Three basic problems of HMMs

Once we have an HMM, there are three problems of interest.

(1)The Evaluation Problem

Given an HMM and a sequence of observations , what is the probability that the observations are generated by the model, ?

(2)The Decoding Problem

Given a model and a sequence of observations , what is the most likely state sequence in the model that produced the observations?

(3)The Learning Problem

Given a model and a sequence of observations , how should we adjust the model parameters in order to maximize

Evaluation problem can be used for isolated (word) recognition. Decoding problem is related to the continuous recognition as well as to the segmentation. Learning problem must be solved, if we want to train an HMM for the subsequent use of recognition tasks.

• The Evaluation Problem and the Forward Algorithm
• The Decoding Problem and the Viterbi Algorithm
• The Learning Problem
  • Maximum Likelihood (ML) criterion
    • Baum-Welch Algorithm
    • Gradient based method
      • gradient wrt transition probabilities
      • gradient wrt observation probabilities
  • Maximum Mutual Information (MMI) criterion
    • gradient wrt transition probabilities
    • gradient wrt observation probabilities

Home Page