Hidden Markov model, three basic problems and corresponding algorithms

The basic problem of hidden Markov model and its corresponding algorithm:

1. Evaluation problem: Probability calculation problem: Given model and observation sequence, the probability of the observed sequence appearing under the model is calculated.

The forward and back algorithm solves an evaluation problem, that is, given a model, the probability of a particular observation sequence is evaluated to evaluate the most matched model of the sequence.

2, Model learning problem: The known observation sequence, estimating the parameters in the model, so that the probability of the observation sequence under the model is the largest, that is, the estimation of parameters by the maximum likelihood estimation method.

Baum-welch algorithm solves a model training problem, that is, parameter estimation, is a unsupervised training method, mainly through the EM iterative implementation, that is, only the observation sequence, no state sequence training model.

Maximum likelihood estimation: A supervised learning algorithm for estimating the parameters of the observed sequence and the corresponding state sequence.

3, decoding problem/prediction problem: The known model and observation sequence, given the observation sequence, to find the most probable corresponding state sequence.

The Viterbi algorithm solves a sequence of states that is most likely to produce this output, given a model and a particular output sequence. such as the change of algae (output sequence) to observe the weather (state sequence), is a prediction problem, communication decoding problem.