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Viterbi Algorithm

Viterbi Algorithm. Ralph Grishman G22.2590 - Natural Language Processing. Computing Probabilities. viterbi [ s, t ] = max(s’) ( viterbi [ s’, t-1] * transition probability P(s | s’) * emission probability P (token[t] | s) ) for each s, t:

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Viterbi Algorithm

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  1. Viterbi Algorithm Ralph Grishman G22.2590 - Natural Language Processing

  2. Computing Probabilities viterbi [ s, t ] = max(s’) ( viterbi [ s’, t-1] *transition probability P(s | s’) *emission probability P (token[t] | s) ) for each s, t: record which s’, t-1 contributed the maximum

  3. Analyzing Fish sleep.

  4. 0.2 0.1 0.8 0.7 0.8 start noun verb end 0.2 0.1 0.1 A Simple POS HMM

  5. Word Emission ProbabilitiesP ( word | state ) • A two-word language: “fish” and “sleep” • Suppose in our training corpus, • “fish” appears 8 times as a noun and 4 times as a verb • “sleep” appears twice as a noun and 6 times as a verb • Emission probabilities: • Noun • P(fish | noun) : 0.8 • P(sleep | noun) : 0.2 • Verb • P(fish | verb) : 0.4 • P(sleep | verb) : 0.6

  6. Viterbi Probabilities

  7. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1

  8. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1 Token 1: fish

  9. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1 Token 1: fish

  10. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1 Token 2: sleep (if ‘fish’ is verb)

  11. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1 Token 2: sleep (if ‘fish’ is verb)

  12. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1 Token 2: sleep (if ‘fish’ is a noun)

  13. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1 Token 2: sleep (if ‘fish’ is a noun)

  14. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1 Token 2: sleeptake maximum,set back pointers

  15. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1 Token 2: sleeptake maximum,set back pointers

  16. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1 Token 3: end

  17. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1 Token 3: endtake maximum,set back pointers

  18. 0.2 0.1 0.8 0.7 0.8 end start noun verb 0.2 0.1 0.1 Decode:fish = nounsleep = verb

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