مدل سازی زبان language modeling

صفحه 1:
Language Modeling Introduction to N- grams 

صفحه 2:
Dan Jurafsky Probabilistic Language Models * Today’s goal: assign a probability to a sentence * Machine Translation: * P(high winds tonite) > P(large winds tonite) * Spell Correction * The office is about fifteen minuets from my house * P(about fifteen minutes from) > P(about fifteen minuets from) * Speech Recognition * P(l saw a van) >> Pleves awe of an) Why? 

صفحه 3:
57 Probabilistic Language Modeling * Goal: compute the probability of a sentence or sequence of words: P(W) = P(w,,W,,W5,W4,Ws...W,) * Related task: probability of an upcoming word: P(w,|W,,W2,W3,W,4) * A model that computes either of these: P(W) or — P(w,,|W,,W5...Wa.2) is called a ee ee 

صفحه 4:
Dan Jurafsky G&S) How to compute P(W) * How to compute this joint probability: *P(its, water, is, so, transparent, that) * Intuition: let’s rely on the Chain Rule of Probability 

صفحه 5:
میم Dan Jurafsky Reminder: The Chain Rule * Recall the definition of conditional probabilities Rewriting: * More variables: P(A,B,C,D) = P(A)P(BJA)P(C|A,B)P(DIA,B,C) * The Chain Rule in General P(x, ,X5,X2,...,X-) = P(x,)P(x5/x,)P(x21x,,x 

صفحه 6:
Dan Jurafsky compute joint probability of 4 words in sentence P(w,w2...W,) = []P0«, lwyw2...W34) P(“its water is so transparent”) = P(its) x P(waterl|its) x P(is|its water) x P(solits water is) x P(transparentlits water is so) 

صفحه 7:
Dan Jurafsky How to estimate these probabilities * Could we just count and divide? P(the lits water is so transparent that) = Count(its water is so transparent that the) Count(its water is so transparent that) Lane ene Lawn! Pome ‏ع اتوم سايم مدت‎ ° We'll never see enough data for estimating these 

صفحه 8:
Dan Jurafsky 6 Markov Assumption ¢ Simplifying assumption: Andrei Markov P(the lits water is so transparent that) = P(the | that) - Ur maype P(the lits water is so transparent that) = P(the | transparent that) 

صفحه 9:
Markov Assumption P(w,w3...w,) =] [Pow, lw,_,...W,4) * In other words, we approximate each component in the product P(w, |w,w,...W,,) = P(w, lw, ...W,,) 

صفحه 10:
Dan Jurafsky Simplest case: Unigram model P(ww,...W,,) = [ [ec ) e automatically generated sentences from a unigram model fifth, an, of, futures, the, an, incorporated, a, a, the, inflation, most, dollars, quarter, in, is, mass thrift, did, eighty, said, hard, 'm, july, bullish that, or, limited, the 

صفحه 11:
Dan Jurafsky Bigram model =| Condition on the previous word: P(w, |w,w,...w,_,) = P(w, |w,_,) texaco, rose, one, in, this, issue, is, pursuing, growth, in, a, boiler, house, said, mr., gurria, mexico, 's, motion, control, proposal, without, permission, from, five, hundred, fifty, five, yen outside, new, car, parking, lot, of, the, agreement, reached this, would, be, a, record, november 

صفحه 12:
Dan Jurafsky N-gram models * We can extend to trigrams, 4-grams, 5- grams * In general this is an insufficient model of language * because language has long-distance dependencies: “The computer which | had just put into the machine room on the fifth floor crashed.” 

صفحه 13:
Language Modeling Estimating N-gram Probabilities aia ‏اه‎ ‎5 i We 81 8 

صفحه 14:
Dan Jurafsky 72 Estimating bigram probabilities * The Maximum Likelihood Estimate count(w, ,.W,) P(w, lw.) = ————— count(w,_,) c(wW,_,.W;) P(w, |w,,) = c(w,_,) 

صفحه 15:
Dan Jurafsky 72 An example <s> 1am Sam </s> <s> Sam |am </s> <s> | do not like green eggs and ham </s> 

صفحه 16:
Dan Jurafsky Berkeley Restaurant Project sentences * can you tell me about any good cantonese restaurants close by * mid priced thai food is what i’m looking for * tell me about chez panisse * can you give me a listing of the kinds of food that are available * i'm looking for a good place to eat breakfast ٠ when is caffe venezia open during the day 

صفحه 17:
food 6 ه ه ه نو من حابر Raw bigram counts chinese 16 con eat Dan Jurafsky * Out of 9222 sentences to اح دوت شرت نم 2 want 827 نت ألم دم دراه Bree 2 i want to eat chinese food Junch spend 

صفحه 18:
Dan Jurafsky Raw bigram probabilities ٠ Normalize by unigrams: i want | 6 eat_| chinese [ food | lunch | spend 2533 927 2417 746 158 1093 341 278 * Result: i want[to [eat | chinese | food [Tunch [ spend i 0002 [0.33 [0 0.0036] 0 0 0 0009 want | 0.0022 |0 —|.0.66 |]0.0011| 0.0065 0006۵ 0.0054] 0.0011 to 0000830 | 0.0017] 0.28 ۰ 0.0025 | 0.087 eat 0 0 0 0.021 | 0.0027] 0.056 | 0 chinese | 00۵6۵ ]0 | 0 0 0 0,52 | 0.0063] 0 food | 0.014 /0 0.014 Jo 0.00092 | 0.0037 | 0 0 lunch | ‏وكممه‎ 0 0 0 0 00020 0 spend | 0.0036 ]0 0 0 0 0 0 

صفحه 19:
Bigram estimates of sentence probabilities P(<s> | want english food </s>) = P(I|<s>) P(want|I) P(english|want) P(food|english) P(</s>|food) = .000031 x x xX X 

صفحه 20:
What kinds of knowledge? P(english|want) = .0011 P(chinese|want) = .0065 ( ( ( ( ( ( P(to|want) = .66 P(eat | to) = .28 P(food | to) = 0 P(want | spend) = 0 P(i| <s>) = .25 

صفحه 21:
Dan Jurafsky 72 Practical Issues ° We do everything in log space *Avoid underflow *(also adding is faster than multiplying) 2۱۷ 2:۷ Ps X P, = log p, + log p, + log p, + log p, 

صفحه 22:
Dan Jurafsky G5) Language Modeling Toolkits ° SRILM وإعاعء زماص/جصمع. امع ۱ ۰ ‎rilm‏ 

صفحه 23:
Language Modeling Evaluation and Perplexity 

صفحه 24:
Dan Jurafsky Evaluation: How good is our model? * Does our language model prefer good sentences to bad ones? * Assign higher probability to “real” or “frequently observed” sentences * Than “ungrammatical” or “rarely observed” sentences? ۰ We train parameters of our model on a training set. ° We test the model’s performance on data we haven't seen. * Atest set is an unseen dataset that is different from our 

صفحه 25:
Dan Jurafsky Extrinsic evaluation of N-gram models * Best evaluation for comparing models A and B * Put each model in a task * spelling corrector, speech recognizer, MT system * Run the task, get an accuracy for A and for B * How many misspelled words corrected properly * How many words translated correctly * Compare accuracy for A andB 

صفحه 26:
Dan Jurafsky Difficulty of extrinsic (in-vivo) evaluation of N-gram models ¢ Extrinsic evaluation * Time-consuming; can take days or weeks * So * Sometimes use intrinsic evaluation: perplexity * Bad approximation ¢ unless the test data looks just like the training data * So generally only useful in pilot experiments e But is helnful to think ahout. 

صفحه 27:
Dan Jurafsky Intuition of Perplexity 0 سسساعیه ] * The Shannon Game: * How well can we predict ۱6 ۱6۷ 0.4 J see 0.01 | always order pizza with cheese and The 33 President of the US was Pred vive (D004 56۷8 (onl desde * Unigrams are terrible at this game. (Why?) * A better model of a text ٠ is one which assigns a higher probability to the word that asks ea |e ecg es 

صفحه 28:
Dan Jurafsky Perplexity The best language model is one that best predicts an unseen test set ره - ره توق یوج رآک‌ ریم ‎the test set, normalized by the ۲ 1‏ 01 number of words: = ‏عط‎ ) ۰۳ - ‏مس[‎ ‎١ Fone Chain rule: ‏اتف‎ 1 = wba) K@kiRIOHASPErplexity is the same as maximizing 

صفحه 29:
The Shannon Game intuition for perplexity From Josh Goodman How hard is the task of recognizing digits ‘0,1,2,3,4,5,6,7,8,9" + Perplexity 10 How hard is recognizing (30,000) names at Microsoft. * Perplexity = 30,000 If a system has to recognize * Operator (1 in 4) * Sales (1 in 4) * Technical Support (1 in 4) * 30,000 names (1 in 120,000 each) * Perplexity is 53 Perplexity is weighted equivalent branching factor 

صفحه 30:
Dan Jurafsky Perplexity as branching factor * Let’s suppose a sentence consisting of random digits * What is the perplexity of this sentence according to a model that assign P=1/10 to each digit? PP(W) = P(wiwy...wy) ® 13 ‏باب‎ ‏)د‎ ( 1 10 10 

صفحه 31:
Lower perplexity = better model * Training 38 million words, test 1.5 million words, WS} 1 Bigram |Trigra gram m Order Perplexi 962 170 109 ty 

صفحه 32:
Language Modeling Generalization and zeros 

صفحه 33:
The Shannon Visualization Method Choose a random bigram <s> I (<s>, w) according to its T want probability want to * Now choose a random to eat bigram (w, x) according éat! Chinese to its probability Chinese food * And so on until we choose food </s> ‏حول‎ I want to eat Chinese food Then string the words together 

صفحه 34:
Dan Jurafsky EB 5 Approximating Shakespeare سوام ‎‘To him swallowed confess bear both, Which, Of save on trail for are ay device and rote life have‏ ‎Every enter now severally so, et‏ ‎Hill be late speaks: or! a more to leg less first you enter‏ ‎Are where exeunt and sighs have rise excelleney took of.. Sleep kuave we. near; vile like‏ Bigram What means, sit. Teonfess she? then all sorts, he is trim, captain. ‘Why dost stand forth thy canopy, forsooth; he is this palpable hit the King Henry. Live king. Follow ‘What we, hath got so she that I rest and sent fo scold and nature bankrupt, nor the first gentleman? Trigram ‘Sweet prince, Falstaff shall die. Harry of Monmout’s grave. ‘This shall forbid it should he branded, if renown made it empty Indeed the duke; and hind a very good friend, Fly, and will rid me these news of price. Therefore the saclness of parting. as they say, tis dane Quadrigram King Henry. What! I will go seek the traitor Gloucester. Exeunt some of the watch. A great banquet serv'd in; Will you not tell me who I am? Tteannot be but so, Indeed the short and the long. Marry tis a noble Lepidas. 

صفحه 35:
Shakespeare as corpus ° N=884,647 tokens, V=29,066 ° Shakespeare produced 300,000 bigram types out of V?= 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 ‎Baer eae |‏ سم ات قاس 0م ‎cmc PR cee:‏ دس ‎١‏ ری ‎ 

صفحه 36:
Dan Jurafsky = The wall street journal is not Gs) shakespeare (no offense) Unigram Months the my and issue of year foreign new exchange’s september were recession ex- change new endorsed a acquire to six executives Bigram Last December through the way to preserve the Hudson corporation N. B. E. C. Taylor would seem to complete the major central planners one point five percent of U. S. E. has already old M. X. corporation of living on information such as more frequently fishing to keep her Trigram They also point to ninety nine point six billion dollars from two hundred four oh six three percent of the rates of interest stores as Mexico and Brazil on market conditions 

صفحه 37:
The perils of overfitting * N-grams only work well for word prediction if the test corpus looks like the training corpus *In real life, it often doesn’t *We need to train robust models that generalize! *One kind of generalization: Zeros! * Things that don’t ever occur in the training set 

صفحه 38:
* Training set: ° Test set .. denied the .., denied the allegations offer .. denied the reports... denied the loan .. denied the claims .. denied the request Pitter. | denied the) = 

صفحه 39:
Dan Jurafsky Zero probability bigrams * Bigrams with zero probability * mean that we will assign 0 probability to the test set! * And hence we cannot compute perplexity (can’t divide by 0)! 

صفحه 40:
Language Modeling Smoothing: Add- one (Laplace) smoothing = Ss al 

صفحه 41:
Dan Jurafsky The tetutiog oP sxooviktay (Pro Dac (eta) en we have sparse statistics: P(w | denied the) 3 allegations 2 reports 1 claims {request tiie 7 total * Steal probability mass to generalize better P(w | denied the) 2.5 allegations 1.5 reports 2 0.5 claims 3 0.5 request 3 a id... aes mi: 7 total 

صفحه 42:
Dan Jurafsky Add-one estimation * Also called Laplace smoothing ° Pretend we saw each word one more time than we did * Just add one to all c(w w.) wie (W, |W.) = 3 cw, i) * MLE estimate: _ €(W,).W)+1 Py Cw, lw.) we ۲ ۷ Add-1 estimate: 

صفحه 43:
Dan Jurafsky Maximum Likelihood Estimates * The maximum likelihood estimate * of some parameter of a model M from a training set T * maximizes the likelihood of the training set T given the model M * Suppose the word “bagel” occurs 400 times in a corpus of a million words * What is the probability that a random word from some other text will be “bagel”? * MLE estimate is 400/1,000,000 = .0004 * This may be a bad estimate for some other corpus * But it is the estimate that makes it most likely that “bagel” will occur 400 times in a million word corpus. 

صفحه 44:
Dan Jurafsky sxoovtked bigrany pours i want | to eat | chinese | food | lunch | spend i 6 828 1 10 1 1 1 3 want 3 2 609 | 2 7 7 6 2 to 3 1 5 687 | 3 1 7 212 eat 1 1 3 1 17 3 43 1 chinese || 2 1 1 1 1 83 2 1 food 16 | 1 16 1 2 5 1 1 Junch 3 1 1 1 1 2 1 1 spend 2 1 2 1 1 1 1 1 

صفحه 45:
spend 0.00075 000084 0.055 0.00046 0.00062 0.00039 0.00036 0.00058 Tunch 0.00025 0.0025 0.0018 0.02 0.0012 0.00039 0.00056 0.00058. Dan Jurafsky Gi) Lepkoe ‏سينا سداس‎ 3 (w, —1Wn ) +1 3 (Wr 1 ) +V eat chinese | food 0.0025 | 0.00025] 0.00025 0.00084| 0.0029 | 0.0029 0.18 0.00078} 6 0.00046} 0.0078 | 0.0014 0.00062] 0.00062) 0.052 0.00039 | 0.00079} 0.002 0.00056} 0.00056] 0.0011 0.00058 | 0.00058] 0.00058 to 0.00025 0.26 0.0013 0.0014 0.00062 0.0063 0.00056 0.0012 want 021 0.00042 0.00026 0.00046 0.00062 0.00039 0.00056 0.00058 P (walwn—1) = i 0.0015 0.0013. 0.00078 22046 0.0012 0.0063, 00017 0.0012 1 want to eat chinese food lunch spend 

صفحه 46:
Dan Jurafsky [COn1Wn) +L x Cn) عع سکس زر رم i want | to eat chinese| 1000| lunch| spend i 3.8 | 527 | 064] 64 0.64 0.64] 0.64 | 19 want 1,2 0.39 238 0.78 27 3: aa 0.78 to 1.9 0.63 3.1 430 19 0.63) 44 133 eat 0.34) 4 1 0.34 58 1 15 034 chinese |] 2 0.098] 0.098) 0.098} 0.098 8.2 0.2 0.098 food 6.9 0.43 6.9 0.43 0.86 2.2 0.43 0.43 lunch 0.57| 0.19 | 0.19 | 0.19 | 0.19 0.38} 0.19 | 0.19 spend 0.32] 6 0.32 0.16 0.16 0.16] 0.16 0.16 

صفحه 47:
Dan Jurafsky eat_| chinese | food | Tunch | spend 1 ۱9 ] 0 yo fo 2 want 1 | 6 6 5 1 to 686 | 2 0 6 21 eat 0 | 16 2 2 |o chinese 0 |] 92 | 1 0 food o ft 4 0 0 ‏سا‎ ۰ 1 0 0 spend 0 ۰ Jo 0 0 ‏كه‎ | chinese | food] lunch] spend 1 64 | 064 | O68] 064 | 19 want 0.78 | 27 27 | 23 | 0.78 to 430 | 19 063} 44 | 133 eat 034 | 58 1 ‏كل‎ | 034 chinese 0098| 0.098) 0.098 | 8.2 0.098, food 0.43 | 0.86 2} 043 | 043 lunch 0.19 | 0.19 0.19 | 0.19 spend 0.16 | 0.16 | 0.16 | 0.16 

صفحه 48:
Dan Jurafsky Add-1 estimation is a blunt instrument * So add-1 isn’t used for N-grams: * We'll see better methods ° But add-1 is used to smooth other NLP models ¢ For text classification *In domains where the number of zeros isn’t so huge. 

صفحه 49:
Language Modeling Interpolation, Backoff, and Web- Scale LMs = Ss al 

صفحه 50:
Dan Jurafsky Qucho PP and Toterpohatiod * Sometimes it helps to use less context * Condition on less context for contexts you haven’t learned much about ° Backoff: * use trigram if you have good evidence, * otherwise bigram, otherwise unigram * Interpolation: * mix unigram, bigram, trigram e Intarnolation workc hatter 

صفحه 51:
Dan Jurafsky Linear Interpolation * Simple interpolation رم رصیق (مو رما 27 هی ‎+A3P(wn) ۶‏ :أا0»© 0۴ 6۵۳0۱۲۱۵۴۵۱ ۵۴۵086 ۰ ۱2 = Pav} PO |Wn2Wn1) ‏هیقب‎ ‎+) 7 

صفحه 52:
Dan Jurafsky How to set the lambdas? * Use a held-out a | ۳ aoe * Choose As to maximi As to maximize the probability of held-out data: * Fix the N-gram probabilities (on the training data) * Then search for As that give largest probability to Nog P(vw,... ww, |M(A,...A,)) = = peek 14 | OM Iw.) 

صفحه 53:
Unknown words: Open versus closed vocabulary tasks * If we know all the words in advanced ٠ Vocabulary V is fixed * Closed vocabulary task * Often we don’t know this * Out Of Vocabulary = OOV words * Open vocabulary task * Instead: create an unknown word token <UNK> * Training of <UNK> probabilities * Create a fixed lexicon L of size V * At text normalization phase, any training word not in L changed to <UNK> * Now we train its probabilities like a normal word * At decoding time ٠١ for any word not in training 

صفحه 54:
Dan Jurafsky Huge web-scale n-grams * How to deal with, e.g., Google N-gram corpus * Pruning * Only store N-grams with count > threshold. * Remove singletons of higher-order n-grams * Entropy-based pruning ° Efficiency * Efficient data structures like tries * Bloom filters: approximate language models * Store words as indexes, not strings * Use Huffman coding to fit large numbers of words into two bytes oe 

صفحه 55:
Dan Jurafsky Smoothing for Web-scale N- grams ٠ “Stupid backoff” (Brants et a/. 2007) * No discounting, just use relative frequencies count(w;, ۳ counts) if count(w;,,,)>0 Sow, Iwi, =} count(w,,) 0.4S(w, lw*],,) otherwise _ count(w, ) S(w,) 55 

صفحه 56:
N-gram Smoothing Summary ۰ ۸00-1 ۰ * OK for text categorization, not for language modeling * The most commonly used method: * Extended Interpolated Kneser-Ney ¢ For very large N-grams like the Web: * Stupid backoff 56 

صفحه 57:
Dan Jurafsky O@dvowed Loaguage Oodetary ۰ Discriminative models: * choose n-gram weights to improve a task, not to fit the training set * Parsing-based models * Caching Models * Recently used words are more likely to appear ۳ c(w E history) -scue Ww lhistory) = APGw, lw, .W,,)+(1- A) thistory! * These perform very poorly for speech recognition (why?) 

صفحه 58:
Language Modeling Advanced: Good Turing Smoothing 

صفحه 59:
Dan Jurafsky ‎(Lapke) Gwoviser‏ ۵404 بطم ‎_ COW. YW, +1 ‎c(w,,)+V ‏م ‎۵4-۱: | Wia ) 

صفحه 60:
‎QOore yeverd Porwuaivds: Odd-+e‏ و ‎“(w,,.w,)+k ‎Pi. (w, lw, ,) = See S a ۴ c(w,_,)+kV c(w,_,,W,)+ m4) ‏و‎ 1۱, ,(< ۲ ‎c(w,,)+m 

صفحه 61:
Dan Jurafsky Gs) QOuigrav prior sxoovtsiay cl, yw.) | pe ‏:)یی‎ ۱۷, ( c(w,,)+m “(w,,.w,)+mP(w,) ۱ ‏ات۳‎ i ‏ی ( ۱۶ )نی‎ 

صفحه 62:
Dan Jurafsky Advanced smoothing algorithms * Intuition used by many smoothing algorithms * Good-Turing * Kneser-Ney * Witten-Bell * Use the count of things we’ve seen once *to help estimate the count of things we’ve ۲: 5۱ 5 ۳ 2 

صفحه 63:
Dan Jurafsky Notation: N, = Frequency of frequency c ¢ N. = the count of things we've seen c times * Sam |am1am Sam | do not eat I 3 sam 2 am 2 N, = 3 do 1 ‏يلا‎ - 2 not 1 eat 1 ‏ولا‎ 1 63 

صفحه 64:
Dan Jurafsky Bord Turtay scoovistary totic ٠ You are fishing (a scenario from Josh Goodman), and caught: * 10 carp, 3 perch, 2 whitefish, 1 trout, 1 salmon, 1 eel = 18 fish ° How likely is it that next species is trout? °1/18 * How likely is it that next species is new (i.e. catfish or bass) * Let’s use our estimate of things-we-saw-once to estimate the new things. © 2/18 (hecalice N —2) 

صفحه 65:
Dan Jurafsky Good ‏همیب‎ P.,(things with zero frequency) = 3 ct a AD N. © Ovsern (buss or caPish) ٠ Gero vor (trout) ٠ ‏دج‎ 0: ۰ 20 ۰ 0۵ p=OM0 =O ۰ 0۵ 2 0 * 9 > (مس*0) ۰ © * 6- هه - حول > ۱6 9/9 = سای ۰ * Pon (wera) = O/O = O10 

صفحه 66:
Dan Jurafsky QResultay GoodTurtay cunbers Numbers from Church and Gale Count | Good Turing (1991) 6 ct * 22 million words of AP 0 -0000270 News | (c+ 1 0.446 —_ 2 1.26 3 2.24 4 3.24 5 4.22 6 5.19 7 6.21 8 7.24 9 8.25 

صفحه 67:
Dan Jurafsky Resultagy GoolTurtay wawbers Numbers from Church and Gale Count | Good Turing (1991) 3 ‏يت‎ ‎* 22 million words of AP 1 -0000270 News | (c+ 1 0.446 —— 2 1.26 3 2.24 4 3.24 5 4.22 6 5.19 7 6.21 * It sure looks like c* = (c - .75) 8 7.24 9 8.25