public void Training()
{
var model = new HiddenMarkovModel(5, 5);
model.InitialStateProbabilities = new double[] { 0.1, 0.3, 0.1, 0.4, 0.1 };
// all emission P should be 0.2
Assert.IsTrue(model.EmissionProbabilities.Cast<double>().All(e => e == 0.2));
int[] observations = new int[] { 4, 2, 3, 0, 1, 3, 2 };
int[] observations2 = new int[] { 3, 4, 0, 2, 1, 1, 4, 1, 3, 2 };
var sequence = Enumerable.Repeat(observations, 10);
var sequence2 = Enumerable.Repeat(observations2, 10);
model.train(sequence);
Assert.AreEqual(model.EmissionProbabilities[1, 2], 0.25491738788355622);
Assert.AreEqual(model.EmissionProbabilities[3, 1], 0.087887575284407757);
model.train(sequence2);
Assert.AreEqual(model.EmissionProbabilities[1, 2], 0.0096840128278279109);
Assert.AreEqual(model.EmissionProbabilities[3, 1], 0.10439889167415384);
Assert.AreEqual(model.TransitionProbabilities[1, 3], 0.35392973024268204);
}
/** Creates a Unit (Quantizer&Model).
*
* @param id
* int representation of a gesture "name"/class.
*/
public GestureModel()
{
this.numStates = 15; // states empirical value
this.numObservations = 20; // observations empirical value
this.markovmodell = new HiddenMarkovModel(numStates, numObservations); // init model
this.quantizer = new Quantizer(numStates); // init quantizer
}
public void Evaluation()
{
// based on http://en.wikipedia.org/wiki/Hidden_Markov_model#A_concrete_example
var model = new HiddenMarkovModel(2, 3);
model.InitialStateProbabilities = new double[] { 0.6, 0.4 };
model.TransitionProbabilities = new double[,]
{
{ 0.7, 0.3 },
{ 0.4, 0.6 }
};
model.EmissionProbabilities = new double[,]
{
{ 0.1, 0.4, 0.5 },
{ 0.6, 0.3, 0.1 }
};
int[] observations = new int[] { 1, 2, 0 };
// hand calculate probability by summing probability of this observation sequence
// over all possible state sequences
/* State sequences:
* 0, 0, 0 : Pa = 0.6 * 0.7 * 0.7 = 0.294
* 0, 0, 1 : Pb = 0.6 * 0.7 * 0.3 = 0.126
* 0, 1, 0 : Pc = 0.6 * 0.3 * 0.4 = 0.072
* 0, 1, 1 : Pd = 0.6 * 0.3 * 0.6 = 0.108
* 1, 0, 0 : Pe = 0.4 * 0.4 * 0.7 = 0.112
* 1, 0, 1 : Pf = 0.4 * 0.4 * 0.3 = 0.048
* 1, 1, 0 : Pg = 0.4 * 0.6 * 0.4 = 0.096
* 1, 1, 1 : Ph = 0.4 * 0.6 * 0.6 = 0.144
* Sanity check, yes they sum to 1
*/
/* Output (1, 2, 0) given state sequence:
* P(o|a) = 0.4 * 0.5 * 0.1 = 0.02
* P(o|b) = 0.4 * 0.5 * 0.6 = 0.12
* P(o|c) = 0.4 * 0.1 * 0.1 = 0.004
* P(o|d) = 0.4 * 0.1 * 0.6 = 0.024
* P(o|e) = 0.3 * 0.5 * 0.1 = 0.015
* P(o|f) = 0.3 * 0.5 * 0.6 = 0.09
* P(o|g) = 0.3 * 0.1 * 0.1 = 0.003
* P(o|h) = 0.3 * 0.1 * 0.6 = 0.018
*/
// Final probability = P(o|a)*P(a) + ... + P(o|h)*P(h) =
// 0.00588 + 0.01512 + 0.000288 + 0.002592 + 0.00168 + 0.00432 + 0.000288 + 0.002592 = 0.03276
var modelProbability = model.getProbability(observations);
Assert.AreEqual(modelProbability, 0.03276);
}
