public override void Run()
{
var prices = GetPrices("SPY").Select(t => t.Item2).ToArray();
var inputs = prices.Take(prices.Length - 1).ToArray();
var inputVectors = inputs.Select(i => Vector.FromArray(new[] { i })).ToArray();
var outputs = prices.Skip(1).ToArray();
// Set up the GP prior, which will be filled in later
var prior = Variable.New<SparseGP>().Named("prior");
// The sparse GP variable - a distribution over functions
var f = Variable<IFunction>.Random(prior).Named("f");
// The locations to evaluate the function
var x = Variable.Observed(inputVectors).Named("x");
var j = x.Range.Named("j");
var y = Variable.Observed(outputs, j).Named("y");
y[j] = Variable.GaussianFromMeanAndVariance(Variable.FunctionEvaluate(f, x[j]), 0.1);
var kf = new SquaredExponential(-0.5);
// The basis
var rand = new Random(Environment.TickCount);
var basis = Enumerable.Range(1, 10).Select(i => Vector.FromArray(new double[1] {i*10})).ToArray();
//var basis = new Vector[] {
// Vector.FromArray(new double[1] {80}),
// Vector.FromArray(new double[1] {90}),
// Vector.FromArray(new double[1] {100})
//};
var gp = new GaussianProcess(new ConstantFunction(0), kf);
prior.ObservedValue = new SparseGP(new SparseGPFixed(gp, basis));
var engine = new InferenceEngine(new ExpectationPropagation());
var sgp = engine.Infer<SparseGP>(f);
var means = sgp.Mean(inputVectors).ToArray();
var stdDevs = inputVectors.Select(iv => Math.Sqrt(sgp.Variance(iv))).ToArray();
this.Series = new[]
{
new LabelledSeries<Tuple<double,double>>(
"input",
Enumerable.Range(0,inputs.Length)
.Select(i=> Tuple.Create((double)i, inputs[i]))),
new LabelledSeries<Tuple<double,double>>(
"infered mean",
Enumerable.Range(0,inputs.Length)
.Select(i=> Tuple.Create((double)i, means[i]))),
new LabelledSeries<Tuple<double,double>>(
"infered stddev",
Enumerable.Range(0,inputs.Length)
.Select(i=> Tuple.Create((double)i, stdDevs[i]))),
};
}
public void Run()
{
InferenceEngine engine = new InferenceEngine();
if (!(engine.Algorithm is ExpectationPropagation))
{
Console.WriteLine("This example only runs with Expectation Propagation");
return;
}
// The data
Vector[] inputs = new Vector[] {
Vector.FromArray(new double[2] {0, 0}),
Vector.FromArray(new double[2] {0, 1}),
Vector.FromArray(new double[2] {1, 0}),
Vector.FromArray(new double[2] {0, 0.5}),
Vector.FromArray(new double[2] {1.5, 0}),
Vector.FromArray(new double[2] {0.5, 1.0})
};
bool[] outputs = { true, true, false, true, false, false };
// Open an evidence block to allow model scoring
Variable<bool> evidence = Variable.Bernoulli(0.5).Named("evidence");
IfBlock block = Variable.If(evidence);
// Set up the GP prior, which will be filled in later
Variable<SparseGP> prior = Variable.New<SparseGP>().Named("prior");
// The sparse GP variable - a distribution over functions
Variable<IFunction> f = Variable<IFunction>.Random(prior).Named("f");
// The locations to evaluate the function
VariableArray<Vector> x = Variable.Observed(inputs).Named("x");
Range j = x.Range.Named("j");
// The observation model
VariableArray<bool> y = Variable.Observed(outputs, j).Named("y");
Variable<double> score = Variable.FunctionEvaluate(f, x[j]);
y[j] = (Variable.GaussianFromMeanAndVariance(score, 0.1) > 0);
// Close the evidence block
block.CloseBlock();
// The basis
Vector[] basis = new Vector[] {
Vector.FromArray(new double[2] {0.2, 0.2}),
Vector.FromArray(new double[2] {0.2, 0.8}),
Vector.FromArray(new double[2] {0.8, 0.2}),
Vector.FromArray(new double[2] {0.8, 0.8})
};
for (int trial = 0; trial < 3; trial++)
{
// The kernel
IKernelFunction kf;
if (trial == 0)
{
kf = new SquaredExponential(-0.0);
}
else if (trial == 1)
{
kf = new SquaredExponential(-0.5);
}
else
{
kf = new NNKernel(new double[] { 0.0, 0.0 }, -1.0);
}
// Fill in the sparse GP prior
GaussianProcess gp = new GaussianProcess(new ConstantFunction(0), kf);
prior.ObservedValue = new SparseGP(new SparseGPFixed(gp, basis));
// Model score
double NNscore = engine.Infer<Bernoulli>(evidence).LogOdds;
Console.WriteLine("{0} evidence = {1}", kf, NNscore.ToString("g4"));
}
// Infer the posterior Sparse GP
SparseGP sgp = engine.Infer<SparseGP>(f);
// Check that training set is classified correctly
Console.WriteLine("");
Console.WriteLine("Predictions on training set:");
for (int i = 0; i < outputs.Length; i++)
{
Gaussian post = sgp.Marginal(inputs[i]);
double postMean = post.GetMean();
string comment = (outputs[i] == (postMean > 0.0)) ? "correct" : "incorrect";
Console.WriteLine("f({0}) = {1} ({2})", inputs[i], post, comment);
}
}
