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Baum-Welch learning algorithm for discrete-density Hidden Markov Models.
Inheritance Hierarchy
System Object
Accord.Statistics.Models.Markov.Learning BaseBaumWelchLearning
Accord.Statistics.Models.Markov.Learning BaumWelchLearning
Namespace: Accord.Statistics.Models.Markov.Learning
Assembly: Accord.Statistics (in Accord.Statistics.dll) Version: 2.9.0.0 (2.9.0.0)
Syntax
public class BaumWelchLearning : BaseBaumWelchLearning, IUnsupervisedLearning, IConvergenceLearning
Remarks
The Baum-Welch algorithm is a kind of Expectation-Maximization algorithm. For discrete models, it estimates the matrix of state transition probabilities A, the matrix of symbol emission probabilities B and the vector of initial state probabilities pi. For increased accuracy, all computations are performed using log-probabilities.
Examples
// We will try to create a Hidden Markov Model which // can detect if a given sequence starts with a zero // and has any number of ones after that. 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 }, }; // Creates a new Hidden Markov Model with 3 states for // an output alphabet of two characters (zero and one) HiddenMarkovModel hmm = new HiddenMarkovModel(3, 2); // Try to fit the model to the data until the difference in // the average log-likelihood changes only by as little as 0.0001 var teacher = new BaumWelchLearning(hmm) { Tolerance = 0.0001, Iterations = 0 }; double ll = teacher.Run(sequences); // Calculate the probability that the given // sequences originated from the model double l1 = hmm.Evaluate(new int[] { 0, 1 }); // 0.999 double l2 = hmm.Evaluate(new int[] { 0, 1, 1, 1 }); // 0.916 // Sequences which do not start with zero have much lesser probability. double l3 = hmm.Evaluate(new int[] { 1, 1 }); // 0.000 double l4 = hmm.Evaluate(new int[] { 1, 0, 0, 0 }); // 0.000 // Sequences which contains few errors have higher probabability // than the ones which do not start with zero. This shows some // of the temporal elasticity and error tolerance of the HMMs. double l5 = hmm.Evaluate(new int[] { 0, 1, 0, 1, 1, 1, 1, 1, 1 }); // 0.034 double l6 = hmm.Evaluate(new int[] { 0, 1, 1, 1, 1, 1, 1, 0, 1 }); // 0.034
See Also