龙星计划课程 : 信息检索 Statistical Language Models for IR

2008 © ChengXiang Zhai Dragon Star Lecture at Beijing University, June 21-30, 2008 1

龙星计划课程 :信息检索 Statistical Language Models for IR

ChengXiang Zhai (翟成祥 ) Department of Computer Science

Graduate School of Library & Information Science

Institute for Genomic Biology, StatisticsUniversity of Illinois, Urbana-Champaign

http://www-faculty.cs.uiuc.edu/~czhai, [email protected]

http://www.cs.uiuc.edu/


Outline• More about statistical language models in general

• Systematic review of language models for IR– The basic language modeling approach – Advanced language models– KL-divergence retrieval model and feedback– Language models for special retrieval tasks



More about statistical language models in general



What is a Statistical LM?• A probability distribution over word sequences

– p(“Today is Wednesday”) 0.001– p(“Today Wednesday is”) 0.0000000000001– p(“The eigenvalue is positive”) 0.00001

• Context/topic dependent!

• Can also be regarded as a probabilistic mechanism for “generating” text, thus also called a “generative” model



Why is a LM Useful?• Provides a principled way to quantify the

uncertainties associated with natural language

• Allows us to answer questions like:– Given that we see “John” and “feels”, how likely will we see “happy”

as opposed to “habit” as the next word? (speech recognition)

– Given that we observe “baseball” three times and “game” once in a news article, how likely is it about “sports”? (text categorization, information retrieval)

– Given that a user is interested in sports news, how likely would the user use “baseball” in a query? (information retrieval)



Source-Channel Framework(Model of Communication System [Shannon 48] )

Source Transmitter(encoder)

DestinationReceiver(decoder)

NoisyChannel

P(X)P(Y|X)

X Y X’P(X|Y)=?

)()|(maxarg)|(maxargˆ XpXYpYXpXXX

When X is text, p(X) is a language model

(Bayes Rule)

Many Examples: Speech recognition: X=Word sequence Y=Speech signal

Machine translation: X=English sentence Y=Chinese sentenceOCR Error Correction: X=Correct word Y= Erroneous wordInformation Retrieval: X=Document Y=QuerySummarization: X=Summary Y=Document



Basic Issues• Define the probabilistic model

– Event, Random Variables, Joint/Conditional Prob’s

– P(w1 w2 ... wn)=f(1, 2 ,…, m)

• Estimate model parameters– Tune the model to best fit the data and our prior

knowledge i=?

• Apply the model to a particular task– Many applications



The Simplest Language Model(Unigram Model)

• Generate a piece of text by generating each word independently

• Thus, p(w1 w2 ... wn)=p(w1)p(w2)…p(wn)

• Parameters: {p(wi)} p(w1)+…+p(wN)=1 (N is voc. size)

• Essentially a multinomial distribution over words

• A piece of text can be regarded as a sample drawn according to this word distribution



Text Generation with Unigram LM (Unigram) Language Model p(w| )

…text 0.2mining 0.1assocation 0.01clustering 0.02…food 0.00001…

Topic 1:Text mining

…food 0.25nutrition 0.1healthy 0.05diet 0.02…

Topic 2:Health

Document d

Text miningpaper

Food nutritionpaper

Sampling

Given , p(d| ) varies according to d



Estimation of Unigram LM(Unigram) Language Model p(w| )=? Document

text 10mining 5

association 3database 3algorithm 2

…query 1

efficient 1

…text ?mining ?assocation ?database ?…query ?…

Estimation

Total #words=100

10/1005/1003/1003/100

1/100

How good is the estimated model ?

It gives our document sample the highest prob,but it doesn’t generalize well… More about this later…



Empirical distribution of words• There are stable language-independent patterns in

how people use natural languages

• A few words occur very frequently; most occur rarely. E.g., in news articles,– Top 4 words: 10~15% word occurrences– Top 50 words: 35~40% word occurrences

• The most frequent word in one corpus may be rare in another



Zipf’s Law

• rank * frequency constant

WordFreq.

Word Rank (by Freq)

Most useful words (Luhn 57)

Biggestdata structure(stop words)

Is “too rare” a problem?

( ) 1, 0.1( )CF w C

r w

( )[ ( ) ]

CF wr w B

Generalized Zipf’s law: Applicable in many domains



More Sophisticated LMs• N-gram language models

– In general, p(w1 w2 ... wn)=p(w1)p(w2|w1)…p(wn|w1 …wn-1)

– n-gram: conditioned only on the past n-1 words– E.g., bigram: p(w1 ... wn)=p(w1)p(w2|w1) p(w3|w2) …p(wn|wn-1)

• Remote-dependence language models (e.g., Maximum Entropy model)

• Structured language models (e.g., probabilistic context-free grammar)

• Will not be covered in detail in this course. If interested, read [Jelinek 98, Manning & Schutze 99, Rosenfeld 00]



Why Just Unigram Models?• Difficulty in moving toward more complex models

– They involve more parameters, so need more data to estimate (A doc is an extremely small sample)

– They increase the computational complexity significantly, both in time and space

• Capturing word order or structure may not add so much value for “topical inference”

• But, using more sophisticated models can still be expected to improve performance ...



Evaluation of SLMs• Direct evaluation criterion: How well does the model fit the

data to be modeled? – Example measures: Data likelihood, perplexity, cross entropy,

Kullback-Leibler divergence (mostly equivalent)

• Indirect evaluation criterion: Does the model help improve the performance of the task?– Specific measure is task dependent– For retrieval, we look at whether a model helps improve retrieval

accuracy– We hope more “reasonable” LMs would achieve better retrieval

performance



What You Should Know• How the source-channel framework can model many

different problems

• Why unigram LMs seem to be sufficient for IR

• Zipf’s law



Systematic Review of Language Models for IR



Representative LMs for IR (up to 2006)1998 1999 2000 2001 2002 2003

Beyond unigram Song & Croft 99

Smoothing examined Zhai & Lafferty 01a

Bayesian Query likelihoodZaragoza et al. 03.

Theoretical justificationLafferty & Zhai 01a,01b

Two-stage LMsZhai & Lafferty 02

Lavrenko 04Kraaij 04

Zhai 02Dissertations Hiemstra 01Berger 01

Ponte 98

Translation modelBerger & Lafferty 99

Basic LM (Query Likelihood)

URL prior Kraaij et al. 02

Lavrenko et al. 02 Ogilvie & Callan 03Zhai et al. 03

Xu et al. 01 Zhang et al. 02Cronen-Townsend et al. 02

Si et al. 02

Special IR tasks

Xu & Croft 99

2004

Parsimonious LMHiemstra et al. 04

Cluster smoothingLiu & Croft 04; Tao et al. 06

Relevance LM Lavrenko & Croft 01

Dependency LMGao et al. 04

Model-based FBZhai & Lafferty 01b

Rel. Query FBNallanati et al 03

Query likelihood scoring Ponte & Croft 98 Hiemstra & Kraaij 99; Miller et al. 99

ParametersensitivityNg 00

Title LMJin et al. 02

Term-specific smoothingHiemstra 02

Concept Likelihood Srikanth & Srihari 03

Time priorLi & Croft 03

Shen et al. 05

Srikanth 04

Kurland & Lee 05

Pesudo QueryKurland et al. 05

Rebust Est.Tao & Zhai 06

Thesauri Cao et al. 05

Query expansionBai et al. 05

2005 -

Markov-chain query modelLafferty & Zhai 01b

Query/RelModel &

Feedback

Cluster LMKurland & Lee 04Improved

Basic LM

Tan et al. 06

Tao 06Kurland 06



Ponte & Croft’s Pioneering Work [Ponte & Croft 98]

• Contribution 1: – A new “query likelihood” scoring method: p(Q|D) – [Maron and Kuhns 60] had the idea of query likelihood, but didn’t

work out how to estimate p(Q|D)

• Contribution 2:– Connecting LMs with text representation and weighting in IR– [Wong & Yao 89] had the idea of representing text with a

multinomial distribution (relative frequency), but didn’t study the estimation problem

• Good performance is reported using the simple query likelihood method



Early Work (1998-1999)• At about the same time as SIGIR 98, in TREC 7, two groups

explored similar ideas independently: BBN [Miller et al., 99] & Univ. of Twente [Hiemstra & Kraaij 99]

• In TREC-8, Ng from MIT motivated the same query likelihood method in a different way [Ng 99]

• All following the simple query likelihood method; methods differ in the way the model is estimated and the event model for the query

• All show promising empirical results

• Main problems: – Feedback is explored heuristically– Lack of understanding why the method works….



Later Work (1999-)• Attempt to understand why LMs work [Zhai & Lafferty

01a, Lafferty & Zhai 01a, Ponte 01, Greiff & Morgan 03, Sparck Jones et al. 03, Lavrenko 04]

• Further extend/improve the basic LMs [Song & Croft 99, Berger & Lafferty 99, Jin et al. 02, Nallapati & Allan 02, Hiemstra 02, Zaragoza et al. 03, Srikanth & Srihari 03, Nallapati et al 03, Li &Croft 03, Gao et al. 04, Liu & Croft 04, Kurland & Lee 04,Hiemstra et al. 04,Cao et al. 05, Tao et al. 06]

• Explore alternative ways of using LMs for retrieval (mostly query/relevance model estimation) [Xu & Croft 99, Lavrenko & Croft 01, Lafferty & Zhai 01a, Zhai & Lafferty 01b, Lavrenko 04, Kurland et al. 05, Bai et al. 05,Tao & Zhai 06]

• Explore the use of SLMs for special retrieval tasks [Xu & Croft 99, Xu et al. 01, Lavrenko et al. 02, Cronen-Townsend et al. 02, Zhang et al. 02, Ogilvie & Callan 03, Zhai et al. 03, Kurland & Lee 05, Shen et al. 05, Balog et al. 06, Fang & Zhai 07]



Review of LM for IR:

Part 1. Basic Language Modeling Approach



The Basic LM Approach[Ponte & Croft 98]

Document

Text miningpaper

Food nutritionpaper

Language Model

…text ?mining ?assocation ?clustering ?…food ?…

…food ?nutrition ?healthy ?diet ?…

Query = “data mining algorithms”

? Which model would most likely have generated this query?



Ranking Docs by Query Likelihood

d1

d2

dN

qd1

d2

dN

Doc LM

p(q| d1)

p(q| d2)

p(q| dN)

Query likelihood



Modeling Queries: Different Assumptions• Multi-Bernoulli: Modeling word presence/absence

– q= (x1, …, x|V|), xi =1 for presence of word wi; xi =0 for absence

– Parameters: {p(wi=1|d), p(wi=0|d)} p(wi=1|d)+ p(wi=0|d)=1

• Multinomial (Unigram LM): Modeling word frequency– q=q1,…qm , where qj is a query word

– c(wi,q) is the count of word wi in query q

– Parameters: {p(wi|d)} p(w1|d)+… p(w|v||d) = 1

| | | | | |

1 | |1 1, 1 1, 0

( ( ,..., ) | ) ( | ) ( 1| ) ( 0 | )i i

V V V

V i i i ii i x i x

p q x x d p w x d p w d p w d

| |( , )

11 1

( ... | ) ( | ) ( | ) i

Vmc w q

m j ij i

p q q q d p q d p w d

[Ponte & Croft 98] uses Multi-Bernoulli; most other work uses multinomialMultinomial seems to work better [Song & Croft 99, McCallum & Nigam 98,Lavrenko 04]



Retrieval as LM Estimation

• Document ranking based on query likelihood | |

1 1

1 2

log ( | ) log ( | ) ( , ) log ( | )

, ...

Vm

i i ii i

m

p q d p q d c w q p w d

where q q q q

• Retrieval problem Estimation of p(wi|d)

• Smoothing is an important issue, and distinguishes different approaches

• Many smoothing methods are available

Document language model



Which smoothing method is the best?

It depends on the data and the task!

Cross validation is generally used to choose the best method and/or set the smoothing parameters…

For retrieval, Dirichlet prior performs well…

Backoff smoothing [Katz 87] doesn’t work well due to a lack of 2nd-stage smoothing…

Note that many other smoothing methods existSee [Chen & Goodman 98] and other publications in speech recognition…



Comparison of Three Methods[Zhai & Lafferty 01a]

Query Type J elinek-Mercer Dirichlet Abs. DiscountingTitle 0.228 0.256 0.237Long 0.278 0.276 0.260

Relative performance of JM, Dir. and AD

0

0.1

0.2

0.3

JM DIR AD

Method

precision

TitleQuery

LongQuery

Comparison is performed on a variety of test collections



The Dual-Role of Smoothing [Zhai & Lafferty 02]

Verbosequeries

Keywordqueries

Why does query type affect smoothing sensitivity?

long

short

short

long



Query = “the algorithms for data mining”

Another Reason for Smoothing

p( “algorithms”|d1) = p(“algorithm”|d2)p( “data”|d1) < p(“data”|d2)

p( “mining”|d1) < p(“mining”|d2)

So we should make p(“the”) and p(“for”) less different for all docs, and smoothing helps achieve this goal…

Content words

Intuitively, d2 should have a higher score, but p(q|d1)>p(q|d2)…

pDML(w|d1): 0.04 0.001 0.02 0.002 0.003 pDML(w|d2): 0.02 0.001 0.01 0.003 0.004

Query = “the algorithms for data mining”P(w|REF) 0.2 0.00001 0.2 0.00001 0.00001Smoothed p(w|d1): 0.184 0.000109 0.182 0.000209 0.000309Smoothed p(w|d2): 0.182 0.000109 0.181 0.000309 0.000409

)!2|()1|(),|(9.0)|(1.0)|( dqpdqpREFwpdwpdwpwithsmoothingAfter DML



Two-stage Smoothing [Zhai & Lafferty 02]

c(w,d)

|d|P(w|d) =

+p(w|C)

+

Stage-1

-Explain unseen words-Dirichlet prior(Bayesian)

Collection LM

(1-) + p(w|U)

Stage-2

-Explain noise in query-2-component mixture

User background modelCan be approximated by p(w|C)



Estimating using leave-one-out [Zhai & Lafferty 02]

P(w1|d- w1)

P(w2|d- w2)

N

i Vw i

ii d

CwpdwcdwcCl1

1 )1||

)|(1),(log(),()|(

log-likelihood

)ˆ C|(μlargmaxμ 1μ

Maximum Likelihood Estimator

Newton’s Method

Leave-one-outw1

w2

P(wn|d- wn)

wn

...



Why would “leave-one-out” work?

abc abc ab c d dabc cd d d

abd ab ab ab abcd d e cd e

20 word by author1

20 word by author2

abc abc ab c d dabe cb e f

acf fb ef aff abefcdc db ge f s

Suppose we keep sampling and get 10 more words. Which author is likely to

“write” more new words?

Now, suppose we leave “e” out…

1 20 1(" " | 1) (" " | 1) (" " | )19 20 19 200 20 0(" " | 2) (" " | 2) (" " | )

19 20 19 20

ml smooth

ml smooth

p e author p e author p e REF

p e author p e author p e REF

must be big! more smoothing

doesn’t have to be big

The amount of smoothing is closely related to the underlying vocabulary size



Estimating using Mixture Model [Zhai & Lafferty 02]

Query

Q=q1…qm

1

N

...

Maximum Likelihood Estimator Expectation-Maximization (EM) algorithm

P(w|d1)d1

P(w|dN)dN

… ...

Stage-1

(1-)p(w|d1)+ p(w|U)

(1-)p(w|dN)+ p(w|U)

Stage-2

ˆ( , ) ( | )( | )

ˆ| |j i j

j ii

c q d p q Cp q d

d

Estimated in stage-1



Collection query Optimal-JM Optimal-Dir Auto-2stageSK 20.3% 23.0% 22.2%*LK 36.8% 37.6% 37.4%SV 18.8% 20.9% 20.4%LV 28.8% 29.8% 29.2%SK 19.4% 22.3% 21.8%*LK 34.8% 35.3% 35.8%SV 17.2% 19.6% 19.9%LV 27.7% 28.2% 28.8%*SK 17.9% 21.5% 20.0%LK 32.6% 32.6% 32.2%SV 15.6% 18.5% 18.1%LV 26.7% 27.9% 27.9%*

AP88-89

WSJ87-92

ZIFF1-2

Automatic 2-stage results Optimal 1-stage results [Zhai & Lafferty 02]

Average precision (3 DB’s + 4 query types, 150 topics)* Indicates significant difference

Completely automatic tuning of parameters IS POSSIBLE!



Variants of the Basic LM Approach• Different smoothing strategies

– Hidden Markov Models (essentially linear interpolation) [Miller et al. 99]

– Smoothing with an IDF-like reference model [Hiemstra & Kraaij 99]

– Performance tends to be similar to the basic LM approach– Many other possibilities for smoothing [Chen & Goodman 98]

• Different priors– Link information as prior leads to significant improvement of Web

entry page retrieval performance [Kraaij et al. 02] – Time as prior [Li & Croft 03]

– PageRank as prior [Kurland & Lee 05]

• Passage retrieval [Liu & Croft 02]




Part 2. Advanced Language Modeling Approaches



Improving the Basic LM Approach• Capturing limited dependencies

– Bigrams/Trigrams [Song & Croft 99]; Grammatical dependency [Nallapati & Allan 02, Srikanth & Srihari 03, Gao et al. 04]

– Generally insignificant improvement as compared with other extensions such as feedback

• Full Bayesian query likelihood [Zaragoza et al. 03]

– Performance similar to the basic LM approach• Translation model for p(Q|D,R) [Berger & Lafferty 99, Jin et al. 02,Cao et al.

05]

– Address polesemy and synonyms; improves over the basic LM methods, but computationally expensive

• Cluster-based smoothing/scoring [Liu & Croft 04, Kurland & Lee 04,Tao et al. 06]

– Improves over the basic LM, but computationally expensive• Parsimonious LMs [Hiemstra et al. 04]:

– Using a mixture model to “factor out” non-discriminative words



Translation Models • Directly modeling the “translation” relationship

between words in the query and words in a doc

• 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] , or thesauri [Cao et al. 05]

1

( | , ) ( | ) ( | )j

m

t i j jw Vi

p Q D R p q w p w D

Basic translation model

Translation model Regular doc LM



Cluster-based Smoothing/Scoring• Cluster-based smoothing: Smooth a document LM with a

cluster of similar documents [Liu & Croft 04]: improves over the basic LM, but insignificantly

• Document expansion smoothing: Smooth a document LM with the neighboring documents (essentially one cluster per document) [Tao et al. 06] : improves over the basic LM more significantly

• Cluster-based query likelihood: Similar to the translation model, but “translate” the whole document to the query through a set of clusters [Kurland & Lee 04]

( | , ) ( | ) ( | )

C Clusters

p Q D R p Q C p C D

How likely doc D

belongs to cluster C

Only effective when interpolated with the basic LM scores

Likelihood of Q given C



Feedback and Doc/Query Generation

( 1| , ) ( | , 1)O R Q D P Q D R

( | , 1)( 1| , )( | , 0)

P D Q RO R Q DP D Q R

Classic Prob. Model

Query likelihood(“Language Model”)

Rel. doc model

NonRel. doc model

“Rel. query” model

P(D|Q,R=1)

P(D|Q,R=0)

P(Q|D,R=1)

(q1,d1,1)(q1,d2,1)(q1,d3,1)(q1,d4,0)(q1,d5,0)

(q3,d1,1)(q4,d1,1)(q5,d1,1)(q6,d2,1)(q6,d3,0)

ParameterEstimation

Initial retrieval: - query as rel doc vs. doc as rel query - P(Q|D,R=1) is more accurate

Feedback: - P(D|Q,R=1) can be improved for the current query and future doc - P(Q|D,R=1) can also be improved, but

for current doc and future query

Doc-based feedbackQuery-based feedback



Overview of Feedback Techniques • Feedback as machine learning: many possibilities

– Standard ML: Given examples of relevant (and non-relevant) documents, learn how to classify a new document as either “relevant” or “non-relevant”.

– “Modified” ML: Given a query and examples of relevant (and non-relevant) documents, learn how to rank new documents based on relevance

– Challenges: • Sparse data • Censored sample• How to deal with query?

– Modeling noise in pseudo feedback (as semi-supervised learning)

• Feedback as query expansion: traditional IR – Step 1: Term selection– Step 2: Query expansion– Step 3: Query term re-weighting

• Traditional IR is still robust (Rocchio), but ML approaches can potentially be more accurate



Difficulty in Feedback with Query Likelihood

• Traditional query expansion [Ponte 98, Miller et al. 99, Ng 99]

– Improvement is reported, but there is a conceptual inconsistency – What’s an expanded query, a piece of text or a set of terms?

• Avoid expansion– Query term reweighting [Hiemstra 01, Hiemstra 02]

– Translation models [Berger & Lafferty 99, Jin et al. 02]– Only achieving limited feedback

• Doing relevant query expansion instead [Nallapati et al 03]

• The difficulty is due to the lack of a query/relevance model

• The difficulty can be overcome with alternative ways of using LMs for retrieval (e.g., relevance model [Lavrenko & Croft 01] , Query model estimation [Lafferty & Zhai 01b; Zhai & Lafferty 01b])



Two Alternative Ways of Using LMs• Classic Probabilistic Model :Doc-Generation as opposed to

Query-generation

– Natural for relevance feedback– Challenge: Estimate p(D|Q,R=1) without relevance feedback;

relevance model [Lavrenko & Croft 01] provides a good solution

• Probabilistic Distance Model :Similar to the vector-space model, but with LMs as opposed to TF-IDF weight vectors– A popular distance function: Kullback-Leibler (KL) divergence,

covering query likelihood as a special case

– Retrieval is now to estimate query & doc models and feedback is treated as query LM updating [Lafferty & Zhai 01b; Zhai & Lafferty 01b]

( | , 1) ( | , 1)( 1| , )( | , 0) ( )

P D Q R P D Q RO R Q DP D Q R P D

Both methods outperform the basic LM significantly

( , ) ( || ), ( | ) log ( | )Q D Q Dw V

score Q D D essentially p w p w



Relevance Model Estimation[Lavrenko & Croft 01]

• Question: How to estimate P(D|Q,R) (or p(w|Q,R)) without relevant documents?

• Key idea: – Treat query as observations about p(w|Q,R) – Approximate the model space with document models

• Two methods for decomposing p(w,Q)– Independent sampling (Bayesian model averaging)

– Conditional sampling: p(w,Q)=p(w)p(Q|w)1

( | , ) ( | ) ( | , ) ( | ) ( | ) ( | )

( | ) ( | ) ( | ) ( | ) ( | )

D D D D D D D

m

D D D D j DD C D C j

p w Q R p w p Q R d p w p R p Q d

p w p R p Q p w p q

1

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

( | ) ( )( ) ( | ) ( ) ( | )( )

m

iD Ci

D C

p w Q R p w p Q w p w p q D p D w

p w D p Dp w p w D p D p D wp w

( | ) ( )( | )( )

p w D p wp D wp D

Original formula in [Lavranko &Croft 01]



Query Model Estimation[Lafferty & Zhai 01b, Zhai & Lafferty 01b]

• Question: How to estimate a better query model than the ML estimate based on the original query?

• “Massive feedback”: Improve a query model through co-occurrence pattern learned from – A document-term Markov chain that outputs the query

[Lafferty & Zhai 01b]– Thesauri, corpus [Bai et al. 05,Collins-Thompson & Callan 05]

• Model-based feedback: Improve the estimate of query model by exploiting pseudo-relevance feedback– Update the query model by interpolating the original query

model with a learned feedback model [ Zhai & Lafferty 01b] – Estimate a more integrated mixture model using pseudo-

feedback documents [ Tao & Zhai 06]




Part 3. KL-divergence retrieval model and feedback



Kullback-Leibler (KL) Divergence Retrieval Model

• Unigram similarity model

• Retrieval Estimation of Q and D

• Special case: = empirical distribution of q recovers “query-likelihood”

ˆ ˆ( ; ) ( || )ˆ ˆ ˆ ˆ( | ) log ( | ) ( ( | ) log ( | ))

Q D

Q D Q Qw w

Sim d q D

p w p w p w p w

query entropy(ignored for ranking)

Q̂

( | ) 0

( | )ˆ( ; ) [ ( | ) log ] log( | )

ii Q

seen ii Q d

w d d ip w

p w dsim q d p wp w C



Feedback as Model Interpolation(Rocchio for Language Models)

Query Q

D

)||( DQD

Document DResults

Feedback Docs F={d1, d2 , …, dn}

FQQ )1('

Generative model

Q

F=0

No feedbackFQ '

=1

Full feedback

QQ '



Generative Mixture Model

w

w

F={d1, …, dn}

log ( | ) ( ; ) log[(1 ) ( | ) ( | )]ii w

p F c w d p w p w C )|(logmaxarg

FpF Maximum Likelihood

P(w| )

P(w| C)

1-

P(source)

Background words

Topic words

= Noise in feedback documents



How to Estimate F?

the 0.2a 0.1we 0.01to 0.02…text 0.0001mining 0.00005…

KnownBackground

p(w|C)

…text =? mining =? association =?word =? …

Unknownquery topicp(w|F)=?

“Text mining”

=0.7

=0.3

ObservedDoc(s)

Suppose, we know the identity of each word ...

MLEstimator



Can We Guess the Identity?

Identity (“hidden”) variable: zi {1 (background), 0(topic)}

thepaperpresentsatextminingalgorithmthepaper...

zi

111100010...

Suppose the parameters are all known, what’s a reasonable guess of zi? - depends on (why?) - depends on p(w|C) and p(w|F) (how?)

( 1) ( | 1)( 1| )

( 1) ( | 1) ( 0) ( | 0)( | )

( | ) (1 ) ( | )

i i ii i

i i i i i i

i

i i F

p z p w zp z w

p z p w z p z p w zp w C

p w C p w

E-step

Initially, set p(w| F) to some random value, then iterate …

M-step

vocabularywjj

nj

iin

iFi

new

j

wzpFwcwzpFwcwp

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

)(



An Example of EM Computation

Iteration 1 Iteration 2 Iteration 3 Word # P(w|C) P(w|F) P(z=1) P(w|F) P(z=1) P(w|F) P(z=1)

The 4 0.5 0.25 0.67 0.20 0.71 0.18 0.74 Paper 2 0.3 0.25 0.55 0.14 0.68 0.10 0.75 Text 4 0.1 0.25 0.29 0.44 0.19 0.50 0.17 Mining 2 0.1 0.25 0.29 0.22 0.31 0.22 0.31

Log-Likelihood -16.96 -16.13 -16.02

Assume =0.5

Expectation-Step:Augmenting data by guessing hidden variables

Maximization-Step With the “augmented data”, estimate parameters

using maximum likelihood

vocabularywjj

nj

iin

iFi

n

Fin

i

iii

n

j

wzpFwcwzpFwcwp

wpCwpCwpwzp

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

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

)(

)()1(

)()(



Example of Feedback Query Model

W p(W| )security 0.0558airport 0.0546

beverage 0.0488alcohol 0.0474bomb 0.0236

terrorist 0.0217author 0.0206license 0.0188bond 0.0186

counter-terror 0.0173terror 0.0142

newsnet 0.0129attack 0.0124

operation 0.0121headline 0.0121

Trec topic 412: “airport security”

W p(W| )the 0.0405

security 0.0377airport 0.0342

beverage 0.0305alcohol 0.0304

to 0.0268of 0.0241

and 0.0214author 0.0156bomb 0.0150

terrorist 0.0137in 0.0135

license 0.0127state 0.0127

by 0.0125

=0.9 =0.7

FF

Mixture model approach

Web database

Top 10 docs



Model-based feedback Improves over Simple LM [Zhai & Lafferty 01b]

Simple LM Mixture Improv. Div.Min. Improv.AvgPr 0.21 0.296 pos +41% 0.295 pos +40%InitPr 0.617 0.591 pos -4% 0.617 pos +0%Recall 3067/4805 3888/4805 pos +27% 3665/4805 pos +19%AvgPr 0.256 0.282 pos +10% 0.269 pos +5%InitPr 0.729 0.707 pos -3% 0.705 pos -3%Recall 2853/4728 3160/4728 pos +11% 3129/4728 pos +10%AvgPr 0.281 0.306 pos +9% 0.312 pos +11%InitPr 0.742 0.732 pos -1% 0.728 pos -2%Recall 1755/2279 1758/2279 pos +0% 1798/2279 pos +2%

collection

AP88-89

TREC8

WEB

Translation models, Relevance models, and Feedback-based query models have all been shown to improve performance significantly over the simple LMs (Parameter tuning is necessary in many cases, but see

[Tao & Zhai 06] for “parameter-free” pseudo feedback)



What Should You Know

• The KL-divergence retrieval formula as a generalization of the query likelihood method

• How the mixture model for feedback works

• Know how to estimate the simple mixture model using EM




Part 4. Language models for special retrieval tasks



Cross-Lingual IR • Use query in language A (e.g., English) to retrieve

documents in language B (e.g., Chinese)

• Cross-lingual p(Q|D,R) [Xu et al 01]

• Cross-lingual p(D|Q,R) [Lavrenko et al 02]

1

( | , ) [ ( | ) (1 ) ( | ) ( | )]Chinese

m

i trans ic Vi

p Q D R p q REF p c D p q c

English Chinese

English Chinese word

1

1

1( , ) 1

11

( , ... )( | , )

( ... )

( , ... ) ( , ) ( | ) ( | )

( , ... ) ( ) ( | ) ( | ) ( | ) ( | ) ( | )

E C

C Chinese

m

m

m

m E C c i EM M M i

m

m C c i C i C trans i CM M c Vi

p c q qp c Q R

p q q

p c q q p M M p c M p q M

p c q q p M p c M p q M p q M p q c p c M

Method 1:

Method 2:

Translation model

Estimate with a bilingual lexicon

Or Parallel corpora

Estimate with parallel corpora



Distributed IR• Retrieve documents from multiple collections

• The task is generally decomposed into two subtasks: Collection selection and result fusion

• Using LMs for collection selection [Xu & Croft 99, Si et al. 02]

– Treat collection selection as “retrieving collections” as opposed to “documents”

– Estimate each collection model by maximum likelihood estimate [Si et al. 02] or clustering [Xu & Croft 99]

• Using LMs for result fusion [ Si et al. 02]

– Assume query likelihood scoring for all collections, but on each collection, a distinct reference LM is used for smoothing

– Adjust the bias score p(Q|D,Collection) to recover the fair score p(Q|D)



1 2

1

11

...

( | , 1) ( | , 1)

( | , 1) ( | , 1)

m

m

ii

m k

j i jji

Q q q q

p Q D R p q D R

s D D R p q D R

Structured Document Retrieval[Ogilvie & Callan 03]

Title

Abstract

Body-Part1

Body-Part2

…

D

D1

D2

D3

Dk

-Want to combine different parts of a document with appropriate weights-Anchor text can be treated as a “part” of a document- Applicable to XML retrieval

“part selection” prob. Serves as weight for Dj

Can be trained using EM

Select Dj and generate a query word using Dj



Personalized/Context-Sensitive Search

[Shen et al. 05, Tan et al. 06]

• User information and search context can be used to estimate a better query model

ˆ arg max ( | , )Q p Query Collection

Refinement of this model leads to specific retrieval formulasSimple models often end up interpolating many unigram language

models based on different sources of evidence, e.g., short-term search history [Shen et al. 05] or long-term search history [Tan et al. 06]

ˆ arg max ( | , , , )Q p Query User SearchContext Collection

Context-independent Query LM:

Context-sensitive Query LM:



Modeling Redundancy• Given two documents D1 and D2, decide how redundant D1 (or D2) is

w.r.t. D2 (or D1)

• Redundancy of D1 “to what extent can D1 be explained by a model estimated based on D2”

• Use a unigram mixture model [Zhai 02]

• See [Zhang et al. 02] for a 3-component redundancy model

• Along a similar line, we could measure document similarity in an asymmetric way [Kurland & Lee 05]

2 2

2

1 1

*1

log ( | , ) ( , ) log[ ( | ) (1 ) ( | )]

arg max log ( | , )

D Dw V

D

p D c w D p w p w REF

p D

Maximum Likelihood estimatorEM algorithm

Reference LMLM for D2

Measure of redundancy



Predicting Query Difficulty [Cronen-Townsend et al. 02]

• Observations:– Discriminative queries tend to be easier– Comparison of the query model and the collection model can

indicate how discriminative a query is

• Method:– Define “query clarity” as the KL-divergence between an

estimated query model or relevance model and the collection LM

– An enriched query LM can be estimated by exploiting pseudo feedback (e.g., relevance model)

• Correlation between the clarity scores and retrieval performance is found

( | )( ) ( | ) log

( | )Q

Qw

p wclarity Q p w

p w Collection



Expert Finding [Balog et al. 06, Fang & Zhai 07]

• Task: Given a topic T, a list of candidates {Ci} , and a collection of support documents S={Di}, rank the candidates according to the likelihood that a candidate C is an expert on T.

• Retrieval analogy:– Query = topic T– Document = Candidate C– Rank according to P(R=1|T,C)– Similar derivations to those on slides 55-56, 64 can be made

• Candidate generation model:

• Topic generation model:

SD

RankRTDpRDCpCTRO )1,|()1,|(),|1(

)0|()1|(

)1,'|()1,|()1,|(),|1(

'

RCpRCp

RDCpRDCpRDTpCTRO

SDSD

Rank



Summary



SLMs vs. Traditional IR• Pros:

– Statistical foundations (better parameter setting)– More principled way of handling term weighting – More powerful for modeling subtopics, passages,..– Leverage LMs developed in related areas – Empirically as effective as well-tuned traditional models with

potential for automatic parameter tuning

• Cons:– Lack of discrimination (a common problem with generative models)– Less robust in some cases (e.g., when queries are semi-structured)– Computationally complex– Empirically, performance appears to be inferior to well-tuned full-

fledged traditional methods (at least, no evidence for beating them)



What We Have Achieved So Far• Framework and justification for using LMs for IR

• Several effective models are developed – Basic LM with Dirichlet prior smoothing is a reasonable baseline– Basic LM with informative priors often improves performance – Translation model handles polysemy & synonyms– Relevance model incorporates LMs into the classic probabilistic IR

model– KL-divergence model ties feedback with query model estimation – Mixture models can model redundancy and subtopics

• Completely automatic tuning of parameters is possible

• LMs can be applied to virtually any retrieval task with great potential for modeling complex IR problems



Challenges and Future Directions• Challenge 1: Establish a robust and effective LM that

– Optimizes retrieval parameters automatically– Performs as well as or better than well-tuned traditional retrieval

methods with pseudo feedback– Is as efficient as traditional retrieval methods

• Challenge 2: Demonstrate consistent and substantial improvement by going beyond unigram LMs– Model limited dependency between terms – Derive more principled weighting methods for phrases

Can LMs consistently (convincingly) outperform traditional methods without sacrificing efficiency?

Can we do much better by going beyond unigram LMs?



Challenges and Future Directions (cont.)

• Challenge 3: Develop LMs that can support “life-time learning” – Develop LMs that can improve accuracy for a current query

through learning from past relevance judgments– Support collaborative information retrieval

• Challenge 4: Develop LMs that can model document structures and subtopics– Recognize query-specific boundaries of relevant passages– Passage-based/subtopic-based feedback – Combine different structural components of a document

How can we learn effectively from past relevance judgments?

How can we break the document unit in a principled way?




• Challenge 5: Develop LMs to support personalized search– Infer and track a user’s interests with LMs– Incorporate user’s preferences and search context in retrieval – Customize/organize search results according to user’s

interests

• Challenge 6: Generalize LMs to handle relational data– Develop LMs for semi-structured data (e.g., XML)– Develop LMs to handle structured queries– Develop LMs for keyword search in relational databases

How can we exploit user information and search context to improve search?

What role can LMs play when combining text with relational data?




• Challenge 7: Develop LMs for hypertext retrieval– Combine LMs with link information – Modeling and exploiting anchor text – Develop a unified LM for hypertext search

• Challenge 8: Develop LMs for retrieval with complex information needs, e.g., – Subtopic retrieval – Readability constrained retrieval– Entity retrieval (e.g. expert search)

How can we exploit LMs to develop models for complex retrieval tasks?

How can we develop an effective unified retrieval model for Web search?



What You Should Know• General picture of language models for IR

• The KL-divergence retrieval formula as a generalization of the query likelihood method

• How the mixture model for feedback works

• Know how to estimate the simple mixture model using EM



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Roadmap• This lecture: systematic review of language models

for IR

• Next lecture: formal retrieval frameworks
