BaumWelchLearning Class

public class BaumWelchLearning : BaseBaumWelchLearningOptions<HiddenMarkovModel, GeneralDiscreteDistribution, int, GeneralDiscreteOptions>

Public Class BaumWelchLearning
	Inherits BaseBaumWelchLearningOptions(Of HiddenMarkovModel, GeneralDiscreteDistribution, Integer, GeneralDiscreteOptions)

// We will create a Hidden Markov Model to detect 
// whether a given sequence starts with a zero.
int[][] sequences = new int[][]
{
    new int[] { 0,1,1,1,1,0,1,1,1,1 },
    new int[] { 0,1,1,1,0,1,1,1,1,1 },
    new int[] { 0,1,1,1,1,1,1,1,1,1 },
    new int[] { 0,1,1,1,1,1         },
    new int[] { 0,1,1,1,1,1,1       },
    new int[] { 0,1,1,1,1,1,1,1,1,1 },
    new int[] { 0,1,1,1,1,1,1,1,1,1 },
};

// Create the learning algorithm
var teacher = new BaumWelchLearning()
{
    Topology = new Ergodic(3), // Create a new Hidden Markov Model with 3 states for
    NumberOfSymbols = 2,       // an output alphabet of two characters (zero and one)
    Tolerance = 0.0001,        // train until log-likelihood changes less than 0.0001
    Iterations = 0             // and use as many iterations as needed
};

// Estimate the model
var hmm = teacher.Learn(sequences);

// Now we can calculate the probability that the given
// sequences originated from the model. We can compute
// those probabilities using the Viterbi algorithm:
double vl1; hmm.Decode(new int[] { 0, 1 }, out vl1);        // -0.69317855
double vl2; hmm.Decode(new int[] { 0, 1, 1, 1 }, out vl2);  // -2.16644878

// Sequences which do not start with zero have much lesser probability.
double vl3; hmm.Decode(new int[] { 1, 1 }, out vl3);        // -11.3580034
double vl4; hmm.Decode(new int[] { 1, 0, 0, 0 }, out vl4);  // -38.6759130

// Sequences which contains few errors have higher probability
//  than the ones which do not start with zero. This shows some
//  of the temporal elasticity and error tolerance of the HMMs.
double vl5; hmm.Decode(new int[] { 0, 1, 0, 1, 1, 1, 1, 1, 1 }, out vl5); // -8.22665
double vl6; hmm.Decode(new int[] { 0, 1, 1, 1, 1, 1, 1, 0, 1 }, out vl6); // -8.22665


// Additionally, we can also compute the probability 
// of those sequences using the forward algorithm:
double fl1 = hmm.LogLikelihood(new int[] { 0, 1 });        // -0.000031369
double fl2 = hmm.LogLikelihood(new int[] { 0, 1, 1, 1 });  // -0.087005121

// Sequences which do not start with zero have much lesser probability.
double fl3 = hmm.LogLikelihood(new int[] { 1, 1 });        // -10.66485629
double fl4 = hmm.LogLikelihood(new int[] { 1, 0, 0, 0 });  // -36.61788687

// Sequences which contains few errors have higher probability
//  than the ones which do not start with zero. This shows some
//  of the temporal elasticity and error tolerance of the HMMs.
double fl5 = hmm.LogLikelihood(new int[] { 0, 1, 0, 1, 1, 1, 1, 1, 1 }); // -3.3744416
double fl6 = hmm.LogLikelihood(new int[] { 0, 1, 1, 1, 1, 1, 1, 0, 1 }); // -3.3744416