I256 Applied Natural Language Processing Fall 2009 Lecture 5 Word Sense Disambiguation (WSD) Intro on Probability Theory Graphical Models Naïve Bayes Naïve Bayes for WSD Barbara Rosario

Word Senses Words have multiple distinct meanings, or senses: Plant: living plant, manufacturing plant, … Title: name of a work, ownership document, form of address, material at the start of a film, … Many levels of sense distinctions Homonymy: totally unrelated meanings (river bank, money bank) Polysemy: related meanings (star in sky, star on tv, title) Systematic polysemy: productive meaning extensions (metonymy such as organizations to their buildings) or metaphor Sense distinctions can be extremely subtle (or not) Granularity of senses needed depends a lot on the task Taken from Dan Klein’s cs 288 slides

Word Sense Disambiguation Determine which of the senses of an ambiguous word is invoked in a particular use of the word Example: living plant vs. manufacturing plant How do we tell these senses apart? “Context” The manufacturing plant which had previously sustained the town’s economy shut down after an extended labor strike. Maybe it’s just text categorization Each word sense represents a topic Why is it important to model and disambiguate word senses? Translation Bank  banca or riva Parsing For PP attachment, for example information retrieval To return documents with the right sense of bank Adapted from Dan Klein’s cs 288 slides

Resources WordNet SensEval SemCor OtherResources Hand-build (but large) hierarchy of word senses Basically a hierarchical thesaurus SensEval AWSD competition Training / test sets for a wide range of words, difficulties, and parts-of-speech Bake-off where lots of labs tried lots of competing approaches SemCor A big chunk of the Brown corpus annotated with WordNet senses OtherResources The Open Mind Word Expert Parallel texts Taken from Dan Klein’s cs 288 slides

Features Bag-of-words (use words around with no order) The manufacturing plant which had previously sustained the town’s economy shut down after an extended labor strike. Bags of words = {after, manufacturing, which, labor, ..} Bag-of-words classification works ok for noun senses 90% on classic, shockingly easy examples (line, interest, star) 80% on senseval-1 nouns 70% on senseval-1 verbs

Verb WSD Why are verbs harder? Verb Example: “Serve” Verbal senses less topical More sensitive to structure, argument choice Better disambiguated by their argument (subject-object): importance of local information For nouns, a wider context likely to be useful Verb Example: “Serve” [function] The tree stump serves as a table [enable] The scandal served to increase his popularity [dish] We serve meals for the homeless [enlist] She served her country [jail] He served six years for embezzlement [tennis] It was Agassi's turn to serve [legal] He was served by the sheriff Different types of information may be appropriate for different part of speech Adapted from Dan Klein’s cs 288 slides

Better features There are smarter features: Subcategorization: Argument selectional preference: serve NP[meals] vs. serve NP[papers] vs. serve NP[country] Subcategorization: [function] serve PP[as] [enable] serve VP[to] [tennis] serve <intransitive> [food] serve NP {PP[to]} Can capture poorly (but robustly) with local windows… but we can also use a parser and get these features explicitly Other constraints (Yarowsky 95) One-sense-per-discourse One-sense-per-collocation (pretty reliable when it kicks in: manufacturing plant, flowering plant) Taken from Dan Klein’s cs 288 slides

Various Approaches to WSD Unsupervised learning We don’t know/have the labels More than disambiguation is discrimination Cluster into groups and discriminate between these groups without giving labels Clustering Example: EM (expectation-minimization), Bootstrapping (seeded with some labeled data) Indirect supervision (See Session 7.3 of Stat NLP book) From thesauri From WordNet From parallel corpora Supervised learning Adapted from Dan Klein’s cs 288 slides

Supervised learning Supervised learning When we know the truth (true senses) (not always true or easy) Classification task Most systems do some kind of supervised learning Many competing classification technologies perform about the same (it’s all about the knowledge sources you tap) Problem: training data available for only a few words Examples: Bayesian classification Naïve Bayes (simplest example of Graphical models) (We’ll talk more about supervised learning/classification during the course) Adapted from Dan Klein’s cs 288 slides

Today Introduction to probability theory Introduction to graphical models Probability theory plus graph theory Naïve bayes (simple graphical model) Naïve bayes for WSD (classification task)

Why Probability? Statistical NLP aims to do statistical inference for the field of NLP Statistical inference consists of taking some data (generated in accordance with some unknown probability distribution) and then making some inference about this distribution.

Why Probability? Examples of statistical inference are WSD, the task of language modeling (ex how to predict the next word given the previous words), topic classification, etc. In order to do this, we need a model of the language. Probability theory helps us finding such model

Probability Theory How likely it is that something will happen Sample space Ω is listing of all possible outcome of an experiment Sample space can be continuous or discrete For language applications it’s discrete (i.e. words) Event A is a subset of Ω Probability function (or distribution)

http://ai.stanford.edu/~paskin/gm-short-course/lec1.pdf

http://ai.stanford.edu/~paskin/gm-short-course/lec1.pdf

http://ai.stanford.edu/~paskin/gm-short-course/lec1.pdf

http://ai.stanford.edu/~paskin/gm-short-course/lec1.pdf

Prior Probability Prior probability: the probability before we consider any additional knowledge

Conditional probability Sometimes we have partial knowledge about the outcome of an experiment Conditional (or Posterior) Probability Suppose we know that event B is true The probability that A is true given the knowledge about B is expressed by

http://ai.stanford.edu/~paskin/gm-short-course/lec1.pdf

Conditional probability (cont) Note: P(A,B) = P(A ∩ B) Chain Rule P(A, B) = P(A|B) P(B) = The probability that A and B both happen is the probability that B happens times the probability that A happens, given B has occurred. P(A, B) = P(B|A) P(A) = The probability that A and B both happen is the probability that A happens times the probability that B happens, given A has occurred. Multi-dimensional table with a value in every cell giving the probability of that specific state occurring

Chain Rule P(A,B) = P(A|B)P(B) = P(B|A)P(A) P(A,B,C,D…) = P(A)P(B|A)P(C|A,B)P(D|A,B,C..)

Chain Rule  Bayes' rule P(A,B) = P(A|B)P(B) = P(B|A)P(A) Bayes' rule Useful when one quantity is more easy to calculate; trivial consequence of the definitions we saw but it’ s extremely useful

Bayes' rule Bayes' rule translates causal knowledge into diagnostic knowledge. For example, if A is the event that a patient has a disease, and B is the event that she displays a symptom, then P(B | A) describes a causal relationship, and P(A | B) describes a diagnostic one (that is usually hard to assess). If P(B | A), P(A) and P(B) can be assessed easily, then we get P(A | B) for free. The Chain Rule is used in many places in Stat NLP such as Markov Model

Example S:stiff neck, M: meningitis P(S|M) =0.5, P(M) = 1/50,000 P(S)=1/20 I have stiff neck, should I worry?

(Conditional) independence Two events A e B are independent of each other if P(A) = P(A|B) Two events A and B are conditionally independent of each other given C if P(A|C) = P(A|B,C)

Back to language Statistical NLP aims to do statistical inference for the field of NLP Topic classification P( topic | document ) Language models P (word | previous word(s) ) WSD P( sense | word) Two main problems Estimation: P in unknown: estimate P Inference: We estimated P; now we want to find (infer) the topic of a document, o the sense of a word

Language Models (Estimation) In general, for language events, P is unknown We need to estimate P, (or model M of the language) We’ll do this by looking at evidence about what P must be based on a sample of data

Estimation of P Frequentist statistics Bayesian statistics Parametric Non-parametric (distribution free) Bayesian statistics Bayesian statistics measures degrees of belief Degrees are calculated by starting with prior beliefs and updating them in face of the evidence, using Bayes theorem 2 different approaches, 2 different philosophies

Inference The central problem of computational Probability Theory is the inference problem: Given a set of random variables X1, … , Xk and their joint density P(X1, … , Xk), compute one or more conditional densities given observations. Compute P(X1 | X2 … , Xk) P(X3 | X1 ) P(X1 , X2 | X3, X4,) Etc … Many problems can be formulated in these terms.

Bayes decision rule w: ambiguous word S = {s1, s2, …, sn } senses for w C = {c1, c2, …, cn } context of w in a corpus V = {v1, v2, …, vj } words used as contextual features for disambiguation Bayes decision rule Decide sj if P(sj | c) > P(sk | c) for sj ≠ sk We want to assign w to the sense s’ where s’ = argmaxsk P(sk | c)

Bayes classification for WSD We want to assign w to the sense s’ where s’ = argmaxsk P(sk | c) We usually do not know P(sk | c) but we can compute it using Bayes rule

Naïve Bayes classifier Naïve Bayes classifier widely used in machine learning Estimate P(c | sk) and P(sk)

Naïve Bayes classifier Estimate P(c | sk) and P(sk) w: ambiguous word S = {s1, s2, …, sn } senses for w C = {c1, c2, …, cn } context of w in a corpus V = {v1, v2, …, vj } words used as contextual features for disambiguation Naïve Bayes assumption:

Naïve Bayes classifier Naïve Bayes assumption: Two consequences All the structure and linear ordering of words within the context is ignored bags of words model The presence of one word in the model is independent of the others Not true but model “easier” and very “efficient” “easier” “efficient” mean something specific in the probabilistic framework We’ll see later (but easier to estimate parameters and more efficient inference) Naïve Bayes assumption is inappropriate if there are strong dependencies, but often it does very well (partly because the decision may be optimal even if the assumption is not correct)

Naïve Bayes for WSD Bayes decision rule Naïve Bayes assumption Estimation Count of vj when sk Prior probability of sk

Naïve Bayes Algorithm for WSD TRAINING (aka Estimation) For all of senses sk of w do For all words vj in the vocabulary calculate end

Naïve Bayes Algorithm for WSD TESTING (aka Inference or Disambiguation) For all of senses sk of w do For all words vj in the context window c calculate end Choose s= sk of w do

Next week Introduction to Graphical Models Part of speech tagging Readings: Chapter 5 NLTL book Chapter 10 of Foundation of Stat NLP