Hidden markov chain and bayes belief networks doctor consortium
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Hidden markov chain and bayes belief networks doctor consortium
- 2. H idden M arkov M odel Zhejiang Univ CCNT Yueshen Xu Middle ware, CCNT, ZJU 10/02/11
- 4. Markov Chain Instance We can regard the weather as three states ： state1 ： Rain state2 ： Cloudy state3 ： Sun We can obtain the transition matrix with long term observation Middleware, CCNT, ZJU 10/02/11 Tomorrow Rain Cloudy Sun Today Rain 0.4 0.3 0.3 Cloudy 0.2 0.6 0.2 Sun 0.1 0.1 0.8
- 5. Definition one-step transition probability That is to say, the evolvement of the stochastic process only relies on the current state and has nothing to do with those states before. Then we call this Markov property , and the process is regarded as Markov Process State Space: Observation Sequence: Middleware, CCNT, ZJU 10/02/11
- 6. Keystone Middleware, CCNT, ZJU state transition matrix 其中： Initial state probability matrix 10/02/11
- 8. Example: S 1 S 2 S 3 What’s the probability of producing the sequence “abb” for this stochastic process? Middleware, CCNT, ZJU 10/02/11 a 11 0.3 a b 0.80.2 a 22 0.4 a b 0.30.7 a 12 0.5 a b 1 0 a 23 0.6 a b 0.50.5 a 13 0.2 a b 0 1
- 9. Instance1: S 1 S 2 S 3 S 1 ->S 1 ->S 2 ->S 3 0.3*0.8*0.5*1.0*0.6*0.5=0.036 Middleware, CCNT, ZJU 10/02/11 a 11 0.3 a b 0.80.2 a 12 0.5 a b 1 0 a 23 0.6 a b 0.50.5 a 13 0.2 a b 0 1 a 22 0.4 a b 0.30.7
- 10. Instance2: S 1 S 2 S 3 S 1 ->S 2 ->S 2 ->S 3 0.5*1.0*0.4*0.3*0.6*0.5=0.018 Middleware, CCNT, ZJU 10/02/11 a 11 0.3 a b 0.80.2 a 12 0.5 a b 1 0 a 23 0.6 a b 0.50.5 a 13 0.2 a b 0 1 a 22 0.4 a b 0.30.7
- 11. Instance3: S 1 S 2 S 3 S 1 ->S 1 ->S 1 ->S 3 0.3*0.8*0.3*0.8*0.2*1.0=0.01152 Therefore, the total probability is: 0.036+0.018+0.01152=0.06552 Middleware, CCNT, ZJU We just know “abb”, but don’t know “S ? S ? S ? ”-----That’s the point. 10/02/11 a 11 0.3 a b 0.80.2 a 12 0.5 a b 1 0 a 23 0.6 a b 0.50.5 a 13 0.2 a b 0 1 a 22 0.4 a b 0.30.7
- 17. Application Context(1): Voice Recognition Middleware, CCNT, ZJU Recognition Framework 10/02/11 Baum-Welch Re-estimation Speech database Feature Extraction Converged? 1 2 7 HMM waveform feature Yes No end
- 19. Application Context(2): Text Information Extraction Middleware, CCNT, ZJU Partition-ing State List Extracted Sequence Document Partitioni-ng Training Sample HMM Extraction Framework country, state , city, street title, author, email, abstract 10/02/11
- 21. Middleware, CCNT, ZJU 10/02/11
- 22. B ayes B elief N etwork Yueshen Xu, too Middle ware, CCNT, ZJU 10/02/11
- 33. Middleware, CCNT, ZJU 10/02/11