/// <summary>
/// Tests the hidden markov model.
/// </summary>
static void TestHiddenMarkovModel()
{
// fix random seed
Rand.Restart(12347);
// model size
int T = 100;
int K = 2;
// set hyperparameters
Dirichlet ProbInitPriorObs = Dirichlet.Uniform(K);
Dirichlet[] CPTTransPriorObs = Enumerable.Repeat(Dirichlet.Uniform(K), K).ToArray();
Gaussian[] EmitMeanPriorObs = Enumerable.Repeat(Gaussian.FromMeanAndVariance(0, 1000), K).ToArray();
Gamma[] EmitPrecPriorObs = Enumerable.Repeat(Gamma.FromShapeAndScale(1000, 0.001), K).ToArray();
// sample model parameters
double[] init = ProbInitPriorObs.Sample().ToArray();
double[][] trans = new double[K][];
for (int i = 0; i < K; i++)
{
trans[i] = CPTTransPriorObs[i].Sample().ToArray();
}
double[] emitMeans = new double[K];
for (int i = 0; i < K; i++)
{
emitMeans[i] = EmitMeanPriorObs[i].Sample();
}
double[] emitPrecs = new double[K];
for (int i = 0; i < K; i++)
{
emitPrecs[i] = EmitPrecPriorObs[i].Sample();
}
// print parameters
HiddenMarkovModel modelForPrinting = new HiddenMarkovModel(T, K);
modelForPrinting.SetParameters(init, trans, emitMeans, emitPrecs);
Console.WriteLine("parameters:");
modelForPrinting.PrintParameters();
Console.WriteLine();
// create distributions for sampling
Discrete initDist = new Discrete(init);
Discrete[] transDist = new Discrete[K];
for (int i = 0; i < K; i++)
{
transDist[i] = new Discrete(trans[i]);
}
Gaussian[] emitDist = new Gaussian[K];
for (int i = 0; i < K; i++)
{
emitDist[i] = Gaussian.FromMeanAndPrecision(emitMeans[i], emitPrecs[i]);
}
// calculate order of actual states
int[] actualStateOrder = argSort(emitDist);
Console.WriteLine("actualStateOrder");
Console.WriteLine(string.Join(",", actualStateOrder));
Console.WriteLine();
// sample state and emission data
int[] actualStates = new int[T];
double[] emissions = new double[T];
actualStates[0] = initDist.Sample();
emissions[0] = emitDist[actualStates[0]].Sample();
for (int i = 1; i < T; i++)
{
actualStates[i] = transDist[actualStates[i - 1]].Sample();
emissions[i] = emitDist[actualStates[i]].Sample();
}
Console.WriteLine("sample data:");
Console.WriteLine(string.Join(",", actualStates));
Console.WriteLine();
// infer model parameters, states and model evidence given priors and emission data
HiddenMarkovModel model = new HiddenMarkovModel(T, K);
model.SetPriors(ProbInitPriorObs, CPTTransPriorObs, EmitMeanPriorObs, EmitPrecPriorObs);
model.ObserveData(emissions);
model.InitialiseStatesRandomly();
model.InferPosteriors();
Console.WriteLine("model likelihood: " + model.ModelEvidencePosterior);
Discrete[] mapStatesDistr = model.StatesPosterior;
int[] mapStates = mapStatesDistr.Select(s => s.GetMode()).ToArray();
Console.WriteLine();
// print maximum a priori states
Console.WriteLine("statesMAP");
Console.WriteLine(string.Join(",", mapStates));
Console.WriteLine();
// print posterior distributions
Console.WriteLine("posteriors");
model.PrintPosteriors();
Console.WriteLine();
// calculate order of MAP states
int[] mapStateOrder = argSort(model.EmitMeanPosterior);
Console.WriteLine("mapStateOrder");
Console.WriteLine(string.Join(",", mapStateOrder));
Console.WriteLine();
// accuracy of MAP estimates
int correctStates = 0;
for (int i = 0; i < actualStates.Length; i++)
{
if (actualStateOrder[actualStates[i]] == mapStateOrder[mapStates[i]])
{
correctStates++;
}
}
Console.WriteLine("correctStates: " + correctStates + " / " + actualStates.Length);
Console.WriteLine();
Console.WriteLine("------------------\n");
}
