1. 1 Hidden Markov Model 報告人：鄒昇龍

2. 2 Outline Introduction to HMM Activity of HMM Problem and Solution Conclusion Reference

3. 3 Introduction to HMM (1) A natural language often exhibits significant structure. In English for example, the letter Q is almost always followed by a U. What is Markov process? Current event depends only on the most recent events. In a hidden Markov model, the observation attached to each state corresponds to an output probability distribution instead of a deterministic event.

4. 4 Introduction to HMM (2) The underlying stochastic process, the state sequence, is hidden, we can only observe it through another set of stochastic processes that produce the sequence of observations. 1 121 1 1 121 1 2 2 2 121 2 2 hidden observed

5. 5 Activity of HMM When initial value be given, HMM can produce a sequence of observation following the procedure: 1). Choose a initial-state by initial value. 2). Set t = 1. 3). Choose an observation by prob. of current-state. 4). Choose a next-state by transition-prob. of current-state 5). t = t + 1; if t < T go to 3 else terminate.

6. 6 Problem and Solution (1) In general, there are three basic problems that must be solved before using HMM. 1). The evaluation problem. 2). The state assignment problem. 3). The estimation problem.

7. 7 Problem and Solution (2) 1) Evaluation problem: Given a model and an observation sequence, determine how likely it is that the model has generated a given set of observations.

8. 8 Problem and Solution (3) 1.0 0.0 0.48 0.2 0.6*0.8 0.4*0.5 1.0*0.3 0.23 0.16 0.6*0.8 0.4*0.5 1.0*0.3 0.03 0.16 0.6*0.2 0.4*0.5 1.0*0.7 AAB t=0t=1t=2t=3

9. 9 Problem and Solution (4) 2) State assignment problem: We can use Viterbi-algorithm to find the best path(State-Sequence). 1.0 0.0 0.48 0.2 0.6*0.8 0.4*0.5 1.0*0.3 0.23 0.09 0.6*0.8 0.4*0.5 1.0*0.3 0.03 0.06 0.6*0.2 0.4*0.5 1.0*0.7 AAB t=0t=1t=2t=3

10. 10 Problem and Solution (5) 3) Estimation problem: Given the model structure and observations, determine the most likely parameter of the model. We can, however, choose the parameters in such a way that this probability is locally maximized using an iterative procedure called Baum-Welch re-estimation.

11. 11 Conclusion Because HMM has memory so good effect on recognition. There are three problem must to be considered, especially how to training HMM.

12. 12 Reference [1]. Eric Keller, “ FUNDAMENTALS OF SPEECH SYNTHESIS AND SPEECH RECOGNITION, ” John Wiley & Sons, 1994. [2]. 陳嘉峰, “ A Study on Speaker Verification System Using Hidden Markov Model, ” Master thesis, Institute of C. C. C., NTUT, June 2000.