainingInputs = trainingData.Select(tup => Vector.FromArray(new double[1] {
tup.x
})).ToArray();
trainingOutputs = trainingData.Select(tup => tup.y).ToArray();
}
else
{
(trainingInputs, trainingOutputs) = GaussianProcessDataGenerator.GenerateRandomData(30, 0.3);
}
InferenceEngine engine = Utilities.GetInferenceEngine();
// First fit standard GP, then fit Student-T GP
foreach (var useStudentTLikelihood in new[] { false, true })
{
var gaussianProcessRegressor = new GaussianProcessRegressor(trainingInputs, useStudentTLikelihood, trainingOutputs);
// Log length scale estimated as -1
var noiseVariance = 0.8;
var kf = new SummationKernel(new SquaredExponential(-1)) + new WhiteNoise(Math.Log(noiseVariance) / 2);
GaussianProcess gp = new GaussianProcess(new ConstantFunction(0), kf);
// Convert SparseGP to full Gaussian Process by evaluating at all the training points
gaussianProcessRegressor.Prior.ObservedValue = new SparseGP(new SparseGPFixed(gp, trainingInputs.ToArray()));
double logOdds = engine.Infer <Bernoulli>(gaussianProcessRegressor.Evidence).LogOdds;
Console.WriteLine("{0} evidence = {1}", kf, logOdds.ToString("g4"));
// Infer the posterior Sparse GP
SparseGP sgp = engine.Infer <SparseGP>(gaussianProcessRegressor.F);
#if NETFULL
string datasetName = useSynthetic ? "Synthetic" : "AIS";
Utilities.PlotPredictions(sgp, trainingInputs, trainingOutputs, useStudentTLikelihood, datasetName);
#endif
}
}