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CS621: Artificial Intelligence

CS621: Artificial Intelligence. Pushpak Bhattacharyya CSE Dept., IIT Bombay Lecture 38,39,40– POS tag corpora; HMM Training; Baum Welch aka Forward Backward Algorithm 26 th Oct , 1 st Nov, 2010. Corpus. Collection of coherent text ^_^ People_N laugh_V aloud_A $_$. Corpus. Spoken.

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CS621: Artificial Intelligence

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  1. CS621: Artificial Intelligence Pushpak BhattacharyyaCSE Dept., IIT Bombay Lecture 38,39,40– POS tag corpora; HMM Training; Baum Welch aka Forward Backward Algorithm 26thOct, 1st Nov, 2010

  2. Corpus • Collection of coherent text • ^_^ People_Nlaugh_Valoud_A $_$ Corpus Spoken Written Brown BNC Switchboard Corpus

  3. Some notable text corpora of English • American National Corpus • Bank of English • British National Corpus • Corpus JurisSecundum • Corpus of Contemporary American English (COCA) 400+ million words, 1990-present. Freely searchable online. • Brown Corpus, forming part of the "Brown Family" of corpora, together with LOB, Frown and F-LOB. • International Corpus of English • Oxford English Corpus • Scottish Corpus of Texts & Speech

  4. Penn Treebank Tagset: sample • 1. CC Coordinating conjunction • 2. CD Cardinal number • 3. DT Determiner • 4. EX Existential there • 5. FW Foreign word • 6. IN Preposition or subordinating conjunction • 7. JJ Adjective • 8. JJR Adjective, comparative • 9. JJS Adjective, superlative • 10. LS List item marker • 11. MD Modal • 12. NN Noun, singular or mass • 13. NNS Noun, plural 1 • 4. NNP Proper noun, singular

  5. HMM Training Baum Welch or Forward Backward Algorithm

  6. Key Intuition a Given: Training sequence Initialization: Probability values Compute: Pr (state seq | training seq) get expected count of transition compute rule probabilities Approach: Initialize the probabilities and recompute them… EM like approach a b a q r a b b b

  7. Baum-Welch algorithm: counts a, b String = abbaaabbbaaa Sequence of states with respect to input symbols a,b r q a,b a,b o/p seq State seq

  8. Calculating probabilities from table Table of counts T=#states A=#alphabet symbols Now if we have a non-deterministic transitions then multiple state seq possible for the given o/p seq (ref. to previous slide’s feature). Our aim is to find expected count through this.

  9. Interplay Between Two Equations wk No. of times the transitions sisj occurs in the string

  10. Illustration a:0.67 b:0.17 q r a:0.16 b:1.0 Actual (Desired) HMM a:0.4 b:0.48 q r a:0.48 b:1.0 Initial guess

  11. One run of Baum-Welch algorithm: string ababa State sequences * εis considered as starting and ending symbol of the input sequence string. Through multiple iterations the probability values will converge.

  12. Computational part (1/2) w0 w1 w2 wk wn-1wn S0  S1  S1  … Si  Sj …  Sn-1  Sn Sn+1

  13. Computational part (2/2) w0 w1 w2 wk wn-1wn S0  S1  S1  … Si  Sj …  Sn-1  Sn Sn+1

  14. Discussions 1. Symmetry breaking: Example: Symmetry breaking leads to no change in initial values 2 Struck in Local maxima 3. Label bias problem Probabilities have to sum to 1. Values can rise at the cost of fall of values for others. a:0.5 b:0.25 a:0.25 s s s s s s b:1.0 a:0.5 a:0.5 b:0.5 a:1.0 b:0.5 a:0.25 b:0.5 b:0.5 Initialized Desired

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