1. HCI/ComS 575X: Computational Perception
Instructor: Alexander Stoytchev

2. Hidden Markov Models (part 1)
March 29, 2006
HCI/ComS 575X: Computational Perception
Iowa State University, SPRING 2006
Copyright © 2006, Alexander Stoytchev

3. ``Theory and Implementation of Hidden Markov Models'',
Rabiner and Juang (1993).
``Theory and Implementation of Hidden Markov Models'',
Chapter 6 in Fundamentals of Speech Recognition, Prentice-Hall, pp

5. Weather Example

6. HMM for the Weather Example

7. HMM for the Weather Example

8. State-Transition Probabilities Matrix

9. Markov Property
The probabilistic dependence is truncated to the previous state. In other words,

10. Markov Property
The probabilistic dependence is truncated to the previous state. In other words,

11. Also, transition probabilities are independent of time

12. Also, transition probabilities are independent of time

18. Coin Tossing Example
Suppose that a hidden set of coin tossing experiments resulted in the following observations:
Which of these 3 models produced these observations.

19. HEADS
TAILS
FIRST COIN
SECOND COIN
COIN #2
COIN #1
COIN #3

20. Example: Urns-and-Balls

21. In-Class Experiment

22. Elements of an HMM
You need to specify only 5 things:

23. Elements of an HMM
1) Number of states in the model - N

24. Elements of an HMM
2) Number of distinct observation symbols per state – M
The individual symbols can be denoted with

25. Elements of an HMM
3) State-Transition Matrix

26. Elements of an HMM
4) Observation Symbol Probability Distribution

27. Elements of an HMM
5) The initial state distribution

28. HMM Generator of Observations

29. HMM Generator of Observations

30. HMMs and Speech Recognition

31. The Three Basic Problems for HMMs

32. The EvaluationProblem

33. Find the “Correct” State Sequence

34. Model Optimization

35. To Be Continued …