BASIC TECHNIQUES IN STATISTICAL NLP.ppt

BASIC TECHNIQUES IN STATISTICAL NLPWord predictionn-gramssmoothingSeptember 20031Statistical Methods in NLElTwo characteristics of NL make it desirable to endow programs with the ability to LEARN from examples of past use:VARIETY(no programmer can really take into account all possibilities)AMBIGUITY(need to have ways of choosing between alternatives)lIn a number of NLE applications,statistical methods are very commonlThe simplest application:WORD PREDICTIONSeptember 20032We are good at word predictionStocks plunged this morning,despite a cut in interestStocks plunged this morning,despite a cut in interestrates by the Federal Reserve,as WallStocks plunged this morning,despite a cut in interestrates by the Federal Reserve,as WallStreet began.September 20033Real Spelling ErrorsThey are leaving in about fifteen minuets to go to her houseThe study was conducted mainly be John Black.The design an construction of the system will take more than one year.Hopefully,all with continue smoothly in my absence.Can they lave him my messages?I need to notified the bank of this problem.He is trying to fine out.September 20034Handwriting recognitionlFrom Woody Allens Take the Money and Run(1969)Allen(a bank robber),walks up to the teller and hands her a note that reads.I have a gun.Give me all your cash.The teller,however,is puzzled,because he reads I have a gub.No,its gun,Allen says.Looks like gub to me,the teller says,then asks another teller to help him read the note,then another,and finally everyone is arguing over what the note means.September 20035Applications of word predictionlSpelling checkerslMobile phone textinglSpeech recognitionlHandwriting recognitionlDisabled usersSeptember 20036Statistics and word predictionlThe basic idea underlying the statistical approach to word prediction is to use the probabilities of SEQUENCES OF WORDS to choose the most likely next word/correction of spelling errorlI.e.,to compute lFor all words w,and predict as next word the one for which this(conditional)probability is highest.P(w|W1.WN-1)September 20037Using corpora to estimate probabilitieslBut where do we get these probabilities?Idea:estimate them by RELATIVE FREQUENCY.lThe simplest method:Maximum Likelihood Estimate(MLE).Count the number of words in a corpus,then count how many times a given sequence is encountered.lMaximum because doesnt waste any probability on events not in the corpusSeptember 20038Maximum Likelihood Estimation for conditional probabilitieslIn order to estimate P(w|W1 WN),we can use instead:lCfr.:P(A|B)=P(A&B)/P(B)September 20039Aside:counting words in corporalKeep in mind that its not always so obvious what a word is(cfr.yesterday)lIn text:He stepped out into the hall,was delighted to encounter a brother.(From the Brown corpus.)lIn speech:I do uh main-mainly business data processinglLEMMAS:cats vs catlTYPES vs.TOKENSSeptember 200310The problem:sparse datalIn principle,we would like the n of our models to be fairly large,to model long distance dependencies such as:Sue SWALLOWED the large green lHowever,in practice,most events of encountering sequences of words of length greater than 3 hardly ever occur in our corpora!(See below)l(Part of the)Solution:we APPROXIMATE the probability of a word given all previous wordsSeptember 200311The Markov AssumptionlThe probability of being in a certain state only depends on the previous state:P(Xn=Sk|X1 Xn-1)=P(Xn=Sk|Xn-1)This is equivalent to the assumption that the next state only depends on the previous m inputs,for m finite (N-gram models/Markov models can be seen as probabilistic finite state automata)September 200312The Markov assumption for language:n-grams modelslMaking the Markov assumption for word prediction means assuming that the probability of a word only depends on the previous n words(N-GRAM model)September 200313Bigrams and trigramslTypical values of n are 2 or 3(BIGRAM or TRIGRAM models):P(Wn|W1.W n-1)P(Wn|W n-2,W n-1)P(W1,Wn)P(Wi|W i-2,W i-1)lWhat bigram model means in practice:Instead of P(rabbit|Just the other day I saw a)We use P(rabbit|a)lUnigram:P(dog)Bigram:P(dog|big)Trigram:P(dog|the,big)September 200314The chain rulelSo how can we compute the probability of sequences of words longer than 2 or 3?We use the CHAIN RULE:lE.g.,P(the big dog)=P(the)P(big|the)P(dog|the big)lThen we use the Markov assumption to reduce this to manageable proportions:September 200315Example:the Berkeley Restaurant Project(BERP)corpuslBERP is a speech-based restaurant consultantlThe corpus contains user queries;examples includeIm looking for Cantonese foodId like to eat dinner someplace nearbyTell me about Chez PanisseIm looking for a good place to eat breakfastSeptember 200316Computing the probability of a sentencelGiven a corpus like BERP,we can compute the probability of a sentence like“I want to eat Chinese food”lMaking the bigram assumption and using the chain rule,the probability can be approximated as follows:P(I want to eat Chinese food)P(I|”sentence start”)P(want|I)P(to|want)P(eat|to)P(Chinese|eat)P(food|Chinese)September 200317Bigram countsSeptember 200318How the bigram probabilities are computedlExample of P(I,I):C(“I”,”I”):8C(“I”):8+1087+13.=3437P(“I”|”I”)=8/3437=.0023September 200319Bigram probabilitiesSeptember 200320The probability of the example sentencelP(I want to eat Chinese food)lP(I|”sentence start”)*P(want|I)*P(to|want)*P(eat|to)*P(Chinese|eat)*P(food|Chinese)=l.25*.32*.65*.26*.002*.60=.000016September 200321Examples of actual bigram probabilities computed using BERPSeptember 200322Visualizing an n-gram based language model:the Shannon/Miller/Selfridge methodlFor unigrams:Choose a random value r between 0 and 1Print out w such that P(w)=rlFor bigrams:Choose a random bigram P(w|)Then pick up bigrams to follow as beforeSeptember 200323The Shannon/Miller/Selfridge method trained on ShakespeareSeptember 200324Approximating Shakespeare,contdSeptember 200325A more formal evaluation mechanismlEntropylCross-entropySeptember 200326The downsidelThe entire Shakespeare oeuvre consists of 884,647 tokens(N)29,066 types(V)300,000 bigramslAll of Jane Austens novels(on Manning and Schuetzes website):N=617,091 tokensV=14,585 typesSeptember 200327Comparing Austen n-grams:unigramsIn personshewasinferiorto1-gramP(.)P(.)P(.)P(.)1the.034the.034the.034the.0342to.032to.032to.032to.0323and.030and.030and.0308was.015was.01513she.0111701inferior.00005September 200328Comparing Austen n-grams:bigramsIn personshewasinferiorto2-gramP(.|person)P(.|she)P(.|was)P(.inferior)1and.099had.0141not.065to.2122who.099was.122a.05223she.009inferior0September 200329Comparing Austen n-grams:trigramsIn personshewasinferiorto3-gramP(.|In,person)P(.|person,she)P(.|she,was)P(.was,inferior)1UNSEENdid.05not.057UNSEEN2was.05very.038inferior0September 200330Maybe with a larger corpus?lWords such as ergativity unlikely to be found outside a corpus of linguistic articleslMore in general:Zipfs lawSeptember 200331Zipfs law for the Brown corpusSeptember 200332Addressing the zeroeslSMOOTHING is re-evaluating some of the zero-probability and low-probability n-grams,assigning them non-zero probabilitiesAdd-oneWitten-BellGood-TuringlBACK-OFF is using the probabilities of lower order n-grams when higher order ones are not availableBackoffLinear interpolationSeptember 200333Add-one(Laplaces Law)September 200334Effect on BERP bigram countsSeptember 200335Add-one bigram probabilitiesSeptember 200336The problemSeptember 200337The problemlAdd-one has a huge effect on probabilities:e.g.,P(to|want)went from.65 to.28!lToo much probability gets removed from n-grams actually encountered(more precisely:the discount factor September 200338Witten-Bell DiscountinglHow can we get a better estimate of the probabilities of things we havent seen?lThe Witten-Bell algorithm is based on the idea that a zero-frequency N-gram is just an event that hasnt happened yetlHow often these events happen?We model this by the probability of seeing an N-gram for the first time(we just count the number of times we first encountered a type)September 200339Witten-Bell:the equationslTotal probability mass assigned to zero-frequency N-grams:(NB:T is OBSERVED types,not V)lSo each zero N-gram gets the probability:September 200340Witten-Bell:why discountinglNow of course we have to take away something(discount)from the probability of the events seen more than once:September 200341Witten-Bell for bigramslWe relativize the types to the previous word:September 200342Add-one vs.Witten-Bell discounts for unigrams in the BERP corpusWordAdd-OneWitten-Bell“I”.68.97“want”.42.94“to”.69.96“eat”.37.88“Chinese”.12.91“food”.48.94“lunch”.22.91September 200343One last discounting method.lThe best-known discounting method is GOOD-TURING(Good,1953)lBasic insight:re-estimate the probability of N-grams with zero counts by looking at the number of bigrams that occurred oncelFor example,the revised count for bigrams that never occurred is estimated by dividing N1,the number of bigrams that occurred once,by N0,the number of bigrams that never occurredSeptember 200344Combining estimatorslA method often used(generally in combination with discounting methods)is to use lower-order estimates to help with higher-order oneslBackoff(Katz,1987)lLinear interpolation(Jelinek and Mercer,1980)September 200345Backoff:the basic ideaSeptember 200346Backoff with discountingSeptember 200347ReadingslJurafsky and Martin,chapter 6lThe Statistics GlossarylWord prediction:For mobile phonesFor disabled userslFurther reading:Manning and Schuetze,chapters 6(Good-Turing)September 200348AcknowledgmentslSome of the material in these slides was taken from lecture notes by Diane Litman&James MartinSeptember 200349