1. Probabilistic Methods in Computational Psycholinguistics Roger Levy University of Edinburgh & University of California – San Diego

2. Course overview Computational linguistics and psycholinguistics have a long-standing affinity Course focus: comprehension (“sentence processing”) CL: what formalisms and algorithms are required to obtain structural representations of a sentence (string)? PsychoLx: how is knowledge of language mentally represented during deployed during comprehension? Probabilistic methods have “taken CL by storm” This course covers application of probabilistic methods from CL to problems in psycholinguistics

3. Course overview (2) Unlike most courses at ESSLLI, our data of primary interest are derived from psycholinguistic experimentation However, because we are using probabilistic methods, naturally occurring corpus data also very important Linking hypothesis: people deploy probabilistic information derived from experience with (and thus reflecting) naturally occurring data

4. Course overview (3) Probabilistic-methods practitioners in psycholinguistics agree that humans use probabilistic information to disambiguate linguistic input But disagree on the linking hypotheses between how probabilistic information is deployed and observable measures of online language comprehension Pruning models Competition models Reranking/attention-shift models Information-theoretic models Connectionist models

5. Course overview (4) Outline of topics & core articles for course: 1.Pruning approaches: Jurafsky 1996 2.Competition models: McRae et al. 1998 3.Reranking/attention-shift models: Narayanan & Jurafsky 2002 4.Information-theoretic models: Hale 2001 5.Connectionist models: Christiansen & Chater 1999 Lots of other related articles and readings, plus some course-related software, on course website Look at core article before each day of lecture http://homepages.inf.ed.ac.uk/rlevy/esslli2006

6. Lecture format I will be covering the major points of each core article Emphasis will be on the major conceptual building components of each approach I’ll be lecturing from slides, but interrupting me (politely ) with questions and discussion is encouraged At various points we’ll have blackboard “brainstorming” sessions as well. *footnotes down here are for valuable points I don’t have time to emphasize in lecture, but feel free to ask about them

7. Today Crash course in probability theory Crash course in natural language syntax and parsing Crash course in psycholinguistic methods Pruning models: Jurafsky 1996

8. Probability theory: what? why? Probability theory is the calculus of reasoning under uncertainty This makes it well-suited to modeling the process of language comprehension Language comprehension involves uncertainty about: What has already been said What has not yet been said The girl saw the boy with the telescope. The children went outside to... (who has the telescope?) (play? chat? …)

9. Event space Ω A function P from subsets of Ω to real numbers such that: Non-negativity: Properness: Disjoint union: An improper function P for which is called deficient Crash course in probability theory

10. Probability: an example Rolling a die has event space Ω ={1,2,3,4,5,6} If it is a fair die, we require of the function P: Disjoint union means that this requirement completely specifies the probability distribution P For example, the event that a roll of the die comes out even is E={2,4,6}. For a fair die, its probability is Using disjoint union to calculate event probabilities is known as the counting method

11. Joint and conditional probability P(X,Y) is called a joint probability e.g., probability of a pair of dice coming out Two events are independent if the probability of the joint event is the product of the individual event probabilities: P(Y|X) is called a conditional probability By definition, This gives rise to Bayes’ Theorem:

12. Estimating probabilistic models With a fair die, we can calculate event probabilities using the counting method But usually, we can’t deduce the probabilities of the subevents involved Instead, we have to estimate them (=statistics!) Usually, this involves assuming a probabilistic model with some free parameters,* and choosing the values of the free parameters to match empirically obtained data *(these are parametric estimation methods)

13. Maximum likelihood Simpler example: a coin flip fair? unfair? Take a dataset of 20 coin flips, 12 heads and 8 tails Estimate the probability p that the next result is heads Method of maximum likelihood: choose parameter values (i.e., p) that maximize the likelihood* of the data Here, maximum-likelihood estimate (MLE) is the relative-frequency estimate (RFE) *likelihood: the data’s probability, viewed as a function of your free parameters

15. Issues in model estimation Maximum-likelihood estimation has several problems: Can’t incorporate a belief that coin is “likely” to be fair MLEs can be biased Try to estimate the number of words in a language from a finite sample MLEs will always underestimate the number of words There are other estimation techniques (Bayesian, maximum-entropy,…) that have different advantages When we have “lots” of data,* the choice of estimation technique rarely makes much difference *unfortunately, we rarely have “lots” of data

16. Generative vs. Discriminative Models Inference makes use of conditional probability distr’s Discriminatively-learned models estimate this conditional distribution directly Generatively-learned models estimate the joint probability of data and observation P(O,H) Bayes’ theorem is used to find c.p.d. and do inference probability of … hidden structure … given observations

17. Generative vs. Discriminative Models in Psycholinguistics Different researchers have also placed the locus of action at generative (joint) versus discriminative (conditional) models Are we interested in P(Tree|String) or P(Tree,String)? This reflects a difference in ambiguity type Uncertainty only about what has been said Uncertainty also about what may yet be said

18. Today Crash course in probability theory Crash course in natural language syntax and parsing Crash course in psycholinguistic methods Pruning models: Jurafsky 1996

19. Crash course in grammars and parsing A grammar is a structured set of production rules Most commonly used for syntactic description, but also useful for (sematics, phonology, …) E.g., context-free grammars: A grammar is said to license a derivation S → NP VP NP → Det N VP → V NP Det → the N → dog N → cat V → chased  OK

20. Bottom-up parsing VP → V NP PP → P NP S → NP VP … Fundamental operation: check whether a sequence of categories matches a rule’s right- hand side Permits structure building inconsistent with global context

21. Top-down parsing Fundamental operation: Permits structure building inconsistent with perceived input, or corresponding to as-yet- unseen input S → NP VP NP → Det N Det → The …

22. Ambiguity There is usually more than one structural analysis for a (partial) sentence Corresponds to choices (non-determinism) in parsing VP can expand to V NP PP or VP can expand to V NP and then NP can expand to NP PP The girl saw the boy with…

23. Serial vs. Parallel processing A serial processing model is one where, when faced with a choice, chooses one alternative and discards the rest A parallel model is one where at least two alternatives are chosen and maintained A full parallel model is one where all alternatives are maintained A limited parallel model is one where some but not necessarily all alternatives are maintained A joke about the man with an umbrella that I heard… *ambiguity goes as the Catalan numbers (Church and Patel 1982)

24. Dynamic programming There is an exponential number of parse trees for a given sentence (Church & Patil 1982) So sentence comprehension can’t entail an exhaustive enumeration of possible structural representations But parsing can be made tractable by dynamic programming

25. Dynamic programming (2) Dynamic programming = storage of partial results There are two ways to make an NP out of… …but the resulting NP can be stored just once in the parsing process Result: parsing time polynomial (cubic for CFGs) in sentence length Still problematic for modeling human sentence proc.

26. Hybrid bottom-up and top-down Many methods used in practice are combinations of top-down and bottom-up regimens Left-corner parsing: bottom-up parsing with top- down filtering Earley parsing: strictly incremental top-down parsing with dynamic programming* *solves problems of left-recursion that occur in top-down parsing

27. Probabilistic grammars A (generative) probabilistic grammar is one that associates probabilities with rule productions. e.g., a probabilistic context-free grammar (PCFG) has rule productions with probabilities like Interpret P(NP → Det N) as P(Det N | NP) Among other things, PCFGs can be used to achieve disambiguation among parse structures

28. a man arrived yesterday 0.3 S  S CC S 0.15 VP  VBD ADVP 0.7 S  NP VP 0.4 ADVP  RB 0.35 NP  DT NN... 0.7 0.15 0.35 0.40.30.030.02 0.07 Total probability: 0.7*0.35*0.15*0.3*0.03*0.02*0.4*0.07= 1.85  10 -7

29. Probabilistic grammars (2) A derivation having zero probability corresponds to it being unlicensed in a non-probabilistic setting But “canonical” or “frequent” structures can be distinguished from “marginal” or “rare” structures via the derivation rule probabilities From a computational perspective, this allows probabilistic grammars to increase coverage (number + type of rules) while maintaining ambiguity management

30. The probabilistic serial ↔ parallel gradient Suppose two incremental interpretations I 1,2 have probabilities p 1 >0.5>p 2 after seeing the last word w i A full-serial model might keep I 1 at activation level 1 and discard I 2 (i.e., activation level 0) A full-parallel model would keep both I 1 and I 2 at probabilities p 1 and p 2 respectively An intermediate model would keep I 1 at a 1 >p 1 and I 2 at a 2 <p 2 (A “hyper-parallel” model might keep I 1 at 0.5 a 2 >p 2 )

31. Today Crash course in probability theory Crash course in natural language syntax and parsing Crash course in psycholinguistic methods Pruning models: Jurafsky 1996

32. Psycholinguistic methodology The workhorses of psycholinguistic experimentation involve behavioral measures What choices do people make in various types of language-producing and language-comprehending situations? and how long do they take to make these choices? Offline measures rating sentences, completing sentences, … Online measures tracking people’s eye movements, having people read words aloud, reading under (implicit) time pressure…

33. Psycholinguistic methodology (2) [self-paced reading experiment demo now]

34. Psycholinguistic methodology (3) Caveat: neurolinguistic experimentation more and more widely used to study language comprehension methods vary in temporal and spatial resolution people are more passive in these experiments: sit back and listen to/read a sentence, word by word strictly speaking not behavioral measures the question of “what is difficult” becomes a little less straightforward

35. Today Crash course in probability theory Crash course in natural language syntax and parsing Crash course in psycholinguistic methods Pruning models: Jurafsky 1996

36. Pruning approaches Jurafsky 1996: a probabilistic approach to lexical access and syntactic disambiguation Main argument: sentence comprehension is probabilistic, construction-based, and parallel Probabilistic parsing model explains human disambiguation preferences garden-path sentences The probabilistic parsing model has two components: constituent probabilities – a probabilistic CFG model valence probabilities

37. Jurafsky 1996 Every word is immediately completely integrated into the parse of the sentence (i.e., full incrementality) Alternative parses are ranked in a probabilistic model Parsing is limited-parallel: when an alternative parse has unacceptably low probability, it is pruned “Unacceptably low” is determined by beam search (described a few slides later)

38. Jurafsky 1996: valency model Whereas the constituency model makes use of only phrasal, not lexical information, the valency model tracks lexical subcategorization, e.g.: P( | discuss ) = 0.24 P( | discuss ) = 0.76 (in today’s NLP, these are called monolexical probabilities) In some cases, Jurafsky bins across categories:* P( | keep) = 0.81 P( | keep ) = 0.19 where XP[+pred] can vary across AdjP, VP, PP, Particle… *valence probs are RFEs from Connine et al. (1984) and Penn Treebank

39. Jurafsky 1996: syntactic model The syntactic component of Jurafsky’s model is just probabilistic context-free grammars (PCFGs) 0.7 0.15 0.35 0.4 0.30.030.02 0.07 Total probability: 0.7*0.35*0.15*0.3*0.03*0.02*0.4*0.07= 1.85  10 -7

40. Modeling offline preferences Ford et al. 1982 found effect of lexical selection in PP attachment preferences (offline, forced- choice): The women discussed the dogs on the beach NP-attachment (the dogs that were on the beach) -- 90% VP-attachment (discussed while on the beach) – 10% The women kept the dogs on the beach NP-attachment – 5% VP-attachment – 95% Broadly confirmed in online attachment study by Taraban and McClelland 1988

41. Modeling offline preferences (2) Jurafsky ranks parses as the product of constituent and valence probabilities:

42. Modeling offline preferences (3)

43. Result Ranking with respect to parse probability matches offline preferences Note that only monotonicity, not degree of preference is matched