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Lexical Analysis using Mutual Information and T-test

This assignment explores the use of Mutual Information and T-test in lexical analysis, focusing on how they can help identify significant patterns and distinguish between near synonyms. The assignment discusses the application of these techniques in different contexts and the advantages of using part-of-speech tags for context analysis.

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Lexical Analysis using Mutual Information and T-test

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  1. Assignments • Basic idea is to choose a topic of your own, or to take a study found in the literature • Report is in two parts • Description of problem and Review of relevant literature (not just the study you are going to replicate, but related things too) • Description and discussion of your own results • First part (1000-1500 words) due in Friday 25 April • Second part (1500-2000 words) due in Friday 9 May • No overlap allowed with LELA30122 projects • Though you are free to use that list of topics for inspiration • See LELA30122 WebCT page, “project report”

  2. Church et al. 1991 K Church, W Gale, P Hanks, D Hindle (1991) Using Statistics in Lexical Analysis, in U Zernik (ed) Lexical Acquisition: Exploiting on-line resources to build a lexicon. Hillsdale NJ (1991): Lawrence Erlbaum, pp. 115-164.

  3. Background • Corpora were becoming more widespread and bigger • Computers becoming more powerful • But tools for handling them still relatively primitive • Use of corpora for lexicology • Written for the First International Workshop on Lexical Acquisition, Detroit 1989 • In fact there was no “Second IWLA” • But this paper (and others in the collection) become much cited and well known

  4. The problem • Assuming a lexicographer has at their disposal a reference corpus of considerable size, … • A typical concordance listing only works well with • words with just two or three major sense divisions • preferably well distinct • and generating only a pageful of hits • Even then, the information you may be interested in may not be in the immediate vicinity

  5. The solution • Information Retrieval faces a comparable problem (overwhelming data), and suggests a solution • Choose an appropriate statistic to highlight information “hidden” in the corpus • Preprocess the corpus to highlight properties of interest • Select an appropriate unit of text to constrain the information extracted

  6. Mutual Information • MI: a measure of similarity • Compares the joint probability of observing two words together with the probabilities of observing them independently (chance) • If there is a genuine association, I(x;y)>>0 • If no association, P(x,y)  P(x)P(y), I(x;y)  0 • If complementary distribution, I(x;y)<<0

  7. Top ten scoring pairs of strong y and powerful y Data from AP corpus, N=44.3m words

  8. Mutual Information • Can be used to demonstrate a strong association • Counts can be based on immediate neighbourhood, as in previous slide, or on co-occurrence within a window (to left or right or both), or within same sentence, paragraph, etc. • MI shows strongly associated word pairs, but cannot show the difference between, eg strong and powerful

  9. t-test • A measure of dissimilarity • How to explain relative strength of collocations such as • strong tea ~ powerful tea • powerful car ~ strong car • The less usual combination is either rejected, or has a marked contrastive meaning • Use example of {strong|powerful} support because tea rather infrequent in AP corpus

  10. {strong|powerful} support • MI can’t help: very difficult to get value for I(powerful;support)<<0 because of size of corpus • Say x and y both occur about 10 times per 1m words in a corpus • P(x) = P(y) = 10-5 and chance P(x)P(y) = 10-10 • I(powerful;support)<<0 means P(x)P(y) << 10-10 • iemuch less than 1 in 10,000,000,000 • Hard to say with confidence

  11. Rephrase the question • Can’t ask “what doesn’t collocate with powerful?” • Also, can’t show that powerful support is less likely than chance: in fact it isn’t • I(powerful;support)=1.74 • 3 x greater than chance! • Try to compare what words are more likely to appear after strong than after powerful • Show that strong support relatively more likely than powerful support

  12. t-test • Null hypothesis (H0) • H0 says that there is no significant difference between the scores • H0 can be rejected if • Difference of at least 1.65 sd’s • 95% confidence • ie the difference is real

  13. t-test • Comparison of powerful support with chance is not significant • t = 0.99 (less than 1 sd!) • But if we compare powerful support with strong support, t = –13 • Strongly suggests there is a difference

  14. MI and t-score show different things

  15. How is this useful? • Helps lexicographers recognize significant patters • Especially useful for learners’ dictionaries to make explicit the difference in distribution between near synonyms • eg what is the difference between a strong nation and a powerful nation? • Strong as in strong defense, strong economy, strong growth • Powerful as in powerful posts, powerful figure, powerful presidency

  16. Taking advantage of POS tags • Looking at context in terms of POS rather than lexical items may be more informative • Example, how can we distinguish to as an infinitive marker from to as a preposition? • Look at words which immediately precede to • able to, began to, … vs back to, according to, … • t-score can show that they have a different distribution

  17. Similar investigation with subordinate conjunction that (fact that, say that, that the, that he) and demonstrative pronoun that (that of, that is, in that, to that) • Look at both preceding and following word • Distribution is so distinctive that this process can help us to spot tagging errors

  18. subordinate conjunction demonstrative pronoun t w that/cs w that/dt w t w that/cs w that/dt w 14.19 227 2 so/cs –12.25 1 151 of/in

  19. If your corpus is parsed • Looking for word sequences can be limiting • More useful if you can extract things like subjects and objects of verbs • (Can be done to some extent by specifying POS tags within a window, but that’s very noisy) • Assuming you can easily extract, eg Ss, Vs, and Os …

  20. What kinds of things do boats do?

  21. What is an appropriate unit of text? • Mostly we have looked at neighbouring words, or words within a defined context • Bigger discourse units can also provide useful information • eg taking entire text as the unit: • How do stories that mention food differ from stories that mention water?

  22. More subtle distinctions can be brought out in this way • What’s the difference between a boat and a ship? • Notice how immediately neighbouring words won’t necessarily tell much of a story • But words found in stories that mention boats/ships help to characterize the difference in distribution, and give a clue as to the difference in meaning • Notice that human lexicographer still has to interpret the data

  23. Word-sense disambiguation • The article also shows how you can distinguish two senses of bank • Identify words which occur in the same text as bankandriver on the one hand, and bank and money on the other

  24. t bank&river bank&money w 6.63 45 4 river 4.90 28 13 River 4.01 20 13 water 3.57 16 11 feet 3.46 23 39 miles 3.44 21 32 near 3.27 12 5 boat 3.06 14 16 south 2.83 8 1 fisherman 2.83 21 49 along 2.76 11 12 border 2.74 17 35 area 2.72 9 6 village 2.71 7 0 drinking 2.70 16 32 across 2.66 9 7 east 2.58 7 2 century 2.53 10 13 missing bank (river) vs bank (money) t bank&river bank&money w -15.95 6 467 money -10.70 2 199 Bank -10.60 0 134 funds -10.46 0 131 billion -10.13 0 124 Washington -10.13 0 124 Federal - 9.43 0 110 cash - 9.03 1 134 interest - 8.79 1 129 financial - 8.79 0 98 Corp - 8.38 1 121 loans - 8.17 0 87 loan - 7.57 0 77 amount - 7.44 0 75 fund - 7.38 1 102 William - 7.31 1 101 company - 7.25 1 101 account - 7.25 0 72 deposits

  25. Bank vs bank Bank bank t Bank bank w t Bank bank w 35.02 1324 24 Gaza -36.48 1284 3362 bank 34.03 1301 36 Palestinian -10.93 900 1161 money 33.60 1316 48 Israeli -10.43 624 859 federal 33.18 1206 26 Strip - 9.59 586 786 company 32.98 1204 29 Palestinians - 8.47 282 430 accounts 32.68 1339 72 Israel - 8.26 544 693 central 31.56 4116 1284 Bank - 8.21 408 554 cash 31.13 1151 47 occupied - 8.21 675 816 business 30.79 1104 40 Arab - 7.74 546 676 loans 27.97 867 21 territories - 7.54 52 140 robbery

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