William Gregory Sakas Hunter College, Department of Computer Science

Introduction to Computational Natural Language LearningLinguistics 79400 (Under: Topics in Natural Language Processing)Computer Science 83000 (Under: Topics in Artificial Intelligence)The Graduate School of the City University of New YorkFall 2001 William Gregory Sakas Hunter College, Department of Computer Science Graduate Center, PhD Programs in Computer Science and Linguistics The City University of New York

Someone shot the servant of the actress who was on the balcony.Who was on the balcony and how did they get there? Lecture 9: Learning the "best" parse from corpora and tree-banks READING :Charniak, E. (1997) Statistical techniques for natural language parsing, AI Magazine. http://www.cs.brown.edu/people/ec/papers/aimag97.ps This is a wonderfully easy to read introduction to how simple patterns in corpora can be used to resolve ambiguities in tagging and parsing. (This is a must read.) Costa et al. (2001) Wide coverage incremental parsing by learning attachment preferences http://www.dsi.unifi.it/~costa/online/AIIA2001.pdf A novel approach to learning parsing preferences that incorporates an artificial neural network. Read Charniak first, but try to get started on this before the meeting after Thanksgiving.

Review: Context-free Grammars The dog ate. The diner ate seafood. The boy ate the fish. Order of rules in a top down parse with one word look-ahead: (see blackboard) • S -> NP VP • VP -> V NP • VP -> V NP NP • NP -> det N • NP -> N • NP -> det N N • NP -> NP NP 10 dollars a share. Just like our first language models, ambiguity plays an important role.

Salespeople sold the dog biscuits. At least three parses. (See Charniak, see blackboard). Wide coverage parsers can generate 100's of parses for every sentence. See Costa et al. for some numbers from the Penn tree-bank. Most are pretty senseless. Traditionally, non-statistically-minded NLP engineering types thought of disambiguation as a post-parsing problem. Statistically-minded NLP engineering folk think more of a continuum parsing and disambiguation go toghether, it's just that some parses are more reasonable than others.

POS tagging: The can will rust. det aux aux noun noun noun verb verb verb • Learning algorithm I • Input for training: A pre-tagged training corpus. • record the frequencies, for each word, of parts of speech. E.g.:The det 1,230 can aux 534 etc noun 56 verb 6 • on an unseen corpus, apply, for each word, the most frequent POS observed from step (1). For words with frequency of 0 (they didin't appear in the training corpus) guess proper-noun. • ACHIEVES 90% (in English)!

Learning algorithm I • Input for training: A pre-tagged training corpus. • record the frequencies, for each word, of parts of speech.The det 1,230 can aux 534 etc noun 56 verb 6 • on an unseen corpus, apply, for each work, the most frequent POS observed from step (1). For words with frequency of 0 (they didin't appear in the training corpus, guess Proper-noun). • ACHIEVES 90%! (But remember totally unambiguous words like "the" are relatively frequent in English which pushes the number way up). • Easy to turn frequencies into approximations of the probability that a POS tag is correct given the word: p(t | w). For can these would be: • p( aux | can) = 534 / (534 + 56 + 6) = .90p(noun | can) = 56 / (534 + 56 + 6) = .09p(verb | can) = 6 / (534 + 56 + 6) = .01

Notation for: the tag (t) out of all possible t's that maximizes the probability of t given the current word (wi ) under consideration: = the tag (t) that generates the maximum p of p( aux | can) = 534 / (534 + 56 + 6) = .90p(noun | can) = 56 / (534 + 56 + 6) = .09p(verb | can) = 6 / (534 + 56 + 6) = .01 = aux Extending the notation for a sequence of tags : This means give the sequence of tags (t1,n), that maximizes the product of the probabilities that a tag is correct for each word.

Secretariat is expected to racetomorrow • Peoplecontinueto inquire the reason for the race for outer space Consider: to/TO race/???? the/Det race/???? • The naive Learning Algorithm I would simply assign the most probable tag – ignoring the preceding word - which would obviously be wrong for one of the two sentences above.

Consider the first sentence, with the "to race." • The (simple bigram) HMM model would choose the greater of the these two probabilities: • p(Verb | TO) p(race | Verb) • p(Noun | TO) p(race | Noun) • Let's look at the first expression: • How likely are we to find a verb given the previous tag TO? • Can find calculate from a training corpus (or corpora), a verb following a tag TO, is 15 times more likely: • p(Verb | TO) = .021 p(Noun | TO) = .34 • The second expression: • Given each tag (Verb and Noun), ask "if were expecting the tag Verb, would the lexical item be "race?" and "if were expecting the tag Noun, would the lexical item be "race?" I.e. want the likelihood of: • p(race | Verb) = .00003 and p(race | Noun) = .00041

Putting them together: • The bigram HMM correctly predicts that race should be a Verbdespite fact that race as a Noun is more common: • p(Verb | TO) p(race|Verb) = 0.00001 • p(Noun | TO) p(race|Noun) = 0.000007 • So a bigram HMM taggers chooses the tage sequence that maximizes (it's easy to increase the number of tags looked at): • p(word|tag) p(tag|previous tag) • a bit more formally: • ti = argmaxjP(tj | tj-1 )P(wi | tj )

After some math (application of Bayes theorem and the chain rule) and Two important simplifying assumptions (the probability of a word depends only on its tag and only the previous tag is enough to approximate the current tag), We have, for a whole sequence of tags t1,n an HMM bigram model for the predicted tag sequence, given words w1 . . . wn :

Want the most likely path trough this graph. noun noun noun DT aux aux verb the can will rust

This is done by the Viterbi algorithm. Accuracy of this method is around 96%. But what about if no training data to calculate likelyhood of tags and words | tags? Can estimate using the forward-backward algorithm. Doesn't work too well without at least a small training set to get it started.

PCFGs Given that there can be many, many parses of a sentence given a typical, large CFG, we should pick the most probable parse as defined by: Probability of a parse of a sentence = the product of the probabilities of all the rules that were applied to expand each constituent. prob of a parse π of sentence s probability of expanding constituent c by context-free rule r product over all constituents in parse π

Some example "toy" probabilites attached to CF rules. • S -> NP VP (1.0) • VP -> V NP (0.8) • VP -> V NP NP (0.2) • NP -> det N (0.5) • NP -> N (0.3) • NP -> det N N (0.15) • NP -> NP NP(0.05) How do we come by these probabilities? Simply count the number of times they are applied in a tree-bank. For example, if the rule: NP -> det N is used 1,000 times, and overall, NP -> X (i.e. any NP rule) is applied 2,000 times, then the probability of NP -> det N = 0.5. Apply to Salespeople sold the dog biscuits see Charniak and blackboard.

Basic tree-bank grammars parse surprising well (at around 75%) But often mis-predict the correct parse (according to humans). The most troublesome report may be the August merchandise trade deficit due out tomorrow. Tree-bank grammar gets the (incorrect) reading: His worst nightmare may be [the telephone bill due] over $200. N ADJ PP NP deficit due out tomorrow Trees on blackboard or can construct from Charniak.

Preferences depend on many factors • On type of verb: The women kept the dogs on the beach The women discussed the dogs on the beach • Kept: • Kept the dogs which were on the beach • Kept them (the dogs), while on the beach • Discussed: • Discussed the dogs which were on the beach • Discussed them (the dogs), while on the beach

Verb-argument relations • Subcategorization • But also selects into the type of the Prepositional Phrase(Hindle and Roth) • Or, even more deeply, seems to depend on the frequency of semantic associations: The actress delivered flowers threw them in the trash The postman delivered flowers threw them in the trash

On ‘selectional’ restrictions • “walking on air”; “skating on ice”, vs. “eating on ice” • Verb takes a certain kind of argument • Subject sometimes must be certain type: John admires honesty vs. ?? Honesty admires John

William Gregory Sakas Hunter College, Department of Computer Science