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Natural Language Processing

Natural Language Processing. Lecture 8—2/5/2015 Susan W. Brown. Today. Part of speech tagging HMMs Basic HMM model Decoding Viterbi Review chapters 1-4. POS Tagging as Sequence Classification. We are given a sentence (an “ observation ” or “ sequence of observations ” )

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Natural Language Processing

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  1. Natural Language Processing Lecture 8—2/5/2015 Susan W. Brown

  2. Today • Part of speech tagging • HMMs • Basic HMM model • Decoding • Viterbi • Review chapters 1-4 Speech and Language Processing - Jurafsky and Martin

  3. POS Tagging as Sequence Classification • We are given a sentence (an “observation” or “sequence of observations”) • Secretariat is expected to race tomorrow • What is the best sequence of tags that corresponds to this sequence of observations? • Probabilistic view • Consider all possible sequences of tags • Out of this universe of sequences, choose the tag sequence which is most probable given the observation sequence of n words w1…wn. Speech and Language Processing - Jurafsky and Martin

  4. Getting to HMMs • We want, out of all sequences of n tags t1…tn the single tag sequence such that P(t1…tn|w1…wn) is highest. • Hat ^ means “our estimate of the best one” • Argmaxx f(x) means “the x such that f(x) is maximized” Speech and Language Processing - Jurafsky and Martin

  5. Getting to HMMs • This equation should give us the best tag sequence • But how to make it operational? How to compute this value? • Intuition of Bayesian inference: • Use Bayes rule to transform this equation into a set of probabilities that are easier to compute (and give the right answer) Speech and Language Processing - Jurafsky and Martin

  6. Bayesian inference • Update the probability of a hypothesis as you get evidence • Rationale: two components • How well does the evidence match the hypothesis? • How probable is the hypothesis a priori? Speech and Language Processing - Jurafsky and Martin

  7. Using Bayes Rule Speech and Language Processing - Jurafsky and Martin

  8. Likelihood and Prior Speech and Language Processing - Jurafsky and Martin

  9. Two Kinds of Probabilities • Tag transition probabilities p(ti|ti-1) • Determiners likely to precede adjs and nouns • That/DT flight/NN • The/DT yellow/JJ hat/NN • So we expect P(NN|DT) and P(JJ|DT) to be high • Compute P(NN|DT) by counting in a labeled corpus: Speech and Language Processing - Jurafsky and Martin

  10. Two Kinds of Probabilities • Word likelihood probabilities p(wi|ti) • VBZ (3sg Pres Verb) likely to be “is” • Compute P(is|VBZ) by counting in a labeled corpus: Speech and Language Processing - Jurafsky and Martin

  11. Example: The Verb “race” • Secretariat/NNP is/VBZ expected/VBN to/TO race/VB tomorrow/NR • People/NNS continue/VB to/TO inquire/VB the/DT reason/NN for/IN the/DTrace/NN for/IN outer/JJ space/NN • How do we pick the right tag? Speech and Language Processing - Jurafsky and Martin

  12. Disambiguating “race” Speech and Language Processing - Jurafsky and Martin

  13. Disambiguating “race” Speech and Language Processing - Jurafsky and Martin

  14. Example • P(NN|TO) = .00047 • P(VB|TO) = .83 • P(race|NN) = .00057 • P(race|VB) = .00012 • P(NR|VB) = .0027 • P(NR|NN) = .0012 • P(VB|TO)P(NR|VB)P(race|VB) = .00000027 • P(NN|TO)P(NR|NN)P(race|NN)=.00000000032 • So we (correctly) choose the verb tag for “race” Speech and Language Processing - Jurafsky and Martin

  15. Question 3020 If there are 30 or so tags in the Penn set And the average sentence is around 20 words... How many tag sequences do we have to enumerate to argmax over in the worst case scenario? Speech and Language Processing - Jurafsky and Martin

  16. Hidden Markov Models • Remember FSAs? • HMMs are a special kind that use probabilities with the transitions • Minimum edit distance? • Viterbi and Forward algorithms • Dynamic programming? • Efficient means of finding most likely path Speech and Language Processing - Jurafsky and Martin

  17. Hidden Markov Models • We can represent our race tagging example as an HMM. • This is a kind of generative model. • There is a hidden underlying generator of observable events • The hidden generator can be modeled as a network of states and transitions • We want to infer the underlying state sequence given the observed event sequence Speech and Language Processing - Jurafsky and Martin

  18. Hidden Markov Models • States Q = q1, q2…qN; • Observations O= o1, o2…oN; • Each observation is a symbol from a vocabulary V = {v1,v2,…vV} • Transition probabilities • Transition probability matrix A = {aij} • Observation likelihoods • Vectors of probabilities associated with the states • Special initial probability vector  Speech and Language Processing - Jurafsky and Martin

  19. HMMs for Ice Cream • You are a climatologist in the year 2799 studying global warming • You can’t find any records of the weather in Baltimore for summer of 2007 • But you find Jason Eisner’s diary which lists how many ice-creams Jason ate every day that summer • Your job: figure out how hot it was each day Speech and Language Processing - Jurafsky and Martin

  20. Eisner Task • Given • Ice Cream Observation Sequence: 1,2,3,2,2,2,3… • Produce: • Hidden Weather Sequence: H,C,H,H,H,C, C… Speech and Language Processing - Jurafsky and Martin

  21. HMM for Ice Cream Speech and Language Processing - Jurafsky and Martin

  22. Ice Cream HMM HHH HHC HCH HCC CCC CCH CHC CHH ArgmaxP(sequence | 1 3 1) • Let’s just do 131 as the sequence • How many underlying state (hot/cold) sequences are there? • How do you pick the right one? Speech and Language Processing - Jurafsky and Martin

  23. Ice Cream HMM Cold as the initial state P(Cold|Start) .2 .5 .4 .4 .3 .5 Observing a 1 on a cold day P(1 | Cold) Hot as the next state P(Hot | Cold) Observing a 3 on a hot day P(3 | Hot) Cold as the next state P(Cold|Hot) .0024 Observing a 1 on a cold day P(1 | Cold) Let’s just do 1 sequence: CHC Speech and Language Processing - Jurafsky and Martin

  24. POS Transition Probabilities Speech and Language Processing - Jurafsky and Martin

  25. Observation Likelihoods Speech and Language Processing - Jurafsky and Martin

  26. Decoding • Ok, now we have a complete model that can give us what we need. Recall that we need to get • We could just enumerate all paths given the input and use the model to assign probabilities to each. • Not a good idea. • Luckily dynamic programming (last seen in Ch. 3 with minimum edit distance) helps us here Speech and Language Processing - Jurafsky and Martin

  27. Intuition • Consider a state sequence (tag sequence) that ends at state j with a particular tag T. • The probability of that tag sequence can be broken into two parts • The probability of the BEST tag sequence up through j-1 • Multiplied by the transition probability from the tag at the end of the j-1 sequence to T. • And the observation probability of the word given tag T. Speech and Language Processing - Jurafsky and Martin

  28. The Viterbi Algorithm Speech and Language Processing - Jurafsky and Martin

  29. Viterbi Summary • Create an array • With columns corresponding to inputs • Rows corresponding to possible states • Sweep through the array in one pass filling the columns left to right using our transition probs and observations probs • Dynamic programming key is that we need only store the MAX prob path to each cell, (not all paths). Speech and Language Processing - Jurafsky and Martin

  30. Evaluation • So once you have you POS tagger running how do you evaluate it? • Overall error rate with respect to a gold-standard test set • With respect to a baseline • Error rates on particular tags • Error rates on particular words • Tag confusions... Speech and Language Processing - Jurafsky and Martin

  31. Error Analysis • Look at a confusion matrix • See what errors are causing problems • Noun (NN) vs ProperNoun (NNP) vs Adj (JJ) • Preterite (VBD) vs Participle (VBN) vs Adjective (JJ) Speech and Language Processing - Jurafsky and Martin

  32. Evaluation • The result is compared with a manually coded “Gold Standard” • Typically accuracy reaches 96-97% • This may be compared with result for a baseline tagger (one that uses no context). • Important: 100% is impossible even for human annotators. • Issues with manually coded gold standards Speech and Language Processing - Jurafsky and Martin

  33. Summary • Parts of speech • Tagsets • Part of speech tagging • HMM Tagging • Markov Chains • Hidden Markov Models • Viterbi decoding Speech and Language Processing - Jurafsky and Martin

  34. Review • Exam readings • Chapters 1 to 6 • Chapter 2 • Chapter 3 • Skip 3.4.1, 3.10, 3.12 • Chapter 4 • Skip 4.7, 4.8-4.11 • Chapter 5 • Skip 5.5.4, 5.6, 5.8-5.10 Speech and Language Processing - Jurafsky and Martin

  35. 3 Formalisms • Regular expressions describe languages (sets of strings) • Turns out that there are 3 formalisms for capturing such languages, each with their own motivation and history • Regular expressions • Compact textual strings • Perfect for specifying patterns in programs or command-lines • Finite state automata • Graphs • Regular grammars • Rules Speech and Language Processing - Jurafsky and Martin

  36. Regular expressions • Anchor expressions • ^, $, \b • Counters • *, +, ? • Single character expressions • ., [ ], [ - ] • Grouping for precedence • ( ) • [dog]* vs. (dog)* • No need to memorize shortcuts • \d, \s Speech and Language Processing - Jurafsky and Martin

  37. FSAs • Components of an FSA • Know how to read one and draw one • Deterministic vs. non-deterministic • How is success/failure different? • Relative power • Recognition vs. generation • How do we implement FSAs for recognition? Speech and Language Processing - Jurafsky and Martin

  38. More Formally • You can specify an FSA by enumerating the following things. • The set of states: Q • A finite alphabet: Σ • A start state • A set of accept states • A transition function that maps QxΣ to Q Speech and Language Processing - Jurafsky and Martin

  39. FSTs Components of an FST Inputs and outputs Relations Speech and Language Processing - Jurafsky and Martin

  40. Morphology • What is a morpheme? • Stems and affixes • Inflectional vs. derivational • Fuzzy -> fuzziness • Fuzzy -> fuzzier • Application of derivation rules • N -> V with –ize • System, chair • Regular vs. irregular Speech and Language Processing - Jurafsky and Martin

  41. Derivational Rules Speech and Language Processing - Jurafsky and Martin

  42. Lexicons • So the big picture is to store a lexicon (list of words you care about) as an FSA. The base lexicon is embedded in larger automata that captures the inflectional and derivational morphology of the language. • So what? Well, the simplest thing you can do with such an FSA is spell checking • If the machine rejects, the word isn’t in the language • Without listing every form of every word Speech and Language Processing - Jurafsky and Martin

  43. Next Time • Three tasks for HMMs • Decoding • Viterbi algorithm • Assigning probabilities to inputs • Forward algorithm • Finding parameters for a model • EM Speech and Language Processing - Jurafsky and Martin

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