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Lecture 7 HMMs – the 3 Problems Forward Algorithm

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1 Lecture 7 HMMs – the 3 Problems Forward Algorithm
CSCE Natural Language Processing Lecture 7 HMMs – the 3 Problems Forward Algorithm Topics Overview Readings: Chapter 6 February 6, 2013

2 Overview Last Time Today Tagging Markov Chains Hidden Markov Models
NLTK book – chapter 5 tagging Today Viterbi dynamic programming calculation Noam Chomsky on You Tube Revisited smoothing Dealing with zeroes Laplace Good-Turing

3 Katz Backoff

4 Back to Tagging Brown Tagset -
In 1967, Kucera and Francis published their classic work Computational Analysis of Present-Day American English – tags added later ~1979 500 texts each roughly 2000 words Zipf’s Law – “the frequency of the n-th most frequent word is roughly proportional to 1/n” Newer larger corpora ~ 100 million words Corpus of Contemporary American English, the British National Corpus or the International Corpus of English

5 Figure 5.4 pronoun in Celex Counts from COBUILD 16-million word corpus

6 Figure 5.6 Penn Treebank Tagset

7 Figure 5.7

8 Figure 5.7 continued

9 Figure 5.8

10 Figure 5.10

11 5.5.4 Extending HMM to Trigrams
Find best tag sequence Bayes rule Markov assumption Extended for Trigrams

12 Chapter 6 - HMMs formalism revisited

13 Markov – Output Independence
Markov Assumption Output Independence: (Eq 6.7)

14 Figure 6.2 initial probabilities

15 Figure 6.3 Example Markov chain Probability of a sequence

16 Figure 6.4 Probability zero links (Bakis model for temporal problems)

17 HMMs – The Three Problems

18 Likelihood Computation – The Forward Algorithm
Computing Likelihood: Given an HMM λ = (A, B) and an observation sequence O = o1, o2, … ot, determine the likelihood P(O | λ)

19 Figure 6.5 B – observational Probabilities for 3 1 3 ice creams

20 Figure 6.6 transitions for 3 1 3 ice creams

21 Likelihood computation

22 Figure 6.7 forward computation

23

24 Figure 6.8

25 Figure 6.9 Forward Algorithm

26 Figure 6.10

27

28 Figure 6.11

29 Figure 6.12

30 Figure 6.13

31 Figure 6.14


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