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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:

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I256 applied natural language processing fall 2009 l.jpg

I256 Applied Natural Language ProcessingFall 2009

Lecture 5

Word Sense Disambiguation (WSD)

Intro on Probability Theory

Graphical Models

Naïve Bayes

Naïve Bayes for WSD

Barbara Rosario


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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


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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


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Resources

  • WordNet

    • 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


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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


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Verb WSD

  • Why are verbs harder?

    • 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


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Better features

  • There are smarter features:

    • 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


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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


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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


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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)


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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.


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Why Probability?

  • Examples of statistical inference are WSD, the task of language modeling(exhow 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


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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)






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Prior Probability

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


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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



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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 l.jpg
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..)


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Bayes' rule

Chain Rule  Bayes' rule

P(A,B) = P(A|B)P(B)

= P(B|A)P(A)

Useful when one quantity is more easy to calculate;

trivial consequence of the definitions we saw but it’ s

extremely useful


Bayes rule l.jpg
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.


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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?


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(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)


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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


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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


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Estimation of P

  • Frequentist 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


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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.


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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’ = argmaxskP(sk | c)


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Bayes classification for WSD

  • We want to assign w to the sense s’ where

    s’ = argmaxskP(sk | c)

  • We usually do not know P(sk | c) but we can compute it using Bayes rule


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Naïve Bayes classifier

  • Naïve Bayes classifier widely used in machine learning

  • Estimate P(c | sk) and P(sk)


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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:


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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)


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Bayes decision rule

Naïve Bayes assumption

Count of vj when sk

Estimation

Prior probability of sk

Naïve Bayes for WSD


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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

  • end

  • For all of senses sk of w do

  • end


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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

  • end

  • Choose s= sk of w do


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Next week

  • Introduction to Graphical Models

  • Part of speech tagging

  • Readings:

    • Chapter 5 NLTL book

    • Chapter 10 of Foundation of Stat NLP


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