(C) 2000, The University of Michigan 1 Language and Information Handout #1 September 7, 2000

Language and Information

Handout #1

September 7, 2000

Course Information

• Instructor: Dragomir R. Radev (radev@si.umich.edu)

• Office: 305A, West Hall

• Phone: (734) 615-5225

• Office hours: TTh 3-4

• Course page: http://www.si.umich.edu/~radev/760

• Class meets on Thursdays, 5-8 PM in 311 West Hall

Introduction

• Google

• AskJeeves

• OneAcross

• Systran

Some Statistics• Business e-mail sent per day in the US: 2.1Billion

• Spam per day: 7 Billion

• First class mail per year: 107 Billion

• Text on Internet (2/99): > 6TB

• indexed: 16% (Lawrence and Giles, Nature 400, 1999)

• Dialog (www.dialog.com): 9 TB

• Average college library: 1 TB

• More statistics: http://www.cyberatlas.internet.com

Languages• Languages: 39,000 languages and dialects (22,000 dialects

in India alone)• Top languages: Chinese/Mandarin (885M), Spanish

(332M), English (322M), Bengali (189M), Hindi (182M), Portuguese (170M), Russian (170M), Japanese (125M)

• Source: www.sil.org/ethnologue, www.nytimes.com• Internet: English (128M), Japanese (19.7M), German

(14M), Spanish (9.4M), French (9.3M), Chinese (7.0M)• Usage: English (1999-54%, 2001-51%, 2003-46%, 2005-

43%)• Source: www.computereconomics.com

Syllabus

• Introduction to the course and linguistic background– The study of language. Computational Linguistics and Psycholinguistics.

• Elementary probability and statistics – Describing data. Measures of central tendency. The z score. Hypothesis

testing.

• Information theory – Entropy, joint entropy, conditional entropy. Relative entropy and mutual

information. Chain rules.

• Data compression and coding – Entropy rate. Language modeling. Examples of codes. Optimal codes.

Huffman codes. Arithmetic coding. The entropy of English.

Syllabus

• Clustering – Cluster analysis. Clustering of terms according to semantic similarity.

Distributional clustering.

• Concordancing and collocations – Concordances. Collocations. Syntactic criteria for collocability.

• Literary detective work – The statistical analysis of writing style. Decipherment and translation.

• Information extraction – Message understanding. Trainable methods.

• Word sense disambiguation and lexical acquisition – Supervised disambiguation. Unsupervised disambiguation. Attachment

ambiguity. Computational lexicography.

Syllabus

• Part-of-speech tagging [*]– Statistical taggers. Transformation-based learning of tags. Maximum

entropy models. Weighted finite-state transducers.

• Question answering – Semantic representation. Predictive annotation.

• Text summarization – Single-document summarization. Multi-document summarization.

Language models. Maximal Marginal Relevance. Cross-document structure theory. Trainable methods. Text categorization.

• Other topics – Text alignment. Word alignment. Statistical machine translation.

Discourse segmentation. Text categorization. Maximum entropy modeling.

Assignments

• Problem sets– The assignments will involve analysis of Web-based

data using both manual and automated techniques

• Project– Data analysis and/or programming involved

• Midterm– A mixture of short-answer and essay-type questions

• Final– A mixture of short-answer and essay-type questions

Projects

Each student will be responsible for designing and completing a research project that demonstrates the ability to use concepts from the class in addressing a practical problem for humanities computing. A significant part of the final grade will depend onthe project assignment. Students will need to submit a project proposal, a progress report, and the project itself. Students can elect to do a project on an assigned topic, or to select a topic of their own.

The final version of the project will be put on the World Wide Web, and will be defended in front of the class at the end of the semester (procedure TBA).In some cases (and only with instructor’s approval), students may be allowed to work in pairs, e.g., students with different backgrounds may collaborate on a larger project.

Readings

• Textbook:– Oakes, Chapter 1, pages 1 – 10, 24 – 35

• Additional readings– M&S, Chapter 2, pages 39 – 54– M&S, Chapter 3, pages 81 – 113

Computational Linguistics

Syntactic categories• Substitution test:

Joseph eats {

Chinese hot freshvegetarian

• Open (lexical) and closed (functional) categories:

No-fly-zoneyadda yadda yadda

Morphology

• Parts of speech: eight (or so) general types

• Inflection (number, person, tense…)

• Derivation (adjective-adverb, noun-verb)

• Compounding (separate words or single word)

• Part-of-speech tagging

• Morphological analysis (prefix, root, suffix, ending)

The dog chased the yellow bird.

Part of Speech Tags

NN /* singular noun */IN /* preposition */AT /* article */NP /* proper noun */JJ /* adjective */, /* comma */ NNS /* plural noun */CC /* conjunction */RB /* adverb */VB /* un-inflected verb */VBN /* verb +en (taken, looked (passive,perfect)) */VBD /* verb +ed (took, looked (past tense)) */CS /* subordinating conjunction */

From Church (1991) - 79 tags

Part of Speech Tags

r RP partitive articles S particlesx SX particlea T nominalu U proper nounv1p V1PPI verb 1st person plural present indicativev1p V1PPM verb 1st person plural present imperativev1p V1PPC verb 1st person plural present conditionalv1p V1PPS verb 1st person plural present subjunctivev1p V1PFI verb 1st person plural future indicativev1p V1PII verb 1st person plural imperfect indicativev1p V1PSI verb 1st person plural simple-past indicativev1p V1PIS verb 1st person plural imperfect subjunctivev2p V2PPI verb 2nd person plural present indicativev2p V2PPC verb 2nd person plural present conditional

From Tzoukermann and Radev (1995) - 258 tags

Jabberwocky (Lewis Carroll)

`Twas brillig, and the slithy tovesDid gyre and gimble in the wabe:All mimsy were the borogoves,And the mome raths outgrabe.

"Beware the Jabberwock, my son!The jaws that bite, the claws that catch!Beware the Jubjub bird, and shunThe frumious Bandersnatch!"

• Nouns: dog, tree, computer, idea

• Nouns vary in number (singular, plural), gender (masculine, feminine, neuter), case (nominative, genitive, accusative, dative)

• Latin: filius (m), filia (f), filium (object)German: Mädchen

• Clitics (‘s)

Pronouns

• Pronouns: she, ourselves, mine• Pronouns vary in person, gender, number, case (in

English: nominative, accusative, possessive, 2nd possessive, reflexive)

Joe bought him an ice cream.Joe bought himself an ice cream.

• Anaphors: herself, each other

Determiners and Adjectives

• Articles: the, a

• Demonstratives: this, that

• Adjectives: describe properties

• Attributive and predicative adjectives

• Agreement: in gender, number

• Comparative and superlative (derivative and periphrastic)

• Positive form

Verbs• Actions, activities, and states (throw, walk, have)

• English: four verb forms

• tenses: present, past, future

• other inflection: number, person

• gerunds and infinitive

• aspect: progressive, perfective

• voice: active, passive

• participles, auxiliaries

• irregular verbs

• French and Finnish: many more inflections than English

Other Parts of Speech

• Adverbs, prepositions, particles• phrasal verbs (the plane took off, take it off)• particles vs. prepositions (she ran up a bill/hill)• Coordinating conjunctions: and, or, but• Subordinating conjunctions: if, because, that,

although• Interjections: Ouch!

Alice bought Bob flowers.Bob bought Alice flowers.

Phrase-structure Grammars

• Constituent order (SVO, SOV)• imperative forms• sentences with auxiliary verbs• interrogative sentences• declarative sentences• start symbol and rewrite rules• context-free view of language

Sample Phrase-structure Grammar

S NP VPNP AT NNSNP AT NNNP NP PPVP VP PP VP VBD VP VBD NP P IN NP

AT theNNS drivers NNS teachers NNS lakes VBD drank VBD ate VBD saw IN in IN of NN cake

Phrase-structure Grammars

• Local dependencies• Non-local dependencies• Subject-verb agreement

The students who wrote the best essays were given a reward.

• wh-extraction

Should Derek read a magazine?Which magazine should Derek read?

• Empty nodes

Dependency: Arguments and Adjuncts

• Event + dependents (verb arguments are usually NPs)

• agent, patient, instrument, goal - semantic roles

• subject, direct object, indirect object

• transitive, intransitive, and ditransitive verbs

• active and passive voice

Sally watched the kids in the car.

Phrase Structure Ambiguity• Grammars are used for generating and parsing sentences

• Parses

• Syntactic ambiguity

• Attachment ambiguity: Visiting relatives can be boring.

• The children ate the cake with a spoon.

• High vs. low attachment

• Garden path sentences: The horse raced past the barn fell. Is the book on the table red?

Ungrammaticality vs. Semantic Abnormality

* Slept children the.# Colorless green ideas sleep furiously.# The cat barked.

Semantics and Pragmatics

• Lexical semantics and compositional semantics• Hypernyms, hyponyms, antonyms, meronyms and

holonyms (part-whole relationship, tire is a meronym of car), synonyms, homonyms

• Senses of words, polysemous words• Homophony (bass).• Collocations: white hair, white wine• Idioms: to kick the bucket

Discourse Analysis• Anaphoric relations:

1. Mary helped Peter get out of the car. He thanked her.

2. Mary helped the other passenger out of the car. The man had asked her for help because of his foot injury.

• Information extraction problems (entity crossreferencing)

Hurricane Hugo destroyed 20,000 Florida homes.At an estimated cost of one billion dollars, the disasterhas been the most costly in the state’s history.

Pragmatics

• The study of how knowledge about the world and language conventions interact with literal meaning.

• Speech acts• Research issues: resolution of anaphoric relations,

modeling of speech acts in dialogues

Other Research Areas• Linguistics is traditionally divided into phonetics,

phonology, morphology, syntax, semantics, and pragmatics.

• Sociolinguistics: interactions of social organization and language.

• Historical linguistics: change over time.

• Linguistic typology

• Language acquisition

• Psycholinguistics: real-time production and perception of language

Ambiguities in Natural Language

• address, resent, entrance, number• Lee: Wait to buy IBM

(http://cnnfn.cnn.com/2000/07/19/investing/q_talking_stocks/)

• Pfizer to buy Warner-Lambert in $90-billion deal (http://detnews.com/2000/business/0002/07/02080007.htm)

My Research Interests

• Text summarization (especially, of multiple documents)

• Text categorization and clustering

• Information extraction

• Question answering

Main Research Forums• Conferences: ACL, SIGIR, ANLP, Coling,

EACL/NAACL, AMTA/MT Summit, ICSLP/Eurospeech• Journals: Computational Linguistics, Natural Language

Engineering, Information Retrieval, Information Processing and Management, ACM Transactions on Information Systems

• University centers: Columbia, CMU, UMass, MIT, UPenn, USC/ISI, NMSU, Brown, Michigan, Maryland, Edinburgh, Cambridge, Saarbrücken, Kyoto, and many others

• Industrial research sites: AT&T, Bell Labs, IBM, Xerox PARC, SRI, BBN/GTE, MITRE, Microsoft

• Startups: Nuance, Ask.com, Inxight

Mathematical Foundations

Probability Spaces• Probability theory: predicting how likely it is that

something will happen

• basic concepts: experiment (trial), basic outcomes, sample space

• discrete and continuous sample spaces

• for NLP: mostly discrete spaces

• events is the certain event while is the impossible event

• event space - all possible events

Probability Spaces

• Probabilities: numbers between 0 and 1• Probability function (distribution): distributes a

probability mass of 1 throughout the sample space .

• Example: coin is tossed three times. What is the probability of 2 heads?

• Uniform distribution

Conditional Probability and Independence

• Prior and posterior probability

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

Conditional Probability and Independence

• The chain rule:

P(A1 … An) = P(A1) P(A2 |A1) P(A3|A1A2 ) … P(An | Ai)n-1

• This rule is used in many ways in statistical NLP more specifically in Markov Models.

• Two events are independent when P(AB) = P(A)P(B)

• Unless P(B)=0 this is equivalent to saying that P(A) = P(A|B)

• If two events are not independent, they are considered dependent

Bayes’ Theorem

P(B|A) = P(BA)

P(B) =

P(A|B)P(B)

• Bayes’ theorem is used to calculate P(A|B) given P(B|A).

Random Variables• Simply a function:

• The numbers are generated by a stochastic process with a certain probability distribution.• Example: the discrete random variable X that is the sum of the faces of two randomly thrown dice.• Probability mass function (pmf) which gives the probability that the random variable has different numeric values:

P(x) = P(X = x) = P(Ax) where Ax = { : X() = x}

Random Variables

• If a random variable X is distributed according to the pmf p(x), the we write X ˜ p(x)

• For a discrete random variable, we have that:

p(xi) = P(Axi) = P() = 1

Expectation and Variance• Expectation = mean (average) of a random variable.

• If X is a random variable with a pmf p(x), such that

|x| p(x) < , then the expectation is:

E(X) =

xp(x)• Example: rolling one die

• Variance = measure of whether the values of the random variable tend to be consistent over trials or to vary a lot.

Var(X) = E((X - E(X))2) = E(X2) - E2(X)

• Standard deviation = square root of variance

Expectation and Variance

• Composition of functions:

E(g(Y)) = g(y)p(y)

• Examples:

If g(Y) = aY + b, then E(g(Y)) = aE(Y) + b

E(X+Y) = E(X) + E(Y)

E(XY) = E(X)E(Y), if X and Y are independent

Joint and Conditional Distributions

• Joint (multivariate) probability distributions:

p(x,y) = P(X = x , Y = y)

• Marginal pmf:

px(x) = yp(x,y) pY(y) = xp(x,y)

• If X and Y are independent:

p(x,y) = pX(x)pY(y)

Joint and Conditional Distributions

• Conditional pmf in terms of the joint distribution:

pX|Y(x|y) =P(x,y)

pY(y) for y such that pY(y) > 0

Determining P

• Estimation

• Example “The cow chewed its cud”

• Relative frequency

• Parametric approach (doesn’t work for distribution of words in newspaper articles in a particular topic category)

• Non-parametric approach

The Binomial Distribution

• The number r of successes out of n trials given that the probability of success in any single trial is p:

B(r; n,p) = ( ) pr (1-p)n-r, where ( ) = n

r (n-r)!r!

• Example: tossing a (possibly weighted) coin n times.

Pascal’s Triangle

The Normal Distribution• Describes a continuous distribution

n(x; ,) = e-(x-)2/(22)

• Standard normal distribution: when = 0 and = 1

• In statistics, normal distribution is often used to approximate the binomial distribution. It should only be used when np(1-p) > 5

• In NLP, such assumptions are unwise. Example: “shade tree mechanics”

Statistics for Corpus Linguistics

• Descriptive statistics: how to describe data

• Describing relationships: the Chi-square test, correlation, regression

• Information theory: information, entropy, coding, redundancy, optimal codes, mutual information

Measures of Central Tendency

• Mode: the most frequent score in a data set

• Median: central score of the distribution

• Mean: average of all scores

Examples

• Split “Moby Dick” into 135 files (“pages”).

• Occurrences of the word “the” in the first 15 pages:

Data: 17 125 99 300 80 36 43 65 78 259 62 36 40 120 45Mean: 93.67Median: 65Mode: 36

Probabilities

• p = a/n, where a is the number of successes, and n is the number of trials.

p (i) = 1the sum of all probabilities is 1:

• Independent probabilities (product of probabilities): P(a AND b) = P(a) * P(b)

Binomial Coefficient

( ) = n!/r!(n-r)!n

rThe probability of success in a single trial is:

( ) pr qn-r

where q = 1 - p

Related Concepts

• For binomial distributions:– standard deviation is the square root of n, p, and q– mean is nxp

• Normal distributions:– same as binomial, for large values of n– asymptotical bell curves

Skewed Normal Distributions

• Positively skewed (most of the data is below the mean)

• Negatively skewed (the opposite)• Bimodal distributions• In corpus analysis: the number of letters in a word

or the length of a verse in syllables is usually positively skewed

• Lognormal distributions

Central Limit Theorem

When samples are repeatedly drawn from a population, the means of the samples are normally distributed around the population mean. This occurs whether or not the actual distribution is normal or not.

Measures of Variability• Variance = (x-)2/N-1

• Range

• Standard deviation is the square root of the variance

• Semi inter-quartile range (25%-75% range): Columbia ACT scores (26-30)

Data: 17 125 99 300 80 36 43 65 78 259 62 36 40 120 45 Mean: 93.67Median: 65Variance: 6729.52Standard Deviation: 82.03

z-score• A measure of how far a value is from the mean, in

terms of standard deviations• Example: = 93, = 82. Let’s consider a page

with 144 occurrences of the word “the”. The z-score for that page is:

z = (144-93)/82 = 0.62

• Using the table on pages 258-259 of Oakes, we find that the new page is at the 26th percentile

Hypothesis Testing

• If two data sets are both normally distributed, and the means and standard deviations are known

• Example: Francis and Kucera reported that the mean sentence length in government documents is 25.48 words, while in the Present-Day Edited American English corpus, the mean length is 19.27 words only

Hypotheses

• Null hypothesis: that the difference can be explained in terms of chance and natural variability

• Statistical significance: when there is less than 5% chance that the null hypothesis holds

T-testing

• Tests the difference between two groups for normally-distributed interval data

• The t-test is normally used with small samples: less than 30 items

• The one-sample study compares a sample mean with an established population

Tobs = (x - ) / stderr

Example 1

• Mixed corpus: 2.5 verbs per sentence with 1.2 standard deviation

• Scientific corpus: 3.5 verbs per sentence with 1.6 standard deviation

• number of sentences in the scientific corpus: 100• standard error in scientific corpus: 3.5/10• observed value of t = (3.5-2.5)/0.35 = 2.86

Example 1 (Cont’d)

• Number of degrees of freedom: in the example: 99• Use table on page 260 of Oakes• Find value: 1.671• The observed value of t is larger, therefore the null

hypothesis can be rejected

Tests for Difference

Tobs = (x1 - x2) / stderr

stderr2 = s12/n1 + s2

Control(n=8)

Test(n=7)

Example 2

stderr = +2.27 x 2.27 2.21 x 2.21

0.736 + 0.611 = 1.347 = 1.161

t = (6-3)/1.161 = 2.584

Example 2 (Cont’d)

• Number of degrees of freedom:7 + 8 - 2 = 13

• critical value of significance at the 5 per cent level is 2.16

• Since the observed value is greater than 2.16, we can reject the null hypothesis

Parametric and Non-parametric Tests

• Four scales of measurement: ratio, interval, ordinal, nominal

• parametric tests (e.g., t-test): interval or ratio-scored dependent variables; assumes independent observations; usually normal distributions only

• non-parametric tests: mostly for frequencies and rank-ordered scales; any type of distributions; less powerful than parametric tests

2 = (O-E)2

Chi-square Test

• Relationship between the frequencies in a display table

• Null hypothesis: no difference in distribution (all distributions are equal)

Special cases

• When the number of degrees of freedom is 1, as in a 2x2 contingency table, Yates’s correction factor is used.

• If O > E, add 0.5 to O, otherwise, subtract 0.5 from O.

• If E < 5, results are not reliable.

Two-dimensional Contingency Table

X = yes X = no

Y = yes

Y = no

2 =N( |ad - bc| - N/2)2

(a+b)(c+d)(a+c)(b+d)

Expected value =Row total x column total

Grand number of items

Third Person Singular Reference (O)Japanese English Total

Ellipsis 104 0 104

Central pronouns 73 314 387

Non-central pronouns 12 28 40

Names 314 291 605

Common NPs 205 174 379

Total 708 807 1515

Third Person Singular Reference (E)Japanese English Total

Ellipsis 48.6 55.4 104

Central pronouns 180.9 206.1 387

Non-central pronouns 18.7 21.3 40

Names 282.7 322.3 605

Common NPs 177.1 201.9 379

Total 708 807 1515

(O-E)2/E for the Two LanguagesJapanese English

Ellipsis 63.2 55.4

Central pronouns 64.4 56.5

Non-central pronouns 2.4 2.1

Names 3.5 3.0

Common NPs 4.4 3.9

S = 258.8; df = (5-1) x (2-1) = 4 --> different at the 0.001 level

Rank Correlation

• Pearson - continuous data

• Spearman’s rank correlation coefficient - non-continuous variables

= 1 - 6 d2

N (N2 - 1)

ExampleS X Y X' Y' d d2

1 894 80.2 2 5 3 9

2 1190 86.9 1 2 1 1

3 350 75.7 6 6 0 0

4 690 80.8 4 4 0 0

5 826 84.5 3 3 0 0

6 449 89.3 5 1 4 16

= 1 - 6 x 26

6 (62 - 1) =

Linear Regression

• Dependent and independent variables

• Regression: used to predict the behavior of the dependent variable

• Needed: X, Y, X, b = slope of Y(X)

b = NXY - XY

NX2 - (X)2

Y’ = Y + b(X - X)

Example

Section X Y X2 XY

1 22 20 484 440

2 49 24 2401 1176

3 80 42 6400 3360

4 26 22 676 572

5 40 23 1600 920

6 54 26 2916 1404

7 91 55 8281 5005

TOTAL 362 212 22758 12877

Example (Cont’d)

a = 5.775

(7 x 12877) - (362 x 212)

(7 x 22758) - (362 x 362)=

90139 - 76744

159306 - 131044=

28262= 0.474b =

Y’ = 5.775 + 0.474 X

N-gram Models

Word Prediction

• Example: “I’d like to make a collect …”

• “I have a gub”

• augmentative communication systems

• “He is trying to fine out”

• “Hopefully, all with continue smoothly in my absence”

• “They are leaving in about fifteen minuets to go to her house”

• “I need to notified the bank of [this problem]

• Language model: a statistical model of word sequences

Counting Words

• Brown corpus (1 million words from 500 texts)

• Example: “He stepped out into the hall, was delighted to encounter a water brother” - how many words?

• Word forms and lemmas. “cat” and “cats” share the same lemma (also tokens and types)

• Shakespeare’s complete works: 884,647 word tokens and 29,066 word types

• Brown corpus: 61,805 types and 37,851 lemmas

• American Heritage 3rd edition has 200,000 “boldface forms” (including some multiword phrases)

Unsmoothed N-grams

• First approximation: each word has an equal probability to follow any other. E.g., with 100,000 words, the probability of each of them at any given point is .00001

• “the” - 69,971 times in BC, while “rabbit” appears 11 times

• “Just then, the white …”

P(w1,w2,…, wn) = P(w1) P(w2 |w1) P(w3|w1w2) … P(wn |w1w2…wn-1)

Replace P(wn |w1w2…wn-1) with P(wn|wn-1)

Bigram model:

Markov Models

• Assumption: we can predict the probability of some future item on the basis of a short history

• Bigrams: first-level Markov models• Bigram grammars: as an N-by-N matrix of probabilities,

where N is the size of the vocabulary that we are modeling.

Relative Frequenciesa aardvark aardwolf aback … zoophyte zucchini

a X 0 0 0 … X X

aardvark 0 0 0 0 … 0 0

aardwolf 0 0 0 0 … 0 0

aback X X X 0 … X X

… … … … … … … …

zoophyte 0 0 0 X … 0 0

zucchini 0 0 0 X … 0 0

(C) 2000, The University of Michigan 1 Language and Information Handout #1 September 7, 2000

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