internal void SoftmaxGWAS()
{
var v = Vector.Zero(1);
var x1 = Variable.VectorGaussianFromMeanAndPrecision(Vector.Zero(1), PositiveDefiniteMatrix.Identity(1));
x1.ObservedValue = v;
var x2 = Variable.VectorGaussianFromMeanAndPrecision(Vector.Zero(1), PositiveDefiniteMatrix.Identity(1));
v[0] = 1;
x2.ObservedValue = v;
Console.WriteLine(x1.ObservedValue);
Console.WriteLine(x2.ObservedValue);
int numExposures = 10;
int numClasses = 5;
int numSamples = 1000;
var c = new Range(numClasses);
var n = new Range(numSamples);
// model
var Bexposures = Variable.Array <Vector>(c);
Bexposures[c] = Variable.VectorGaussianFromMeanAndPrecision(
Vector.Zero(numExposures),
PositiveDefiniteMatrix.Identity(numExposures))
.ForEach(c);
var exposures = Variable.Array <Vector>(n);
var Bgenotype = Variable.Array <double>(c);
Bgenotype[c] = Variable.GaussianFromMeanAndPrecision(0, 1).ForEach(c);
var genotypes = Variable.Array <double>(n);
var mean = Variable.Array <double>(c);
mean[c] = Variable.GaussianFromMeanAndPrecision(0, 1).ForEach(c);
var g = Variable.Array(Variable.Array <double>(c), n);
g[n][c] = Bgenotype[c] * genotypes[n] + Variable.InnerProduct(Bexposures[c], exposures[n]) + mean[c];
var classProbs = Variable.Array <Vector>(n);
classProbs[n] = Variable.Softmax(g[n]);
var classAssignments = Variable.Array <int>(n);
classAssignments[n] = Variable.Discrete(classProbs[n]);
// generate data
var exposuresObs = new Vector[numSamples];
var genotypeObs = new double[numSamples];
var classObs = new int[numSamples];
var trueBexposures = new Vector[numClasses];
var trueBgenotype = new double[numClasses];
Rand.Restart(123);
for (int i = 0; i < numClasses; i++)
{
trueBexposures[i] = VectorGaussian.SampleFromMeanAndVariance(Vector.Zero(numExposures), PositiveDefiniteMatrix.Identity(numExposures));
trueBgenotype[i] = Rand.Normal();
}
for (int i = 0; i < numSamples; i++)
{
exposuresObs[i] = VectorGaussian.SampleFromMeanAndVariance(Vector.Zero(numExposures), PositiveDefiniteMatrix.Identity(numExposures));
genotypeObs[i] = Rand.Double() < .5 ? 0.0 : 1.0;
var gt = new double[numClasses];
for (int j = 0; j < numClasses; j++)
{
gt[j] = genotypeObs[i] * trueBgenotype[j] + exposuresObs[i].Inner(trueBexposures[j]);
}
var p = MMath.Softmax(gt);
classObs[i] = Discrete.Sample(p);
}
Rand.Restart(DateTime.Now.Millisecond);
exposures.ObservedValue = exposuresObs;
genotypes.ObservedValue = genotypeObs;
classAssignments.ObservedValue = classObs;
// inference
var ie = new InferenceEngine(new VariationalMessagePassing());
var bPost = ie.Infer <Gaussian[]>(Bgenotype);
for (int i = 0; i < numClasses; i++)
{
Console.WriteLine("Inferred: " + bPost[i] + " truth: " + trueBgenotype[i]);
}
}