Statistical Translation Language Model Maryam Karimzadehgan mkarimz2@illinois.edu University of Illinois at Urbana-Champaign 1 Outline • Motivation & Background – Language model (LM) for IR – Smoothing methods for IR • Statistical Machine Translation – Cross-Lingual – Motivation – IBM Model 1 • Statistical Translation Language Model – Monolingual – Synthetic Queries – Mutual Information-based approach – Regularization of self-translation probabilities • Smoothing in Statistical Translation Language Model 2 The Basic LM Approach ([Ponte & Croft 98], [Hiemstra & Kraaij 98], [Miller et al. 99]) Document Language Model … Text mining paper text ? mining ? assocation ? clustering ? … food ? … Food nutrition paper … food ? nutrition ? healthy ? diet ? … Query = “data mining algorithms” ? Which model would most likely have generated this query? Ranking Docs by Query Likelihood Doc LM Query likelihood d1 d1 p(q| d1) d2 d2 p(q| d2) p(q| dN) dN dN q Retrieval as LM Estimation • Document ranking based on query likelihood m |V | log p(q | d ) log p(qi | d ) c( wi , q) log p( wi | d ) i 1 where, q q1q2 ...qm i 1 Document language model • Retrieval problem Estimation of p(wi|d) • Smoothing is an important issue, and distinguishes different approaches How to Estimate p(w|d)? • Simplest solution: Maximum Likelihood Estimator – P(w|d) = relative frequency of word w in d – What if a word doesn’t appear in the text? P(w|d)=0 • In general, what probability should we give a word that has not been observed? • If we want to assign non-zero probabilities to such words, we’ll have to discount the probabilities of observed words • This is what “smoothing” is about … 6 Language Model Smoothing P(w) Max. Likelihood Estimate p ML ( w ) count of w count of all words Smoothed LM w Smoothing Methods for IR (Zhai & Lafferty 01) • Method 1(Linear interpolation, JelinekMercer): c( w, d ) p( w | d ) (1 ) p( w | REF ) |d | ML estimate parameter • Method 2 (Dirichlet Prior/Bayesian): p (w | d ) c ( w;d ) p ( w| REF ) |d | |d | |d | c( w, d ) |d | p( w | REF ) |d | parameter Outline • Motivation & Background – Language model (LM) for IR – Smoothing methods for IR • Statistical Machine Translation – Cross-Lingual – Motivation – IBM Model 1 • Statistical Translation Language Model – Monolingual – Synthetic Queries – Mutual Information-based approach – Regularization of self-translation probabilities • Smoothing in Statistical Translation Language Model 9 A Brief History • Machine translation was one of the first applications envisioned for computers • Warren Weaver (1949): “I have a text in front of me which is written in Russian but I am going to pretend that it is really written in English and that it has been coded in some strange symbols. All I need to do is strip off the code in order to retrieve the information contained in the text.” • First demonstrated by IBM in 1954 with a basic word-for-word translation system 10 Interest in Machine Translation • Commercial interest: – U.S. has invested in MT for intelligence purposes – MT is popular on the web—it is the most used of Google’s special features – EU spends more than $1 billion on translation costs each year. – (Semi-)automated translation could lead to huge savings 11 Interest in Machine Translation • Academic interest: – One of the most challenging problems in NLP research – Requires knowledge from many NLP sub-areas, e.g., lexical semantics, parsing, morphological analysis, statistical modeling,… – Being able to establish links between two languages allows for transferring resources from one language to another 12 Word-Level Alignments • Given a parallel sentence pair we can link (align) words or phrases that are translations of each other: 13 Machine Translation -- Concepts • We are trying to model P(e|f) – I give you a French sentence – You give me back English • How are we going to model this? – The maximum likelihood estimation of P(e | f) is: freq(e,f)/freq(f). – Way too specific to get any reasonable frequencies! Vast majority of unseen data will have zero counts! Machine Translation – Alternative way • We could use Bayes rule P (e | f ) P ( f | e) P (e) P ( f | e) P (e) P( f ) Given a French sentence f, we could do a search for an e that maximizes p(e|f). e arg max P ( f | e ) P ( e ) e • Why using Bayes rule and not directly estimating p(e|f) ? It is important that our model for p(e|f) concentrates its probability as much as possible on well-formed English sentences. But it is not important that our model for P(f|e) concentrate its probability on well-formed French sentences. Statistical Machine Translation • The noisy channel model Language Model P e e f Translation Model P f e Decoder eˆ arg max e P e f eˆ e: English f: French eak fk ea j |e|=l f j |f|=m – Assumptions: • An English word can be aligned with multiple French words while each French word is aligned with at most one English word • Independence of the individual word-to-word translations 16 Estimation of Probabilities -- IBM Model 1 • Simplest of the IBM models. (There are 5 models) • Does not consider word order (bag-ofwords approach) • Does not model one-to-many alignments • Computationally inexpensive • Useful for parameter estimations that are passed on to more elaborate models 17 IBM Model 1 • Three important components involved – Language model • Give the probability p(e). – Translation model • Estimate the Translation Probability p(f|e). – Decoder eˆ arg max P e f arg max e e p e p f e p f arg max p e p f e e 18 IBM Model 1- Translation Model • Joint probability of P(F=f, E=e, A=a) where A is an alignment between two sentences. = (, |) • Assume each French word has exactly one connection. 19 IBM Model 1- Translation Model • • Assume, |e|=l and |f|=m, then the alignment can be represented by a series a = a1a2…am Each alignment is between 0 and l such that if the word in position j of the French sentence is connected to the word in position i of the English sentence, then aj=i and if it not connected to any English word, then aj=0. 1 (+1) =1 ( | ) • , = • The alignment is determined by specifying the values of aj for j from 1 to m, each of which can take any value from 0 to l. 20 IBM Model 1 – Translation Model = (, |) 1 , = ( + 1) – = 1 (+1) 1 =0 … ( | ) =1 =0 =1 ( all possible alignments (the English word that a French word fj is aligned with) . translation probability EM algorithm is used to estimate the translation probabilities. 21 Outline • Motivation & Background – Language model (LM) for IR – Smoothing methods for IR • Statistical Machine Translation – Cross-Lingual – Motivation – IBM Model 1 • Statistical Translation Language Model – Monolingual – Synthetic Queries – Mutual Information-based approach – Regularization of self-translation probabilities • Smoothing in Statistical Translation Language Model 22 The Problem of Vocabulary Gap Query = auto wash P(“auto”) P(“wash”) d1 d2 d3 auto wash … auto buy … auto car wash vehicle How to support inexact matching? {“car” , “vehicle”} == “auto” “buy” ==== “wash” P(“auto”) P(“wash”) 23 Translation Language Models for IR [Berger & Lafferty 99] Query = auto wash “translate” d1 d2 auto wash … Query = car wash “car” p(w | d ) |d3)= p ml (ux p| (“auto”| d ) p t “car”) (w | u ) P(“auto” p(“car”|d3) auto buy auto t u + p(“vehicle”|d3) x pt(“auto”| “vehicle”) P(“car”|d3) d3 “auto” “auto” car wash vehicle “car” How to estimate? Pt(“auto”| “car”) P(“auto”) P(“wash”) “auto” “vehicle” P(“vehicle”|d3) P (“auto”| “vehicle”) t 24 Estimation of Translation Model: pt(w|u) • When relevance judgments are available, (q,d) serves as data to train the translation model • Without relevance judgments, we can use synthetic data [Berger & Lafferty 99], <title, body>[Jin et al. 02] pt ( w | d ) Basic translation model p t ( w | u ) p (u | d ) w d Translation model Regular doc LM Estimation of Translation Model – Synthetic Queries ([Berger & Lafferty 99]) • Select words that are representative of a document. • Calculate a Mutual information for each word in (,) a document: I(w,d) = p(w,d)log (|) • Synthetic queries are sampled based on normalized mutual information. • The resulting (d,q) of documents and synthetic queries are used to estimate the probabilities using EM algorithm (IBM Model 1). Estimation of Translation Model – Synthetic Queries Algorithm ([Berger & Lafferty 99]) Limitations: 1.Can’t translate into words not seen in the training queries 2.Computational complexity Training data A simpler and more efficient method for estimating pt(w|u) with higher coverage was proposed in: M. Karimzadehgan and C. Zhai. Estimation of Statistical Translation Models Based on Mutual Information for Ad Hoc Information Retrieval. ACM SIGIR, pages 323-330, 2010 28 Estimation of Translation Model Based on Mutual Information 1. Calculate Mutual information for each pair of two words in the collection (measuring co-occurrences) I(X w; X u ) p ( X w , X u ) log X w { 0 ,1} X u { 0 ,1} p( X w , X u ) p( X w ) p( X u ) presence/absence of word w in a document 2. Normalize mutual information score to obtain a translation probability: p mi ( w | u ) I(X w; X u ) I(X w' ;Xu) w' 29 Computation Detail I(X w; X u ) p ( X w , X u ) log X w 0 ,1 X u 0 , 1 p ( X w 1) Xw D1 D2 D3 …. … DN Xu 0 1 1 0 1 0 0 0 p( X w , X u ) p( X w ) p( X u ) c ( X w 1) N p ( X u 1) c ( X u 1) N N Xw=1 p ( X w 1, X u 1) Xu=1 c ( X w 1, X u 1) N Exploit index to speed up computation 30 Sample Translation Probabilities (AP90) p(w| “everest”) Mutual Information Synthetic Query q p(q|w) q p(q|w) everest 0.1051 everest 0.079 climber 0.0423 climber 0.042 mount 0.0339 climb 0.0365 028 0.0308 mountain 0.0359 expedit 0.0303 mount 0.033 peak 0.0155 reach 0.0312 himalaya 0.01532 expedit 0.0314 nepal 0.015 summit 0.0253 sherpa 0.01431 whittak 0.016 hillari 0.01431 peak 0.0149 31 Regularizing Self-Translation Probability • Self-translation probability can be underestimated p t ( w | u ) p t ( w | w ) An exact match would be counted less than an exact match • Solution: Interpolation with “1.0 self-translation” (1 ) p ( u | u ) w = u pt ( w | u ) wu (1 ) p ( w | u ) = 1 basic query likelihood model = 0 original MI estimate 32 Query Likelihood and Translation Language Model • Document ranking based on query likelihood m |V | log p(q | d ) log p(qi | d ) c( wi , q) log p( wi | d ) i 1 i 1 where, q q1q2 ...qm Document language model • Translation Language Model pt ( w | d ) p t ( w | u ) p (u | d ) w d Do you see any problem? Further Smoothing of Translation Model for Computing Query Likelihood • Linear interpolation (Jelinek-Mercer): p t ( w | d ) (1 )[ p t ( w | u ) p ml ( u | d )] p ( w | C ) ud pml(w|d) • Bayesian interpolation (Dirichlet prior): pt ( w | d ) |d | | d | [ p t ( w | u ) p ml ( u | d )] ud | d | p(w | C ) pml(w|d) 34 Experiment Design • MI vs. Synthetic query estimation – Data Sets: Associated Press (AP90) and San Jose Mercury News (SJMN) + TREC topics 51-100 – Relatively small data sets in order to compare our results with Synthetic queries in [Berger& Lafferty 99]. • MI Translation model vs. Basic query likelihood – Larger Data Sets: TREC7, TREC8 (plus AP90, SJMN) – TREC topics 351-400 for TREC7 and 401-450 for TREC8 • Additional issues – Regularization of self-translation? – Influence of smoothing on translation models? – Translation model + pseudo feedback? 35 Mutual information outperforms synthetic queries in both MAP and P@10 AP90 + queries 51-100, Dirichlet Prior Smoothing MI Syn. Query MI Syn. Query 36 Upper Bound Comparison of Mutual Information and Synthetic Queries Dirichlet Prior Smoothing Data Precision @10 MAP Mutual Info Syn. Query Mutual Info. Syn. Query AP90 0.272* 0.251 0.423 0.404 SJMN 0.2* 0.195 0.28 0.266 JM Smoothing Data Precision @10 MAP Mutual Info Syn. Query Mutual Info. Syn. Query AP90 0.264* 0.25 0.381 0.357 SJMN 0.197* 0.189 0.252 0.267 37 Mutual information translation model outperforms basic query likelihood Data Dir. Prior Smoothing MAP Basic QL MI Trans. Basic QL MI Trans. AP90 0.248 0.272* 0.398 0.423 SJMN 0.195 0.2* 0.266 0.28 TREC7 0.183 0.187* 0.412 0.404 TREC8 0.248 0.249 0.452 0.456 Data JM Smoothing Precision @10 MAP Precision @10 Basic QL MI Trans. Basic QL MI Trans. AP90 0.246 0.264* 0.357 0.381 SJMN 0.188 0.197* 0.252 0.267 TREC7 0.165 0.172 0.354 0.362 TREC8 0.236 0.244* 0.428 0.436 38 Translation model appears to need less collection smoothing than basic QL Translation model Basic query likelihood 39 Translation model and pseudo feedback exploit word co-occurrences differently JM Smoothing Data MAP Precision @10 BL PFB PFB+TM BL PFB PFB+TM AP90 0.246 0.271 0.298 0.357 0.383 0.411 SJMN 0.188 0.229 0.234 0.252 0.316 0.313 TREC7 0.165 0.209 0.222 0.354 0.38 0.384 TREC8 0.236 0.240 0.281 0.428 0.4 0.452 p ( w | q ) log p t ( w | d ) p ( w | q ) Query model from pseudo FB Smoothed Translation Model 40 Regularization of self-translation is beneficial AP Data Set, Dirichlet Prior 41 Summary • Statistical Translation language model are effective for bridging the vocabulary gap. • Mutual information is more effective and more efficient than synthetic queries for estimating translation model probabilities. • Regularization of self-translation is beneficial • Translation model outperforms basic query likelihood on small and large collections and is more robust • Translation model and pseudo feedback exploit word cooccurrences differently and can be combined to further improve performance 42 References • [1] A. Berger and J. Lafferty. Information Retrieval as Statistical Translation. ACM SIGIR, pages 222–229, 1999. • [2] P. Brown, S. A. D. Pietra, V. J. D. Pietra, and R. Mercer. The mathematics of statistical machine translation: Parameter estimation. Computational Linguistics, 19(2):263–311, 1993. • [3] M. Karimzadehgan and C. Zhai. Estimation of Statistical Translation Models Based on Mutual Information for Ad Hoc Information Retrieval. ACM SIGIR, pages 323-330, 2010. 43

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# A General Optimization Framework for Smoothing …