Hidden Markov Models

In this chapter theory of Hidden Markov Models is described. Specially the gradient based ML and MMI training is treated mathematically in detail. Finally it is shown how the idea of HMMs can be used in isolated and continuous recognition.

• Introduction
• Definition of Hidden Markov Model
• Assumptions in the theory of HMMs
• Three basic problems of HMMs
  • 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
    • Maximum Mutual Information (MMI) criterion
      • gradient wrt transition probabilities
      • gradient wrt observation probabilities
• Use of HMMs in isolated recognition
  • Training
  • recognition
• Use of HMMs in continuous recognition
  • Statistical Language models
  • Training of a HMM based continuous recognizer
    • ML training
    • MMI training
  • recognition using a HMM continuous recognizer
    • Viterbi based recognition
    • Level Building
    • N-best search
    • Calculation of the recognizer performance

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