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CMSC 723 / LING 645: Intro to Computational Linguistics

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CMSC 723 / LING 645: Intro to Computational Linguistics

September 22, 2004: Dorr

Porter Stemmer,Intro to Probabilistic NLP and N-grams (chap 6.1-6.3)

Prof. Bonnie J. DorrDr. Christof MonzTA: Adam Lee

Computational Morphology (continued)

- The Rules and the Lexicon
- General versus Specific
- Regular versus Irregular
- Accuracy, speed, space
- The Morphology of a language

- Approaches
- Lexicon only
- Lexicon and Rules
- Finite-state Automata
- Finite-state Transducers

- Rules only

Lexicon-Free Morphology:Porter Stemmer

- Lexicon-Free FST Approach
- By Martin Porter (1980)http://www.tartarus.org/%7Emartin/PorterStemmer/
- Cascade of substitutions given specific conditions
GENERALIZATIONS

GENERALIZATION

GENERALIZE

GENERAL

GENER

Porter Stemmer

- Definitions
- C = string of one or more consonants, where a consonant is anything other than A E I O U or (Y preceded by C)
- V = string of one or more vowels
- M = Measure, roughly with number of syllables
- Words = (C)*(V*C*)M(V)*
- M=0 TR, EE, TREE, Y, BY
- M=1 TROUBLE, OATS, TREES, IVY
- M=2 TROUBLES, PRIVATE, OATEN, ORRERY

- Conditions
- *S - stem ends with S
- *v* - stem contains a V
- *d - stem ends with double C, e.g., -TT, -SS
- *o - stem ends CVC, where second C is not W, X or Y, e.g., -WIL, HOP

*<S> = ends with <S>

*v* = contains a V

*d = ends with double C

*o = ends with CVC second C is not W, X or Y

Porter StemmerStep 1: Plural Nouns and Third Person Singular Verbs

SSES SS caresses caress

IES I ponies poni

ties ti

SS SS caress caress

S cats cat

Step 2a: Verbal Past Tense and Progressive Forms

(M>0) EED EE feed feed, agreed agree

i (*v*) ED plastered plaster, bled bled

ii (*v*) ING motoring motor, sing sing

Step 2b: If 2a.i or 2a.ii is successful, Cleanup

AT ATE conflat(ed) conflate

BL BLE troubl(ed) trouble

IZ IZE siz(ed) size

(*d and not (*L or *S or *Z)) hopp(ing) hop, tann(ed) tan

single letter hiss(ing) hiss, fizz(ed) fizz

(M=1 and *o) E fail(ing) fail, fil(ing) file

*<S> = ends with <S>

*v* = contains a V

*d = ends with double C

*o = ends with CVC second C is not W, X or Y

Porter StemmerStep 3: Y I

(*v*) Y I happy happi

sky sky

Porter Stemmer

Step 4: Derivational Morphology I: Multiple Suffixes

(m>0) ATIONAL -> ATE relational -> relate

(m>0) TIONAL -> TION conditional -> condition

rational -> rational

(m>0) ENCI -> ENCE valenci -> valence

(m>0) ANCI -> ANCE hesitanci -> hesitance

(m>0) IZER -> IZE digitizer -> digitize

(m>0) ABLI -> ABLE conformabli -> conformable

(m>0) ALLI -> AL radicalli -> radical

(m>0) ENTLI -> ENT differentli -> different

(m>0) ELI -> E vileli - > vile

(m>0) OUSLI -> OUS analogousli -> analogous

(m>0) IZATION -> IZE vietnamization -> vietnamize

(m>0) ATION -> ATE predication -> predicate

(m>0) ATOR -> ATE operator -> operate

(m>0) ALISM -> AL feudalism -> feudal

(m>0) IVENESS -> IVE decisiveness -> decisive

(m>0) FULNESS -> FUL hopefulness -> hopeful

(m>0) OUSNESS -> OUS callousness -> callous

(m>0) ALITI -> AL formaliti -> formal

(m>0) IVITI -> IVE sensitiviti -> sensitive

(m>0) BILITI -> BLE sensibiliti -> sensible

Porter Stemmer

Step 5: Derivational Morphology II: More Multiple Suffixes

(m>0) ICATE -> IC triplicate -> triplic

(m>0) ATIVE -> formative -> form

(m>0) ALIZE -> AL formalize -> formal

(m>0) ICITI -> IC electriciti -> electric

(m>0) ICAL -> IC electrical -> electric

(m>0) FUL -> hopeful -> hope

(m>0) NESS -> goodness -> good

*<S> = ends with <S>

*v* = contains a V

*d = ends with double C

*o = ends with CVC second C is not W, X or Y

Porter StemmerStep 6: Derivational Morphology III: Single Suffixes

(m>1) AL -> revival -> reviv

(m>1) ANCE -> allowance -> allow

(m>1) ENCE -> inference -> infer

(m>1) ER -> airliner -> airlin

(m>1) IC -> gyroscopic -> gyroscop

(m>1) ABLE -> adjustable -> adjust

(m>1) IBLE -> defensible -> defens

(m>1) ANT -> irritant -> irrit

(m>1) EMENT -> replacement -> replac

(m>1) MENT -> adjustment -> adjust

(m>1) ENT -> dependent -> depend

(m>1 and (*S or *T)) ION -> adoption -> adopt

(m>1) OU -> homologou -> homolog

(m>1) ISM -> communism -> commun

(m>1) ATE -> activate -> activ

(m>1) ITI -> angulariti -> angular

(m>1) OUS -> homologous -> homolog

(m>1) IVE -> effective -> effect

(m>1) IZE -> bowdlerize -> bowdler

*<S> = ends with <S>

*v* = contains a V

*d = ends with double C

*o = ends with CVC second C is not W, X or Y

Porter StemmerStep 7a: Cleanup

(m>1) E probate probat

rate rate

(m=1 and not *o) E cease ceas

Step 7b: More Cleanup

(m > 1 and *d and *L) controll control

single letter roll roll

Porter Stemmer

- Errors of Omission
- European Europe
- analysis analyzes
- matrices matrix
- noise noisy
- explain explanation

- Errors of Commission
- organization organ
- doing doe
- generalization generic
- numerical numerous
- university universe

From Krovetz ‘93

Why (not) Statistics for NLP?

- Pro
- Disambiguation
- Error Tolerant
- Learnable

- Con
- Not always appropriate
- Difficult to debug

Weighted Automata/Transducers

- Speech recognition: storing a pronunciation lexicon
- Augmentation of FSA: Each arc is associated with a probability

Pronunciation network for “about”

Probability Definitions

- Experiment (trial)
- Repeatable procedure with well-defined possible outcomes

- Sample space
- Complete set of outcomes

- Event
- Any subset of outcomes from sample space

- Random Variable
- Uncertain outcome in a trial

More Definitions

- Probability
- How likely is it to get a particular outcome?
- Rate of getting that outcome in all trials
Probability of drawing a spade from 52 well-shuffled playing cards:

- Distribution: Probabilities associated with each outcome a random variable can take
- Each outcome has probability between 0 and 1
- The sum of all outcome probabilities is 1.

A,B

B

Conditional Probability- What is P(A|B)?
- First, what is P(A)?
- P(“It is raining”) = .06

- Now what about P(A|B)?
- P(“It is raining” | “It was clear 10 minutes ago”) = .004

Note: P(A,B)=P(A|B) · P(B)

Also: P(A,B) = P(B,A)

Independence

- What is P(A,B) if A and B are independent?
- P(A,B)=P(A) ·P(B) iff A,B independent.
- P(heads,tails) = P(heads) · P(tails) = .5 · .5 = .25
- P(doctor,blue-eyes) = P(doctor) · P(blue-eyes) = .01 · .2 = .002

- What if A,B independent?
- P(A|B)=P(A) iff A,B independent
- Also: P(B|A)=P(B) iff A,B independent

Bayes Theorem

- Swap the order of dependence
- Sometimes easier to estimate one kind of dependence than the other

P(O|H)

Best H

Best H =

=

likelihood

prior

argmax

argmax P(H|O)

H

H

What does this have to do with the Noisy Channel Model?(O)

(H)

Noisy Channel Applied to Word Recognition

- argmaxw P(w|O) = argmaxw P(O|w) P(w)
- Simplifying assumptions
- pronunciation string correct
- word boundaries known

- Problem:
- Given [n iy], what is correct dictionary word?

- What do we need?

[ni]: knee, neat, need, new

Word

P(O|w)

freq(w)

P(w)

P(w)

P(O|w)P(w)

new

new

2625

.36

.001

.001

.00036

neat

neat

.52

338

.00013

.00013

.000068

need

need

.11

1417

.00056

.00056

.000062

knee

knee

1.00

61

.000024

.000024

.000024

What is the most likely word given [ni]?- Compute prior P(w)

- Now compute likelihood P([ni]|w), then multiply

P(O|w)

P(w)

P(O|w)P(w)

new

.36

.001

.00036

neat

.52

.00013

.000068

need

.11

.00056

.000062

knee

1.00

.000024

.000024

P([ni]|new)P(new)

P([ni]|neat)P(neat)

P([ni]|need)P(need)

P([ni]|knee)P(knee)

Why N-grams?- Compute likelihood P([ni]|w), then multiply

- Unigram approach: ignores context
- Need to factor in context (n-gram)
- Use P(need|I) instead of just P(need)
- Note: P(new|I) < P(need|I)

Next Word Prediction[borrowed from J. Hirschberg]

From a NY Times story...

- Stocks plunged this ….
- Stocks plunged this morning, despite a cut in interest rates
- Stocks plunged this morning, despite a cut in interest ratesby the Federal Reserve, as Wall ...
- Stocks plunged this morning, despite a cut in interest rates by the Federal Reserve, as Wall Street began

Next Word Prediction (cont)

- Stocks plunged this morning, despite a cut in interest rates by the Federal Reserve, as Wall Street began trading for the first time since last…

- Stocks plunged this morning, despite a cut in interest rates by the Federal Reserve, as Wall Street began trading for the first time since lastTuesday's terrorist attacks.

Human Word Prediction

- Domain knowledge
- Syntactic knowledge
- Lexical knowledge

Claim

- A useful part of the knowledge needed to allow Word Prediction can be captured using simple statistical techniques.
- Compute:
- probability of a sequence
- likelihood of words co-occurring

Why would we want to do this?

- Rank the likelihood of sequences containing various alternative alternative hypotheses
- Assess the likelihood of a hypothesis

Why is this useful?

- Speech recognition
- Handwriting recognition
- Spelling correction
- Machine translation systems
- Optical character recognizers

Handwriting Recognition

- Assume a note is given to a bank teller, which the teller reads as I have a gub. (cf. Woody Allen)
- NLP to the rescue ….
- gub is not a word
- gun, gum, Gus, and gull are words, but gun has a higher probability in the context of a bank

Real Word Spelling Errors

- They are leaving in about fifteen minuets to go to her house.
- The study was conducted mainly be John Black.
- The design an construction of the system will take more than a year.
- Hopefully, all with continue smoothly in my absence.
- Can they lave him my messages?
- I need to notified the bank of….
- He is trying to fine out.

For Spell Checkers

- Collect list of commonly substituted words
- piece/peace, whether/weather, their/there ...

- Example:“On Tuesday, the whether …’’“On Tuesday, the weather …”

Language Model

- Definition: Language model is a model that enables one to compute the probability, or likelihood, of a sentence S, P(S).
- Let’s look at different ways of computing P(S) in the context of Word Prediction

Word Prediction: Simple vs. Smart

- Simple:Every word follows every other word w/ equal probability (0-gram)
- Assume |V| is the size of the vocabulary
- Likelihood of sentence S of length n is = 1/|V| × 1/|V| … × 1/|V|
- If English has 100,000 words, probability of each next word is 1/100000 = .00001

- Smarter:Probability of each next word is related to word frequency (unigram)
– Likelihood of sentence S = P(w1) × P(w2) × … × P(wn)

– Assumes probability of each word is independent of probabilities of other words.

- Even smarter: Look at probability given previous words (N-gram)
– Likelihood of sentence S = P(w1) × P(w2|w1) × … × P(wn|wn-1)

– Assumes probability of each word is dependent on probabilities of other words.

Chain Rule

- Conditional Probability
- P(A1,A2) = P(A1) · P(A2|A1)

- The Chain Rulegeneralizes to multiple events
- P(A1, …,An) = P(A1) P(A2|A1) P(A3|A1,A2)…P(An|A1…An-1)

- Examples:
- P(the dog) = P(the) P(dog | the)
- P(the dog bites) = P(the) P(dog | the) P(bites| the dog)

Relative Frequencies and Conditional Probabilities

- Relative word frequencies are better than equal probabilities for all words
- In a corpus with 10K word types, each word would have P(w) = 1/10K
- Does not match our intuitions that different words are more likely to occur (e.g. the)

- Conditional probability more useful than individual relative word frequencies
- Dog may be relatively rare in a corpus
- But if we see barking, P(dog|barking) may be very large

1

For a Word String- In general, the probability of a complete string of words w1…wn is:
P(w )

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

=

- But this approach to determining the probability of a word sequence is not very helpful in general….

k=1

n

Markov Assumption- How do we compute P(wn|w1n-1)? Trick: Instead of P(rabbit|I saw a), we use P(rabbit|a).
- This lets us collect statistics in practice
- A bigram model: P(the barking dog) = P(the|<start>)P(barking|the)P(dog|barking)

- Markov models are the class of probabilistic models that assume that we can predict the probability of some future unit without looking too far into the past
- Specifically, for N=2 (bigram): P(w1) ≈Π P(wk|wk-1)

- Order of a Markov model: length of prior context
- bigram is first order, trigram is second order, …

Counting Words in Corpora

- What is a word?
- e.g., arecatand cats the same word?
- September and Sept?
- zeroand oh?
- Is seventy-two one word or two? AT&T?
- Punctuation?

- How many words are there in English?
- Where do we find the things to count?

Corpora

- Corpora are (generally online) collections of text and speech
- Examples:
- Brown Corpus (1M words)
- Wall Street Journal and AP News corpora
- ATIS, Broadcast News (speech)
- TDT (text and speech)
- Switchboard, Call Home (speech)
- TRAINS, FM Radio (speech)

Training and Testing

- Probabilities come from a training corpus, which is used to design the model.
- overly narrow corpus: probabilities don't generalize
- overly general corpus: probabilities don't reflect task or domain

- A separate test corpus is used to evaluate the model, typically using standard metrics
- held out test set
- cross validation
- evaluation differences should be statistically significant

Terminology

- Sentence: unit of written language
- Utterance: unit of spoken language
- Word Form: the inflected form that appears in the corpus
- Lemma: lexical forms having the same stem, part of speech, and word sense
- Types (V): number of distinct words that might appear in a corpus (vocabulary size)
- Tokens (N): total number of words in a corpus
- Types seen so far (T): number of distinct words seen so far in corpus (smaller than V and N)

Simple N-Grams

- An N-gram model uses the previous N-1 words to predict the next one:P(wn | wn-N+1 wn-N+2… wn-1 )
- unigrams: P(dog)
- bigrams: P(dog | big)
- trigrams: P(dog | the big)
- quadrigrams: P(dog | chasing the big)

n-1

n

k=1

n

Using N-Grams- Recall that
- N-gram: P(wn|w1 ) ≈P(wn|wn-N+1)
- Bigram: P(w1) ≈Π P(wk|wk-1)

- For a bigram grammar
- P(sentence) can be approximated by multiplying all the bigram probabilities in the sequence

- Example:P(I want to eat Chinese food) = P(I | <start>) P(want | I) P(to | want) P(eat | to) P(Chinese | eat) P(food | Chinese)

Computing Sentence Probability

- P(I want to eat British food) = P(I|<start>) P(want|I) P(to|want) P(eat|to) P(British|eat) P(food|British) = .25×.32×.65×.26×.001×.60 = .000080
- vs. I want to eat Chinese food = .00015
- Probabilities seem to capture “syntactic” facts, “world knowledge”
- eat is often followed by a NP
- British food is not too popular

- N-gram models can be trained by counting and normalization

BERP Bigram Probabilities: Use Unigram Count

- Normalization: divide bigram count by unigram count of first word.

- Computing the probability of I I
- P(I|I) = C(I,I)/C(I) = 8 / 3437 = .0023

- A bigram grammar is an NxN matrix of probabilities, where N is the vocabulary size

Learning a Bigram Grammar

- The formula P(wn|wn-1) = C(wn,wn-1)/C(wn-1) is used for bigram “parameter estimation”
- Relative Frequency
- Maximum Likelihood Estimation (MLE): Parameter set maximizes likelihood of training set T given model M — P(T|M).

What do we learn about the language?

- What's being captured with ...
- P(want | I) = .32
- P(to | want) = .65
- P(eat | to) = .26
- P(food | Chinese) = .56
- P(lunch | eat) = .055

- What about...
- P(I | I) = .0023
- P(I | want) = .0025
- P(I | food) = .013

Readings for next time

- J&M Chapter 5, 7.1-7.3

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