1. Part 4 c Baum-Welch Algorithm CSE717, SPRING 2008 CUBS, Univ at Buffalo

2. Review of Last Class Production Probability Forward-backward Algorithm Dynamic programming Decoding Problem Viterbi Algorithm Dynamic programming

3. Parameter Estimation in HMM (Known Hidden States) Parameters in HMM Initial state probability State transition probabilities State sequence

4. Parameter Estimation in HMM (Unknown Hidden States) Parameters in HMM Initial state probability State transition probabilities Possible state sequences E-Step M-Step

5. E-Step (Baum-Welch)

6. M-Step (Baum-Welch)

7. Termination Condition of Baum-Welch Algorithm if the quality measure is considerably improved by the updated model, continue with the E/M steps otherwise stop!

8. Multiple Observation Sequences Small modification is needed for multiple observation sequences For example: Single Observation O Multiple Observations

9. Updating Observation Likelihood (Discrete HMM: is represented non-parametrically)

10. Updating Observation Likelihood (Continuous HMM: is represented by mixture model) Observation Likelihood represented by Mixture density model Multivariate Normal Distribution

11. E-Step: Given observation O, estimating current state and model labeling

12. M-Step: Updating parameters of mixture model

13. Updating Observation Likelihood (Semi-continuous HMM) All states share a single set of component densities for building the mixture model

14. E-Step: Given observation O, estimating current state and model labeling

15. M-Step: Updating parameters of mixture model