Introduction to Language Modeling Alex Acero. Acknowledgments Joshua Goodman, Scott MacKenzie for...

Introduction to Language Modeling

Alex Acero

Acknowledgments

• Joshua Goodman, Scott MacKenzie for many slides

Outline

• Prob theory intro• Text prediction• Intro to LM• Perplexity• Smoothing• Caching• Clustering• Parsing• CFG• Homework

Outline

Probability – definition

P(X) means probability that X is trueP(baby is a boy) 0.5 (% of total that are boys)

P(baby is named John) 0.001 (% of total named John)

BabiesBaby boys

Joint probabilities

• P(X, Y) means probability that X and Y are both true, e.g. P(brown eyes, boy)

BabiesBaby boys

JohnBrown eyes

Conditional probabilities

• P(X|Y) means probability that X is true when we already know Y is true

– P(baby is named John | baby is a boy) 0.002– P(baby is a boy | baby is named John ) 1

BabiesBaby boys

Bayes rule

P(X|Y) = P(X, Y) / P(Y)

P(baby is named John | baby is a boy)

=P(baby is named John, baby is a boy) / P(baby is a boy)

= 0.001 / 0.5 = 0.002

BabiesBaby boys

Outline

90% Removed

k r ce r oz y t a e t h c o , d o a a o b a a e g v t a l a ss m n t i s n f d w i t l h e n s - w le e a r i w f e n t e h r w e , h v e r d l Wi

80% Removed

D r s r s n h s d f w e e b e i e in th w i r o a t e t ar e t e k i t i c i ver e . as d on, ho ve n o n an o h t h sp r f a e of s a h o a u o e e n a n s - au h m r s s o h l e ld a e s n in i f li w h mas u i e i m g in i i o i t e o t w t a g z a N n d

70% Removed

D uc ore frown d on i h r id n ter a h t ee a ent o e whi e in ffro y seeme t l a s ac c s e ad A l ei d h h lf wa s a s, th mo t, a ha th p o v at sa s e a a i i g t aught m r t h y ne s a g t at wa m es e e o i laug s e fr s p k f h gr nes i f t e fu an i c u l s m of r i u l f a he ef rt o il , v , ro ar t land il

60% Removed

k ruc res f w n th r id t e fr z n t r y. T r d stri d b a rece t n t w i cove n o r s a d t e e e to e n h ot er, l o no s e ad ng l g . A st n eig d v el d. h n t e w a d s ti , i es , wi mo e t, so a d co t a pi it i as ev hat dn ss he a n it a ht r b t f l u e te bl t n ess a u e t r e sthe sm e t p i ugh o d a he fr d p ta in h g ne s llib l It as e a ful d mm c le w e nity lau h g a t e l t o and ff t . I a he W d s ge fr z a e N th a W ld

50% Removed

D k r ce fore t o on i h r si the fr en wa erw tr s ha ee i ed y a ec nt wi d f the r whit erin o f an e e med t lean t war ch o er, ck a d mi ou in g i t. t le r ig d r hel d la d t el as d so i if , w t o m v ent, s lone d d hat h spi t f t was t ven th sa e s h as a h nt n i f aug t , t f l u t mo e ter ble than an a ss - lau ter hat as m h ast s ile f he ph n a ghte ol as he os a d r a ing e grimn ss o n a il y. a h m s er u in om a i d e it laug n a t fu i y f l e he ff t of if . It he W l , t e s ag , f e - ed N r n ld

40% Removed

Dark s r c res ow e n eit er side the froze w erwa . T trees h d b n tr p d b c t w n o heir white c v ring off s and h y s med e n towa ds e c o her la k and i o s, i e f l gh . A as ilence reig ed o he and. The lan e f a a de l tion, life e s, i mo ment, so n nd cold h the pi t o it s n t ev n hato sa nes . h e wa hin n it of laughter, bu a lau h r e t rib e a dn - laught r a was mi hle s asthe i e of t e s a la hte ol as he ro t a d ar ak n f th g mne of inf llib i . It wa he mas erful n incom un b e w s om of t rnity l ugh n at e lity f fe nd e effort f ife. I as t e , savage, fro n-h a r hland Wi d.

30% Removed

Da s ruce fores r on ith r i e the froz n ater ay Thet s ha een st ippe b re e wi d f heir white c vering of ost, an they e d o ean towards eac othe , lac a dom nou , n t e f in ight. A vast il nc re ned o e hela d. The l d s l wa d s a ion, if s, withoutm men o e and old that t e pi t of it was not e en tha o sadnes T ere s a hint in t of laug r, ut o a laugh e o er ble t n a y sadn s a la ghte at as irthless sthe mil o h phi x, a ghter cold as the fro t a d par ak ng f the grim es of n al b l ty was th m s r ul and co mu i able wi m of ter la ghi t t e futil ty o if an the ef rt of li e. It as the Wild, h avage, froze -hearte Northland Wil .

20% Removed

Dark spruce forest frowned n either side the roze ate wa . Thetrees had ee stripp d by ecent wi d f thei white coverin offrost d they eemed to lean towa ds e ch o h r, bl ck and mino s, in the ad ng l ght. A vas sil n e reigned over theland. The land i sel was e olatio , ifeless, wit outmovem n , s lon n cold ha e spi it of s n t eve hat adn s. The e was hi i it of a ght , but f a laughter ore ible t an any s ne s - a laughter t a was mi hless as he mile of he sphinx, a aug ter col as the f ost nd arta in of th grimn ss of i fall bility It as the asterful andinc mmunicabl wisdo of e ernity ugh ng at the futilit of li and t e for of ife. It w the Wild, the avage, rozen-hea t d N rthla d W ld.

10% Removed

Dark s ru e forest frowned on either side the frozen waterw y. Thetrees had bee stripped by a recent ind of t eir w ite covering of rost, and they seemed o lean towards each ot er, black andominous, in the fading li h . A vast silence reigned ver theland The land itself w s a deso ation, lifel ss, without ovement, s l n and cold hat the spiri of it wa not even thatof sa ness. here was a hint in it of laughte , but of a l ug termore terrible than any sadness - a ughte that as mirthless s he smile of the sphinx a laug ter cold as the rost a d p rt k ngof the grimness of infal i ility. It as the masterful andincommunica le wisdom of eternity laughing at th futility of lifean the effort f life. It was e Wild, the sa ag , froz n- earte Northland Wild.

0% Removed

Dark spruce forest frowned on either side the frozen waterway. Thetrees had been stripped by a recent wind of their white covering offrost, and they seemed to lean towards each other, black andominous, in the fading light. A vast silence reigned over theland. The land itself was a desolation, lifeless, withoutmovement, so lone and cold that the spirit of it was not even thatof sadness. There was a hint in it of laughter, but of a laughtermore terrible than any sadness - a laughter that was mirthless asthe smile of the sphinx, a laughter cold as the frost and partakingof the grimness of infallibility. It was the masterful andincommunicable wisdom of eternity laughing at the futility of lifeand the effort of life. It was the Wild, the savage, frozen-hearted Northland Wild.

From Jack London’s “White Fang”

Language as Information

• Information is commonly measured in “bits”• Since language is highly redundant, perhaps it can be

viewed somewhat like information• Can language be measured or coded in “bits”?• Sure. Examples include…

– ASCII (7 bits per “symbol”)– Unicode (16 bits per symbol)– But coding schemes, such as ASCII or Unicode, do not account

for the redundancy In the language

• Two questions:1. Can a coding system be developed for a language (e.g., English)

that accounts for the redundancy in the language?2. If so, how may bits per symbol are required?

How many bits?

• ASCII codes have seven bits• 27 = 128 codes• Codes include…

– 33 control codes– 95 symbols, including 26 uppercase letters, 26 lowercase letters,

space, 42 “other” symbols

• In general, if we have n symbols, the number of bits to encode them is log2n (Note: log2128 = 7)

• What about bare bones English – 26 letters plus space?• How many bits?

How many bits? (2)

• It takes log227 = 4.75 bits/character to encode bare bones English

• But, what about redundancy in English?• Since English is highly redundant, is there a way to encode

letters in fewer bits?– Yes

• How many bits?– The answer (drum roll please)…

How many bits? (3)

• The minimum number of bits to encode English is (approximately)…

– 1 bit/character

• How is this possible?– E.g., Huffman coding– ngrams

• More importantly, how is this answer computed?• Want to learn how? Read…

Shannon, C. E. (1951). Prediction and entropy of printed English. The Bell System Technical Journal, 30, 51-64.

Disambiguation

• A special case of prediction is disambiguation• Consider the telephone keypad…

• Is it possible to enter text using this keypad?• Yes. But the keys are ambiguous.

Ambiguity Continuum

53 keys

27 keys8 keys

LessAmbiguity

MoreAmbiguity

Coping With Ambiguity

• There are two approaches to disambiguating the telephone keypad

– Explicit

• Use additional keys or keystrokes to select the desired letter

• E.g., multitap– Implicit

• Add “intelligence” (i.e., a language model) to the interface to guess the intended letter

• E.g., T9, Letterwise

Multitap

• Press a key once for the 1st letter, twice for the 2nd letter, and so on

• Example...

84433.778844422255.22777666966.33366699.th e q u i c k b r o wn f o x

58867N7777.66688833777.84433.55529999N999.36664.ju mp s o v e r th e l az y do g

But, there is a problem. When consecutive letters are on the same key, additional disambiguation is needed. Two techniques: (i) timeout, (ii) a special “next letter” (N) key1 to explicitly segment the letters. (See above: “ps” in “jumps” and “zy” in “lazy”).

1 Nokia phones: timeout = 1.5 seconds, “next letter” = down-arrow

• Product of Tegic Communications (www.tegic.com), a subsidiary of Nuance Communications

• Licensed to many mobile phone companies• The idea is simple:

– one key = one character

• A language model works “behind the scenes” to disambiguate

• Example (next slide)...

Guess the Word

Number of word stems to consider…

3 x 3 x 3 x 4 x 3 x 3 x 3 x 4 = 11,664

C O M P U T E R

“Quick Brown Fox” Using T9

843.78425.27696.369.58677.6837.843.5299.364.the quick brown fox jumps over the lazy dog

But, there is problem. The key sequences are ambiguous and other words may exist for some sequences. See below.

DecreasingProbability

843.78425.27696.369.58677.6837.843.5299.364.the quick brown fox jumps over the jazz dogtie stick crown lumps muds tie lazy fogvie vie

Keystrokes Per Character (KSPC)

• Earlier examples used the “quick brown fox” phrase, which has 44 characters (including one character after each word)

• Multitap and T9 require very different keystroke sequences• Compare…

MethodNumber of Keystrokes

Number of Characters

Keystrokes per

Character

Qwerty 44 44 1.000

Multitap 88 44 2.000

T9 45 44 1.023

Phrase: the quick brown fox jumps over the lazy dog.

Formulas

Outline

Feature Extraction

Language Model

Word Lexicon

Confidence Scoring

Pattern Classification

(Decoding, Search)

Pattern Classification

(Decoding, Search)

Acoustic Model

Input Speech “Hello World”

(0.9) (0.8)

Speech Recognition

TTS ASR

Language Modeling in ASR

• Some sequences of words sounds alike, but not all of them are good English sentences.

– I went to a party – Eye went two a bar tea

Rudolph the Red Nose reigned here.

Rudolph the Red knows rain, dear.

Rudolph the red nose reindeer.

)()|(maxarg

)|(maxarg

WordspWordsAcousticsp

AcousticsWordspWords

Language Modeling in ASR• This lets the recognizer make the right guess when two different

sentences sound the same.

For example:• It’s fun to recognize speech?• It’s fun to wreck a nice beach?

Humans have a Language Model

Ultimate goal is that a speech recognizer performs a good as human being.

In psychology a lot of research has been done.• The *eel was on the shoe• The *eel was on the car

People capable to adjusting to right context• removes ambiguities • limits possible words

Already very good language models for dedicated applications (e.g. medical, a lot of standardization)

A bad language model

is reprin

ith pe

rmissio

n from L

Stock L

icensin

g Inc., O

a. All righ

ts reserved

A bad language model

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• Machine translation • Handwriting recognition• Spelling correction• Optical character recognition• Typing in Chinese or Japanese

• (and anyone doing statistical modeling)

How Language Models work

Hard to compute P(“And nothing but the truth”)

Step 1: Decompose probabilityP(“And nothing but the truth” )= P(“And”) P(“nothing” | “And”) x P(“but” | “And nothing”) x P(“the” | “And nothing but”) x P(“truth” | “And nothing but the”)

Step 2: Approximate with trigramsP(“And nothing but the truth” )≈ P(“And”) P(“nothing” | “And”) x P(“but” | “And nothing”) x P(“the” | “nothing but”) x P(“truth” | “but the”)

example

How do we find probabilities?

Get real text, and start counting!

P(“the | nothing but”) C(“nothing but the”) / C(“nothing but”)

Training set:

“John read her book”

“I read a different book”

“John read a book by Mulan”

)/,()|/(

),()|(

sbookCbooksP

bookaCabookP

areadCreadaP

readJohnCJohnreadP

JohnsCsJohnP

example

These bigram probabilities help us estimate the probability for the sentence as:

P(John read a book)

= P(John|<s>)P(read|John)P(book|a)P(</s>|book)

= 0.148

Then cross entropy: -1/4*2log(0.148) = 0.689

So perplexity = 20.689 = 1.61

Comparison: Wall street journal text (5000 words) has a bigram perplexity of 128

gram example

To calculate this probability, we need to compute both the number of times "am" is preceded by "I" and the number of times "here" is preceded by "I am."

All four sounds the same, right decision can only be made by language model.

Outline

Evaluation

• How can you tell a good language model from a bad one?• Run a machine translation system, a speech recognizer (or

your application of choice), calculate word error rate– Slow– Specific to your system

Evaluation: Perplexity Intuition

• Ask a speech recognizer to recognize digits: “0, 1, 2, 3, 4, 5, 6, 7, 8, 9” – easy – perplexity 10

• Ask a speech recognizer to recognize names at Microsoft – hard – 30,000 – perplexity 30,000

• Ask a speech recognizer to recognize “Operator” (1 in 4), “Technical support” (1 in 4), “sales” (1 in 4), 30,000 names (1 in 120,000) each – perplexity 54

• Perplexity is weighted equivalent branching factor.

Evaluation: perplexity

• “A, B, C, D, E, F, G…Z”: perplexity is 26• “Alpha, bravo, charlie, delta…yankee, zulu”: perplexity is 26• Perplexity measures language model difficulty, not acoustic

difficulty• High perplexity means that the number of words branching

from a previous word is larger on average.• Low perplexity does not guarantee good performance. • For example B,C,D,E,G,P,T has 7 but does not take into

account acoustic confusability

Perplexity: Math

• Perplexity is geometric average inverse probability • Imagine “Operator” (1 in 4), “Technical support” (1 in 4), “sales” (1 in 4), 30,000 names (1 in 120,000)• Model thinks all probabilities are equal (1/30,003) • Average inverse probability is 30,003

iii wwPPerplexity

Perplexity: Math

• Imagine “Operator” (1 in 4), “Technical support” (1 in 4), “sales” (1 in 4), 30,000 names (1 in 120,000)

• Correct model gives these probabilities• ¾ of time assigns probability ¼, ¼ of time assigns probability 1/120,000

• Perplexity is 54 (compare to 30,003 for simple model)

• Remarkable fact: the true model for data has the lowest possible perplexity

Perplexity:Is lower better?

• Remarkable fact: the true model for data has the lowest possible perplexity

• Lower the perplexity, the closer we are to true model.

• Typically, perplexity correlates well with speech recognition word error rate

– Correlates better when both models are trained on same data

– Doesn’t correlate well when training data changes

Perplexity: The Shannon Game

• Ask people to guess the next letter, given context. Compute perplexity.

– (when we get to entropy, the “100” column corresponds to the “1 bit per character” estimate)

Char n-gram Low Char Upper char Low word Upper word1 9.1 16.3 191,237 4,702,5115 3.2 6.5 653 29,532

10 2.0 4.3 45 2,99815 2.3 4.3 97 2,998

100 1.5 2.5 10 142

Homework

• Write a program to estimate the Entropy of written text (Shannon, 1950)

• Input: a text document (you pick it, the larger the better)• Write a program that predicts the next letter given the past

letters on a different text (make it interactive?)– Hint: use character ngrams

• Check it does a perfect job on the training text• Due 5/21

Evaluation: entropy

• Entropy =

log2 perplexity

Should be called “cross-entropy of Should be called “cross-entropy of model on test data.”model on test data.” Remarkable fact: entropy is average Remarkable fact: entropy is average number of bits per word required to number of bits per word required to encode test data using this probability encode test data using this probability model, and an optimal coder. Called model, and an optimal coder. Called bits.bits.

iii wwP

11:12 |log

perplexity

Encode text W using –2logP(W) bits.

Then the cross-entropy H(W) is:

Where N is the length of the text.

The perplexity is then defined as:

)(log1

)( 2 WPN

)(2)( WHWPP

Word Rank vs. Probability

0.00000100

0.00001000

0.00010000

0.00100000

0.01000000

0.10000000

1.00000000

1 10 100 1000 10000

Word Rank

Hmm… There appears to be a relationship between word rank and word probability. Plotting both on log scales, as above, reveals a linear, or straight line, relationship. How strong is this relation? (next slide)

Outline

Smoothing: None

• Called Maximum Likelihood estimate.• Lowest perplexity trigram on training data.• Terrible on test data: If no occurrences of C(xyz),

probability is 0.

xyzCxyzp

Smoothing: Add One

• What is P(sing|nuts)? Zero? Leads to infinite perplexity!• Add one smoothing:

Works very badly. DO NOT DO THIS

• Add delta smoothing:

Still very bad. DO NOT DO THIS

xyzCxyzp

1)()|(

xyzCxyzp

Smoothing: Simple Interpolation

• Trigram is very context specific, very noisy• Unigram is context-independent, smooth• Interpolate Trigram, Bigram, Unigram for best combination

• Find 0<<1 by optimizing on “held-out” data• Almost good enough

xyzCxyzp

• Split data into training, “heldout”, test• Try lots of different values for on heldout data, pick best

• Test on test data• Sometimes, can use tricks like “EM” (estimation maximization) to find values

• I prefer to use a generalized search algorithm, “Powell search” – see Numerical Recipes in C

• How much data for training, heldout, test?• Some people say things like “1/3, 1/3, 1/3” or “80%, 10%,

10%” They are WRONG• Heldout should have (at least) 100-1000 words per

parameter.• Answer: enough test data to be statistically significant. (1000s

of words perhaps)

• Be careful: WSJ data divided into stories. Some are easy, with lots of numbers, financial, others much harder. Use enough to cover many stories.

• Be careful: Some stories repeated in data sets.• Can take data from end – better – or randomly from within training. Temporal effects like “Swine flu”

Smoothing: Jelinek-Mercer

• Simple interpolation:

• Better: smooth a little after “The Dow”, lots after “Adobe acquired”

)|()1()(

)()|( yzP

xyzCxyzP smoothsmooth

)|())(1()(

)()()|( yzPxyC

xyzCxyCxyzP smoothsmooth

Smoothing: Jelinek-Mercer

• Put s into buckets by count• Find s by cross-validation on held-out data• Also called “deleted-interpolation”

)|())(1()(

)()()|( yzPxyC

xyzCxyCxyzP smoothsmooth

Smoothing: Katz

• Compute discount using “Good-Turing” estimate• Only use bigram if trigram is missing

• Works pretty well, except not good for 1 counts• is calculated so probabilities sum to 1

otherwiseyzPxy

xyzCifxyC

xyzDCxyzCxyzP

)()()|(

Smoothing: Interpolated Absolute Discount

• JM, Simple Interpolation overdiscount large counts, underdiscount small counts

• “San Francisco” 100 times, “San Alex” once, should we use a big discount or a small one?

– Absolute discounting takes the same from everyone

)|())(1()(

)()( yzPxyC

xyzCxyC smooth

)|()()(

)()|( intint yzPxy

DxyzCxyzP erpabserpabs

Smoothing: Interpolated Multiple Absolute Discounts• One discount is good

• Different discounts for different counts

• Multiple discounts: for 1 count, 2 counts, >2

)|()()(

)(int yzPxy

DxyzCerpabs

)|()()(

)( yzPxyxyC

DxyzCerpabs

Smoothing: Kneser-Ney

P(Francisco | eggplant) vs P(stew | eggplant)• “Francisco” is common, so backoff, interpolated methods say

it is likely• But it only occurs in context of “San”• “Stew” is common, and in many contexts• Weight backoff by number of contexts word occurs in

Smoothing: Kneser-Ney

• Interpolated Absolute-discount• Modified backoff distribution• Consistently best technique

wyzCwxy

0)(|)(

Smoothing: Chart

Outline

Caching

• If you say something, you are likely to say it again later

• Interpolate trigram with cache

)|()1()|()|(

historylength

historyzChistoryzP

historyzPxyzPhistoryzP

cachesmooth

Caching: Real Life

• Someone says “I swear to tell the truth”• System hears “I swerve to smell the soup”• Cache remembers!• Person says “The whole truth”, and, with cache, system hears “The whole soup.” – errors are locked in.

• Caching works well when users correct as they go, poorly or even hurts without correction.

Cache Results

100,000 1,000,000 10,000,000 all

Training Data Size

unigram + condbigram + condtrigramunigram + condtrigram

trigram

bigram

unigram

5-grams

• Why stop at 3-grams?• If P(z|…rstuvwxy) P(z|xy) is good, then

P(z|…rstuvwxy) P(z|vwxy) is better!• Very important to smooth well• Interpolated Kneser-Ney works much better than Katz on 5-

gram, more than on 3-gram

N-gram versus smoothing algorithm

1 2 3 4 5 6 7 8 9 10 20

n-gram order

100,000 Katz

100,000 KN

1,000,000 Katz

1,000,000 KN

10,000,000 Katz

10,000,000 KN

all Katz

all KN

Speech recognizer mechanics

• Keep many hypotheses alive

• Find acoustic, language model scores– P(acoustics | truth = .3), P(truth | tell the) = .1– P(acoustics | soup = .2), P(soup | smell the) = .01

“…tell the” (.01)“…smell the” (.01)

“…tell the truth” (.01 .3 .1)“…smell the soup” (.01 .2 .01)

Speech recognizer slowdowns

• Speech recognizer uses tricks (dynamic programming) to merge hypotheses

Trigram: Fivegram:

“…tell the”“…smell the”

“…swear to tell the”“…swerve to smell the”“…swear too tell the”

“…swerve too smell the”“…swerve to tell the”

“…swerve too tell the”…

Speech recognizer vs. n-gram

• Recognizer can threshold out bad hypotheses• Trigram works so much better than bigram, better

thresholding, no slow-down • 4-gram, 5-gram start to become expensive

Speech recognizer with language model

• In theory,

• In practice, language model is a better predictor -- acoustic probabilities aren’t “real” probabilities

• In practice, penalize insertions

)()|(maxarg cewordsequenPcewordsequenacousticsPcewordsequen

)(8 1.)(

)|(maxarg cewordsequenlength

cewordsequen cewordsequenP

cewordsequenacousticsP

Skipping

• P(z|…rstuvwxy) P(z|vwxy)• Why not P(z|v_xy) – “skipping” n-gram – skips value of 3-

back word.• Example: “P(time | show John a good)” ->

P(time | show ____ a good)• P(…rstuvwxy) P(z|vwxy) + P(z|vw_y) + (1--)P(z|v_xy)

5-gram Skipping Results

10000 100000 1000000 10000000 1E+08 1E+09

Training Size

vwyx, vxyw, wxyv,vywx, yvwx, xvwy,wvxyvw_y, v_xy, vwx_ --skipping

xvwy, wvxy, yvwx, --rearranging

vwyx, vxyw, wxyv --rearranging

vwyx, vywx, yvwx --rearranging

vw_y, v_xy -- skipping

(Best trigram skipping result: 11% reduction)

Outline

Clustering

• CLUSTERING = CLASSES (same thing)• What is P(“Tuesday | party on”)• Similar to P(“Monday | party on”)• Similar to P(“Tuesday | celebration on”)• Put words in clusters:

– WEEKDAY = Sunday, Monday, Tuesday, …– EVENT=party, celebration, birthday, …

Clustering overview

• Major topic, useful in many fields• Kinds of clustering

– Predictive clustering– Conditional clustering– IBM-style clustering

• How to get clusters– Be clever or it takes forever!

Predictive clustering

• Let “z” be a word, “Z” be its cluster• One cluster per word: hard clustering

– WEEKDAY = Sunday, Monday, Tuesday, …– MONTH = January, February, April, May, June, …

P(Tuesday | party on WEEKDAY)• Psmooth(z|xy) Psmooth (Z|xy) Psmooth (z|xyZ)

Predictive clustering example

Find P(Tuesday | party on) Psmooth (WEEKDAY | party on) Psmooth (Tuesday | party on WEEKDAY)C( party on Tuesday) = 0C(party on Wednesday) = 10C(arriving on Tuesday) = 10C(on Tuesday) = 100

Psmooth (WEEKDAY | party on) is high

Psmooth (Tuesday | party on WEEKDAY) backs off to Psmooth (Tuesday | on WEEKDAY)

Cluster Results

100,000 1,000,000 10,000,000

Training Size

Kneser-Neytrigram

Predict

Full IBMPredict

All Combine

Clustering: how to get them

• Build them by hand– Works ok when almost no data

• Part of Speech (POS) tags– Tends not to work as well as automatic

• Automatic Clustering– Swap words between clusters to minimize perplexity

Clustering: automatic

Minimize perplexity of P(z|Y) Mathematical tricks speed it up

Use top-down splitting,

not bottom up merging!

Two actual WSJ classes

• MONDAYS • FRIDAYS • THURSDAY • MONDAY • EURODOLLARS • SATURDAY• WEDNESDAY• FRIDAY• TENTERHOOKS • TUESDAY • SUNDAY• CONDITION

• PARTY• FESCO• CULT• NILSON • PETA • CAMPAIGN • WESTPAC • FORCE • CONRAN • DEPARTMENT • PENH• GUILD

Sentence Mixture Models

• Lots of different sentence types:– Numbers (The Dow rose one hundred seventy three

points)– Quotations (Officials said “quote we deny all wrong doing

”quote)– Mergers (AOL and Time Warner, in an attempt to control

the media and the internet, will merge)

• Model each sentence type separately

Sentence Mixture Models

• Roll a die to pick sentence type, sk with probability k

• Probability of sentence, given sk

• Probability of sentence across types:

ikiiik swwwP

1 112 )|(

Sentence Model Smoothing

• Each topic model is smoothed with overall model• Sentence mixture model is smoothed with overall model

(sentence type 0)

i iiik

kiiikk wwwP

0 1 12

)|()1(

Sentence Mixture Results

1 2 4 8 16 32 64 128

Number of Sentence Types

ion all 3gram

all 5gram

10,000,000 3gram

10,000,000 5gram

1,000,000 3gram

1,000,000 5gram

100,000 5gram

100,000 3gram

Sentence Clustering

• Same algorithm as word clustering

• Assign each sentence to a type, sk

• Minimize perplexity of P(z|sk ) instead of P(z|Y)

Outline

Structured Language Model

“The contract ended with a loss of 7 cents after”

Thanks to Ciprian Chelba for this figure

How to get structure data?

• Use a Treebank (a collection of sentences with structure hand annotated) like Wall Street Journal, Penn Tree Bank.

• Problem: need a treebank.• Or – use a treebank (WSJ) to train a parser; then parse new training data (e.g. Broadcast News)

• Re-estimate parameters to get lower perplexity models.

Parsing vs. Trigram Eugene Charniaks’s Experiments

All experiments are trained on one million words of Penn tree-bank data, and tested on 80,000 words.

Thanks to Eugene Charniak for this slide

Model Perplexity

Trigram poor smoothing 167

Trigram deleted-interpolation 155

Trigram Kneser-Ney 145

Parsing 119

Structured Language Models

• Promising results• But: time consuming; language is right branching; 5-grams,

skipping, capture similar information. • Interesting applications to parsing

– Combines nicely with parsing MT systems

N-best lists

• Make list of 100 best translation hypotheses using simple bigram or trigram

• Rescore using any model you want– Cheaply apply complex models– Perform Source research separately from Channel

• For long, complex sentences, need exponentially many more hypotheses

Lattices for MTCompact version of n-best list

From Ueffing, Och and Ney, EMNLP ‘02

Tools: CMU Language Modeling Toolkit

• Can handle bigram, trigrams, more• Can handle different smoothing schemes • Many separate tools – output of one tool is input to next: easy to use

• Free for research purposes• http://svr-www.eng.cam.ac.uk/~prc14/toolkit.html

Tools: SRI Language Modeling Toolkit

• More powerful than CMU toolkit• Can handles clusters, lattices, n-best lists, hidden tags

• Free for research use• http://www.speech.sri.com/projects/srilm

Small enough

• Real language models are often huge• 5-gram models typically larger than the training data

• Use count-cutoffs (eliminate parameters with fewer counts) or, better

• Use Stolcke pruning – finds counts that contribute least to perplexity reduction,

– P(City | New York) P(City | York)– P(Friday | God it’s) P(Friday | it’s)

• Remember, Kneser-Ney helped most when lots of 1 counts

Combining Data

• Often, you have some “in domain” data and some “out of domain data”

• Example: Microsoft is working on translating computer manuals

– Only about 3 million words of Brazilian computer manuals

• Can combine computer manual data with hundreds of millions of words of other data

– Newspapers, web, encylcopedias,usenet…

How to combine

• Just concatenate – add them all together– Bad idea – need to weight the “in domain” data more heavily

• Take out of domain data and multiple copies of in domain data (weight the counts)

– Bad idea – doesn’t work well, and messes up most smoothing techniques

How to combine

• A good way: take weighted average, e.g.

Pmanuals (z|xy) + Pweb(z|xy) + (1- - ) Pnewspaper(z|xy)

• Can apply to channel models too (e.g. combine Hansard with computer manuals for French translation)

• Lots of research in other techniques– Maxent-inspired models, non-linear interpolation (log

domain), cluster models, etc. Minimal improvement (but see work by Rukmini Iyer)

• Handwriting Recognition– P(observed ink|words) P(words)

• Telephone Keypad input– P(numbers|words) P(words)

• Spelling Correction– P(observed keys|words) P(words)

• Chinese/Japanese text entry– P(phonetic representation|characters) P(characters)

Other Language Model Uses

Language Model

Some Experiments

• Joshua Goodman re-implemented almost all techniques

• Trained on 260,000,000 words of WSJ• Optimize parameters on heldout• Test on separate test section• Some combinations extremely time-consuming (days of CPU time)

– Don’t try this at home, or in anything you want to ship

• Rescored N-best lists to get results– Maximum possible improvement from 10% word error

rate absolute to 5%

Overall Results: Perplexity

Katz skip

all-cache-sentence

all-cache-skipall-cache

all-cache-5gram

all-cache-cluster

all-cache-KN

KN 5gram

KN SkipKN Sentence

KN Cluster

Katz ClusterKatz Sentence

Katz 5-gramKN

8.8 9 9.2 9.4 9.6 9.8 10

Word Error Rate

Outline

LM types

Language models used in speech recognition can be classified into the following categories:

• Uniform models: the chance a word occurs is 1 / V. V is the size of the vocabulary

• Finite state machines• Grammar models: they use context free grammars• Stochastic models: they determine the chance of a word on it’s

preceding words (eg n-grams)

CFGA grammar is defined by:

G = (V, T, P, S) where:

V contains the set of all non-terminal symbols. T contains the set of all terminal symbols. P is a set of production or production rules. S is a special symbol called the start symbol.

Example of rules:S -> NP VP

VP -> V NPNP -> NOUNNP -> NAMENOUN -> speechNAME -> Julie Ethan VERB -> loves chases

Parsing

• bottom up where you start with the input sentence and try to reach the start symbol

• Top down, you start with the starting symbol and try to reach the input sentence by applying the appropriate rules. Left recursion is a problem. (A -> Aa)

Advantage bottom up:“What is the weather forecast for this

afternoon?”

A lot of parsing algorithms available from computer science

Problem: people don’t follow the rules of grammar strictly, especially in spoken language. Creating a grammar that covers all this constructions is unfeasible.

probabilistic CFG

A mixture between formal language and probabilistic models is the PCFG

If there are m rules for left-hand side non terminal node

Then probability of these rules is

Where C denotes the number of times each rule is used.

mAAAA ...,,: 21

)(/)()|(1

ijj ACACGAP

Outline

Homework

• Write a program to estimate the Entropy of written text (Shannon, 1950)

• Input: a text document (you pick it, the larger the better)• Write a program that predicts the next letter given the past

letters on a different text (make it interactive?)– Hint: use character ngrams

• Check it does a perfect job on the training text• Due 5/21

Introduction to Language Modeling Alex Acero. Acknowledgments Joshua Goodman, Scott MacKenzie for...

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