1. Learning Bit by Bit Hidden Markov Models

2. Weighted FSA weather The is outside 1.0.7.3

3. Markov Chain Computing probability of an observed sequence of events

4. Markov Chain weather The is outside.7.3 Observation = “The weather outside” wind.5.1.9

5. Parts of Speech Grammatical constructs like noun, verb

6. POS examples Nnounchair, bandwidth, pacing Vverbstudy, debate, munch ADJadjectivepurple, tall, ridiculous ADVadverbunfortunately, slowly Pprepositionof, by, to PROpronounI, me, mine DETdeterminerthe, a, that, those

7. Parts of Speech-uses Speech recognition Speech synthesis Data mining Translation

8. POS Tagging Words often have more than one POS: back – The back door = JJ – On my back = NN – Win the voters back = RB – Promised to back the bill = VB The POS tagging problem is to determine the POS tag for a particular instance of a word.

9. POS Tagging Sentence = sequence of observations Ie. “Secretariat is expected to race tomorrow”

10. Disambiguating “race”

11. Hidden Markov Model Observed Hidden

12. Hidden Markov Model 2 kinds of probabilities: – Tag transitions – Word likelihoods

13. Hidden Markov Model Tag transition prob = P( tag | previous tag) – ie. P(VB | TO)

14. Hidden Markov Model Word likelihood probability = P(word | tag) – ie. P(“race” | VB)

15. Actual probabilities: – P (NN | TO) =.00047 – P (VB | TO) =.83

16. Actual probabilities: – P (NR| VB) =.0027 – P (NR| NN) =.0012

17. Actual probabilities: – P (race | NN) =.00057 – P (race | VB) =.00012

19. Hidden Markov Model Probability “to race tomorrow” =“TO VB NR” P(VB|TO) * P(NR|VB) * P(race|VB).83 *.0027 *.00012 = 0.00000026892

20. Hidden Markov Model Probability “to race tomorrow” =“TO NN NR” P(NN|TO) * P(NR|NN) * P(race|NN).00047*.0012*.00057 = 0.00000000032148

21. Hidden Markov Model Probability “to race tomorrow” =“TO NN NR” = 0.00000000032148 Probability “to race tomorrow” =“TO VB NR” = 0.00000026892

22. Bayesian Inference Correct answer = max (P (hypothesis | observed))

23. Bayesian Inference Prior probability = likelihood of the hypothesis

24. Bayesian Inference Likelihood = probability that the evidence matches the hypothesis

25. Bayesian Inference Bayesian vs. Frequentists Subjectivity

26. Examples