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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
• Prob theory intro• Text prediction• Intro to LM• Perplexity• Smoothing• Caching• Clustering• Parsing• CFG• Homework
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
John
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
John
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
John
Outline
• Prob theory intro• Text prediction• Intro to LM• Perplexity• Smoothing• Caching• Clustering• Parsing• CFG• Homework
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
1 key
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
T9
• 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
• Prob theory intro• Text prediction• Intro to LM• Perplexity• Smoothing• Caching• Clustering• Parsing• CFG• Homework
Feature Extraction
Feature Extraction
Language Model
Language Model
Word Lexicon
Word Lexicon
Confidence Scoring
Confidence Scoring
Pattern Classification
(Decoding, Search)
Pattern Classification
(Decoding, Search)
Acoustic Model
Acoustic Model
Input Speech “Hello World”
(0.9) (0.8)
Speech Recognition
SLU
TTS ASR
DM
SLG
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
Words
Words
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
A bad language model
A bad language model
He
rman
is reprin
ted w
ith pe
rmissio
n from L
augh
ing
Stock L
icensin
g Inc., O
ttawa
Ca
nad
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”
3
2
)(
)/,()|/(
2
1
)(
),()|(
3
2
)(
),()|(
2
2
)(
),()|(
3
2
)(
),()|(
bookC
sbookCbooksP
aC
bookaCabookP
readC
areadCreadaP
JohnC
readJohnCJohnreadP
sC
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
• Prob theory intro• Text prediction• Intro to LM• Perplexity• Smoothing• Caching• Clustering• Parsing• CFG• Homework
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
nn
iii wwPPerplexity
1
11:1|
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.
nn
iii wwP
1
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
WH
)(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
Wor
d P
roba
bilit
y
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
• Prob theory intro• Text prediction• Intro to LM• Perplexity• Smoothing• Caching• Clustering• Parsing• CFG• Homework
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.
w
xywC
xyzC
xyC
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
VxyC
xyzCxyzp
)(
1)()|(
VxyC
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
)(
)()1(
)(
)(
)(
)()|(
C
zC
yC
yzC
xyC
xyzCxyzp
Smoothing: Simple Interpolation
• 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
Smoothing: Simple Interpolation
• 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)
Smoothing: Simple Interpolation
• 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
xyC
xyzCxyzP smoothsmooth
)|())(1()(
)()()|( yzPxyC
xyC
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
xyC
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
Katz
Katz
)|()(
0)()(
)()()|(
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
xyC
xyzCxyC smooth
)|()()(
)()|( intint yzPxy
xyC
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
xyC
DxyzCerpabs
)|()()(
)(int
)( yzPxyxyC
DxyzCerpabs
xyzC
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
v
xyzC
wyvCw
wyzCwxy
xyC
DxyzC
0)(|
0)(|)(
)(
)( )(
Smoothing: Chart
Outline
• Prob theory intro• Text prediction• Intro to LM• Perplexity• Smoothing• Caching• Clustering• Parsing• CFG• Homework
Caching
• If you say something, you are likely to say it again later
• Interpolate trigram with cache
)(
)()|(
)|()1()|()|(
historylength
historyzChistoryzP
historyzPxyzPhistoryzP
cache
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
0
5
10
15
20
25
30
35
40
100,000 1,000,000 10,000,000 all
Training Data Size
Per
plex
ity
Red
ucti
on
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
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10
1 2 3 4 5 6 7 8 9 10 20
n-gram order
En
trop
y
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
0
1
2
3
4
5
6
7
10000 100000 1000000 10000000 1E+08 1E+09
Training Size
Pe
rple
xit
y R
ed
uc
tio
n
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
• Prob theory intro• Text prediction• Intro to LM• Perplexity• Smoothing• Caching• Clustering• Parsing• CFG• Homework
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(z|xy) = P(Z|xy) P(z|xyZ)• P(Tuesday | party on) = P(WEEKDAY | party on)
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
-20
-15
-10
-5
0
5
10
15
20
100,000 1,000,000 10,000,000
Training Size
Per
ple
xity
Red
uct
ion
Kneser-Neytrigram
Predict
IBM
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:
m
k
n
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)
m
k
n
i iiik
kiiikk wwwP
swwwP
0 1 12
12
)|()1(
)|(
Sentence Mixture Results
0
2
4
6
8
10
12
14
16
18
20
1 2 4 8 16 32 64 128
Number of Sentence Types
Per
ple
xity
Red
uct
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
• Prob theory intro• Text prediction• Intro to LM• Perplexity• Smoothing• Caching• Clustering• Parsing• CFG• Homework
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.
18%
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
Katz
70
75
80
85
90
95
100
105
110
115
8.8 9 9.2 9.4 9.6 9.8 10
Word Error Rate
Per
ple
xity
Outline
• Prob theory intro• Text prediction• Intro to LM• Perplexity• Smoothing• Caching• Clustering• Parsing• CFG• Homework
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
CFG
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
i
m
ijj ACACGAP
Outline
• Prob theory intro• Text prediction• Intro to LM• Perplexity• Smoothing• Caching• Clustering• Parsing• CFG• Homework
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
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