NLP new words

Lecture 1, 7/21/2005 Natural Language Processing 1

CS60057Speech &Natural Language

Processing

Autumn 2007

Lecture 5

2 August 2007


WORDSThe Building Blocks of Language


Language can be divided up into pieces of varying sizes, ranging from morphemes to paragraphs.

Words -- the most fundamental level for NLP.


Tokens, Types and Texts

This process of segmenting a string of characters into words is known as tokenization.

>>> sentence = "This is the time -- and this is the record of the time." >>> sentence = "This is the time -- and this is the record of the time." >>> words = sentence.split() >>> words = sentence.split() >>> len(words) >>> len(words) 13

Compile a list of the unique vocabulary items in a string by using set() to eliminate duplicates

>>> len(set(words)) >>> len(set(words)) 10 10

A word token is an individual occurrence of a word in a concrete context.A word type is what we're talking about when we say that the three occurrences

of the in sentence are "the same word."


>>> set(words) set(['and', 'this', 'record', 'This', 'of', 'is', '--', 'time.', 'time', 'the']

Extracting text from files >>> f = open('corpus.txt', 'rU') >>> f.read() 'Hello World!\nThis is a test file.\n'

We can also read a file one line at a time using the for loop construct: >>> f = open('corpus.txt', 'rU') >>> for line in f: ... print line[:-1] Hello world! This is a test file.

Here we use the slice [:-1] to remove the newline character at the end of the input line.


Extracting text from the Web

>>> from urllib import urlopen >>> page = urlopen("http://news.bbc.co.uk/").read() >>> print page[:60] <!doctype html public "-//W3C//DTD HTML 4.0 Transitional//EN"

Web pages are usually in HTML format. To extract the text, we need to strip out the HTML markup, i.e. remove all material enclosed in angle brackets. Let's digress briefly to consider how to carry out this task using regular expressions. Our first attempt might look as follows:

>>> line = '<title>BBC NEWS | News Front Page</title>‘>>> new = re.sub(r'<.*>', '', line) >>> new ‘ '


What has happened here? 1. The wildcard '.' matches any character other than '\n', so it will match '>'

and '<'. 2. The '*' operator is "greedy", it matches as many characters as it can. In the

above example, '.*' will return not the shortest match, namely 'title', but the longest match, 'title>BBC NEWS | News Front Page</title'. To get the shortest match we have to use the '*?' operator. We will also normalise whitespace, replacing any sequence of one or more spaces, tabs or newlines (these are all matched by '\s+') with a single space character:

>>> page = re.sub('<.*?>', '', page) >>> page = re.sub('\s+', ' ', page) >>> print page[:60] BBC NEWS | News Front Page News Sport Weather World Service


Extracting text from NLTK Corpora

NLTK is distributed with several corpora and corpus samples and many are supported by the corpus package.

>>> corpus.gutenberg.items ['austen-emma', 'austen-persuasion', 'austen-sense', 'bible-kjv', 'blake-

poems', 'blake-songs', 'chesterton-ball', 'chesterton-brown', 'chesterton-thursday', 'milton-paradise', 'shakespeare-caesar', 'shakespeare-hamlet', 'shakespeare-macbeth', 'whitman-leaves']

Next we iterate over the text content to find the number of word tokens: >>> count = 0 >>> for word in corpus.gutenberg.read('whitman-leaves'): ... count += 1 >>> print count 154873


Brown Corpus

The Brown Corpus was the first million-word, part-of-speech tagged electronic corpus of English, created in 1961 at Brown University. Each of the sections a through r represents a different genre.

>>> corpus.brown.items ['a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'j', 'k', 'l', 'm', 'n', 'p', 'r'] >>> corpus.brown.documents['a'] 'press: reportage' We can extract individual sentences (as lists of words) from the corpus

using the read() function. Here we will specify section a, and indicate that only words (and not part-of-speech tags) should be produced.

>>> a = corpus.brown.tokenized('a') >>> a[0] ['The', 'Fulton', 'County', 'Grand', 'Jury', 'said', 'Friday', 'an', 'investigation',

'of', "Atlanta's", 'recent', 'primary', 'election', 'produced', '``', 'no', 'evidence', "''", 'that', 'any', 'irregularities', 'took', 'place', '.']


Corpus Linguistics

1. Text-corpora: Brown corpus. One million words, tagged, representative of American English.

2. Text-corpora: Project Gutenberg. 17,000 uncopyrighted literary texts (Tom Sawyer, etc.)

3. Text-corpora: OMIM: Comprehensive list of medical conditions. 4. Word frequencies. 5. Zipf's First Law.


What’s a word?

I have a can opener; but I can’t open these cans. how many words?

Word form inflected form as it appears in the text can and cans ... different word forms

Lemma a set of lexical forms having the same stem, same POS and same meaning can and cans … same lemma

Word token: an occurrence of a word I have a can opener; but I can’t open these cans. 11 word tokens (not counting

punctuation)

Word type: a different realization of a word I have a can opener; but I can’t open these cans. 10 word types (not counting

punctuation)


Another example

Mark Twain’s Tom Sawyer 71,370 word tokens 8,018 word types tokens/type ratio = 8.9 (indication of text complexity)

Complete Shakespeare work 884,647 word tokens 29,066 word types tokens/type ratio = 30.4


Some Useful Empirical Observations

A small number of events occur with high frequency A large number of events occur with low frequency You can quickly collect statistics on the high frequency events You might have to wait an arbitrarily long time to get valid

statistics on low frequency events Some of the zeroes in the table are really zeros But others are

simply low frequency events you haven't seen yet. How to address?


Common words in Tom Sawyer

but words in NL have an uneven distribution…


Text properties (formalized)Sample word frequency data


Frequency of frequencies most words are rare

3993 (50%) word types appear only once they are called happax legomena (read

only once)

but common words are very common 100 words account for 51% of all tokens

(of all text)


Zipf’s Law

1. Count the frequency of each word type in a large corpus2. List the word types in order of their frequency Let:

f = frequency of a word type r = its rank in the list

Zipf’s Law says: f 1/r In other words:

there exists a constant k such that: f × r = k The 50th most common word should occur with 3 times the

frequency of the 150th most common word.


Zipf’s Law

If probability of word of rank r is pr and N is the total number of word occurrences:

1.0 const. indp. corpusfor ArA

Nfpr


Zipf curve


Predicting Occurrence Frequencies By Zipf, a word appearing n times has rank rn=AN/n If several words may occur n times, assume rank rn applies to the last of these. Therefore, rn words occur n or more times and rn+1 words occur n+1 or more times. So, the number of words appearing exactly n times is:

)1(11

nn

ANnAN

nANrrI nnn

Fraction of words with frequency n is:

Fraction of words appearing only once is therefore ½.)1(

1

nnD

In


Explanations for Zipf’s Law

- Zipf’s explanation was his “principle of least effort.” Balance between speaker’s desire for a small vocabulary and hearer’s desire for a large one.


Zipf’s First Law

1. f 1/r∝ , f = word-frequency, r = word-frequency rank, m = number of meetings per word.

2. There exists a k such that f × r = k. 3. Alternatively, log f = log k - log r. 4. English literature, Johns Hopkins Autopsy Resource, German,

and Chinese. 5. Most famous of Zipf’s Laws.


Zipf’s Second Law

1. Meanings, m √f∝ 2. There exists a k such that k × f = m2. 3. Corollary: m 1/√r∝


Zipf’s Third Law

1. Frequency ∝ 1/wordlength: 2. There exists a k such that f × wordlength = k. 3. Many other minor laws stated.


Zipf’s Law Impact on Language Analysis

Good News: Stopwords will account for a large fraction of text so eliminating them greatly reduces size of vocabulary in a text

Bad News: For most words, gathering sufficient data for meaningful statistical analysis (e.g. for correlation analysis for query expansion) is difficult since they are extremely rare.


Vocabulary Growth

How does the size of the overall vocabulary (number of unique words) grow with the size of the corpus?

This determines how the size of the inverted index will scale with the size of the corpus.

Vocabulary not really upper-bounded due to proper names, typos, etc.


Heaps’ Law

If V is the size of the vocabulary and the n is the length of the corpus in words:

Typical constants: K 10100 0.40.6 (approx. square-root)

10 , constants with KKnV


Heaps’ Law Data


Word counts are interesting...

As an indication of a text’s style As an indication of a text’s author

But, because most words appear very infrequently, it is hard to predict much about the behavior of words

(if they do not occur often in a corpus) --> Zipf’s Law


Zipf’s Law on Tom Saywer

k ≈ 8000-9000 except for

The 3 most frequent wordsWords of frequency ≈ 100


Plot of Zipf’s LawOn chap. 1-3 of Tom Sawyer (≠ numbers from p. 25&26)

f×r = k

Zipf

0

50

100

150

200

250

300

350

0 500 1000 1500 2000

Rank

Freq


Plot of Zipf’s Law (con’t)On chap. 1-3 of Tom Sawyer f×r = k ==> log(f×r) = log(k) ==> log(f)+log(r) = log(k)

Zipf's Law

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7 8

log(rank)

log(

freq

)


Zipf’s Law, so what?

There are: A few very common words A medium number of medium frequency words A large number of infrequent words

Principle of Least effort: Tradeoff between speaker and hearer’s effort Speaker communicates with a small vocabulary of common words (less

effort) Hearer disambiguates messages through a large vocabulary of rare

words (less effort)

Significance of Zipf’s Law for us: For most words, our data about their use will be very sparse Only for a few words will we have a lot of examples


N-Grams and Corpus Linguistics


A bad language model

N-grams & Language Modeling



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ll rights reserved.


What’s a Language Model

A Language model is a probability distribution over word sequences

P(“And nothing but the truth”) 0.001

P(“And nuts sing on the roof”) 0


What’s a language model for?

Speech recognition Handwriting recognition Spelling correction Optical character recognition Machine translation

(and anyone doing statistical modeling)


Next Word Prediction

From a NY Times story... Stocks ... Stocks plunged this …. Stocks plunged this morning, despite a cut in interest rates Stocks plunged this morning, despite a cut in interest rates by

the Federal Reserve, as Wall ... Stocks plunged this morning, despite a cut in interest rates by

the Federal Reserve, as Wall Street began


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 last Tuesday's terrorist attacks.


Human Word Prediction

Clearly, at least some of us have the ability to predict future words in an utterance.

How? 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

In particular, we'll rely on the notion of the probability of a sequence (a phrase, a sentence)


Applications

Why do we want to predict a word, given some preceding words? Rank the likelihood of sequences containing various

alternative hypotheses, e.g. for ASRTheatre owners say popcorn/unicorn sales have

doubled... Assess the likelihood/goodness of a sentence, e.g. for

text generation or machine translationThe doctor recommended a cat scan.El doctor recommendó una exploración del gato.


Simple N-Grams

Assume a language has V word types in its lexicon, how likely is word x to follow word y? Simplest model of word probability: 1/V Alternative 1: estimate likelihood of x occurring in new text based

on its general frequency of occurrence estimated from a corpus (unigram probability)

popcorn is more likely to occur than unicorn Alternative 2: condition the likelihood of x occurring in the

context of previous words (bigrams, trigrams,…)mythical unicorn is more likely than mythical popcorn


N-grams

A simple model of language Computes a probability for observed input. Probability is the likelihood of the observation being generated by

the same source as the training data Such a model is often called a language model


Computing the Probability of a Word Sequence

P(w1, …, wn) =

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

P(the mythical unicorn) = P(the) P(mythical|the) P(unicorn|the mythical) The longer the sequence, the less likely we are to find it in a training

corpus P(Most biologists and folklore specialists believe that in fact the

mythical unicorn horns derived from the narwhal) Solution: approximate using n-grams


Bigram Model

Approximate by

P(unicorn|the mythical) by P(unicorn|mythical)

Markov assumption: the probability of a word depends only on the probability of a limited history

Generalization: the probability of a word depends only on the probability of the n previous words trigrams, 4-grams, … the higher n is, the more data needed to train backoff models

)11|( nn wwP )|( 1nn wwP


Using N-Grams For N-gram models

P(wn-1,wn) = P(wn | wn-1) P(wn-1) By the Chain Rule we can decompose a joint

probability, e.g. P(w1,w2,w3)P(w1,w2, ...,wn) = P(w1|w2,w3,...,wn) P(w2|w3, ...,wn) … P(wn-1|

wn) P(wn)For bigrams then, the probability of a sequence is just the product

of the conditional probabilities of its bigramsP(the,mythical,unicorn) = P(unicorn|mythical) P(mythical|

the) P(the|<start>)

)11|( nn wwP )1

1|(

nNnn wwP

n

kkkn wwPwP

111 )|()(

http://www.dcs.qmul.ac.uk/~norman/BBNs/Chain_rule.htm


The n-gram ApproximationAssume each word depends only on the previous (n-1) words (n words

total)

For example for trigrams (3-grams): P(“the|… whole truth and nothing but”)

P(“the|nothing but”)

P(“truth|… whole truth and nothing but the”) P(“truth|but the”)


n-grams, continued

How do we find probabilities?

Get real text, and start counting! P(“the | nothing but”) C(“nothing but the”) / C(“nothing but”)


Unigram probabilities (1-gram) http://www.wordcount.org/main.php Most likely to transition to “the”, least likely to transition

to “conquistador”.

Bigram probabilities (2-gram) Given “the” as the last word, more likely to go to

“conquistador” than to “the” again.

http://www.wordcount.org/main.php


N-grams for Language Generation C. E. Shannon, ``A mathematical theory of communication,'' Bell System Technical Journal, vol. 27, pp.

379-423 and 623-656, July and October, 1948.

Unigram:5. …Here words are chosen independently but with their appropriate frequencies.

REPRESENTING AND SPEEDILY IS AN GOOD APT OR COME CAN DIFFERENT NATURAL HERE HE THE A IN CAME THE TO OF TO EXPERT GRAY COME TO FURNISHES THE LINE MESSAGE HAD BE THESE.

Bigram:6. Second-order word approximation. The word transition probabilities are correct but no further structure is included.

THE HEAD AND IN FRONTAL ATTACK ON AN ENGLISH WRITER THAT THE CHARACTER OF THIS POINT IS THEREFORE ANOTHER METHOD FOR THE LETTERS THAT THE TIME OF WHO EVER TOLD THE PROBLEM FOR AN UNEXPECTED.


N-Gram Models of Language

Use the previous N-1 words in a sequence to predict the next word

Language Model (LM) unigrams, bigrams, trigrams,…

How do we train these models? Very large corpora


Counting Words in Corpora

What is a word? e.g., are cat and cats the same word? September and Sept? zero and oh? Is _ a word? * ? ‘(‘ ? How many words are there in don’t ? Gonna ? In Japanese and Chinese text -- how do we identify a

word?


Terminology Sentence: unit of written language Utterance: unit of spoken language Word Form: the inflected form that appears in the corpus Lemma: an abstract form, shared by word forms having the

same stem, part of speech, and word sense Types: number of distinct words in a corpus (vocabulary size) Tokens: total number of words


Corpora

Corpora are online collections of text and speech Brown Corpus Wall Street Journal AP news Hansards DARPA/NIST text/speech corpora (Call Home, ATIS,

switchboard, Broadcast News, TDT, Communicator) TRAINS, Radio News


Simple N-Grams

Assume a language has V word types in its lexicon, how likely is word x to follow word y? Simplest model of word probability: 1/V Alternative 1: estimate likelihood of x occurring in new text based

on its general frequency of occurrence estimated from a corpus (unigram probability)

popcorn is more likely to occur than unicorn Alternative 2: condition the likelihood of x occurring in the

context of previous words (bigrams, trigrams,…)mythical unicorn is more likely than mythical popcorn


Computing the Probability of a Word Sequence

Compute the product of component conditional probabilities? P(the mythical unicorn) = P(the) P(mythical|the) P(unicorn|the

mythical) The longer the sequence, the less likely we are to find it in a training

corpus P(Most biologists and folklore specialists believe that in fact the

mythical unicorn horns derived from the narwhal) Solution: approximate using n-grams


Bigram Model

Approximate by

P(unicorn|the mythical) by P(unicorn|mythical)

Markov assumption: the probability of a word depends only on the probability of a limited history

Generalization: the probability of a word depends only on the probability of the n previous words trigrams, 4-grams, … the higher n is, the more data needed to train backoff models

)11|( nn wwP )|( 1nn wwP


Using N-Grams

For N-gram models P(wn-1,wn) = P(wn | wn-1) P(wn-1) By the Chain Rule we can decompose a joint

probability, e.g. P(w1,w2,w3)P(w1,w2, ...,wn) = P(w1|w2,w3,...,wn) P(w2|w3, ...,wn) … P(wn-1|

wn) P(wn)For bigrams then, the probability of a sequence is just the product

of the conditional probabilities of its bigramsP(the,mythical,unicorn) = P(unicorn|mythical) P(mythical|

the) P(the|<start>)

)11|( nn wwP )1

1|(

nNnn wwP

n

kkkn wwPwP

111 )|()(

http://www.dcs.qmul.ac.uk/~norman/BBNs/Chain_rule.htm


Training and Testing

N-Gram probabilities come from a training corpus 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; development test set cross validation results tested for statistical significance


A Bigram Grammar Fragment from BERP

.001Eat British.03Eat today

.007Eat dessert.04Eat Indian

.01Eat tomorrow.04Eat a

.02Eat Mexican.04Eat at

.02Eat Chinese.05Eat dinner

.02Eat in.06Eat lunch

.03Eat breakfast.06Eat some

.03Eat Thai.16Eat on


.01British lunch.05Want a

.01British cuisine.65Want to

.15British restaurant.04I have

.60British food.08I don’t

.02To be.29I would

.09To spend.32I want

.14To have.02<start> I’m

.26To eat.04<start> Tell

.01Want Thai.06<start> I’d

.04Want some.25<start> I


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 an NP British food is not too popular

N-gram models can be trained by counting and normalization


BERP Bigram Counts

0100004Lunch

000017019Food

112000002Chinese

522190200Eat

12038601003To

686078603Want

00013010878I

lunchFoodChineseEatToWantI


BERP Bigram Probabilities Normalization: divide each row's counts by appropriate unigram

counts for wn-1

Computing the bigram probability of I I C(I,I)/C(all I) p (I|I) = 8 / 3437 = .0023

Maximum Likelihood Estimation (MLE): relative frequency of e.g.

4591506213938325612153437

LunchFoodChineseEatToWantI

)()(

1

2,1

wfreqwwfreq


P(I | I) = .0023 I I I I want P(I | want) = .0025 I want I want P(I | food) = .013 the kind of food I want is ...


Approximating Shakespeare

As we increase the value of N, the accuracy of the n-gram model increases, since choice of next word becomes increasingly constrained

Generating sentences with random unigrams... Every enter now severally so, let Hill he late speaks; or! a more to leg less first you enter

With bigrams... What means, sir. I confess she? then all sorts, he is trim,

captain. Why dost stand forth thy canopy, forsooth; he is this palpable hit

the King Henry.


Trigrams Sweet prince, Falstaff shall die. This shall forbid it should be branded, if renown

made it empty. Quadrigrams

What! I will go seek the traitor Gloucester. Will you not tell me who I am?


There are 884,647 tokens, with 29,066 word form types, in about a one million word Shakespeare corpus

Shakespeare produced 300,000 bigram types out of 844 million possible bigrams: so, 99.96% of the possible bigrams were never seen (have zero entries in the table)

Quadrigrams worse: What's coming out looks like Shakespeare because it is Shakespeare


N-Gram Training Sensitivity

If we repeated the Shakespeare experiment but trained our n-grams on a Wall Street Journal corpus, what would we get?

This has major implications for corpus selection or design


Some Useful Empirical Observations

A small number of events occur with high frequency A large number of events occur with low frequency You can quickly collect statistics on the high frequency events You might have to wait an arbitrarily long time to get valid statistics on

low frequency events Some of the zeroes in the table are really zeros But others are simply

low frequency events you haven't seen yet. How to address?


Smoothing Techniques

Every n-gram training matrix is sparse, even for very large corpora (Zipf’s law)

Solution: estimate the likelihood of unseen n-grams Problems: how do you adjust the rest of the corpus to

accommodate these ‘phantom’ n-grams?

http://linkage.rockefeller.edu/wli/zipf/


Smoothing Techniques Every n-gram training matrix is sparse, even for very large

corpora (Zipf’s law) Solution: estimate the likelihood of unseen n-grams Problems: how do you adjust the rest of the corpus to

accommodate these ‘phantom’ n-grams?

http://linkage.rockefeller.edu/wli/zipf/


Add-one Smoothing

For unigrams: Add 1 to every word (type) count Normalize by N (tokens) /(N (tokens) +V (types)) Smoothed count (adjusted for additions to N) is

Normalize by N to get the new unigram probability:

For bigrams: Add 1 to every bigram c(wn-1 wn) + 1 Incr unigram count by vocabulary size c(wn-1) + V

VNNci

1

VNc

ipi

1*


Discount: ratio of new counts to old (e.g. add-one smoothing changes the BERP bigram (to|want) from 786 to 331 (dc=.42) and p(to|want) from .65 to .28)

But this changes counts drastically: too much weight given to unseen ngrams in practice, unsmoothed bigrams often work better!


A zero ngram is just an ngram you haven’t seen yet…but every ngram in the corpus was unseen once…so... How many times did we see an ngram for the first time? Once

for each ngram type (T) Est. total probability of unseen bigrams as

View training corpus as series of events, one for each token (N) and one for each new type (T)TN

T

Witten-Bell Discounting


We can divide the probability mass equally among unseen bigrams….or we can condition the probability of an unseen bigram on the first word of the bigram

Discount values for Witten-Bell are much more reasonable than Add-One


Re-estimate amount of probability mass for zero (or low count) ngrams by looking at ngrams with higher counts Estimate

E.g. N0’s adjusted count is a function of the count of ngrams that occur once, N1

Assumes: word bigrams follow a binomial distribution We know number of unseen bigrams (VxV-seen)

NcNccc 11*

Good-Turing Discounting


Backoff methods (e.g. Katz ‘87)

For e.g. a trigram model Compute unigram, bigram and trigram probabilities In use:

Where trigram unavailable back off to bigram if available, o.w. unigram probability

E.g An omnivorous unicorn


Summary

N-gram probabilities can be used to estimate the likelihood Of a word occurring in a context (N-1) Of a sentence occurring at all

Smoothing techniques deal with problems of unseen words in a corpus

NLP new words

Technology

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