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, Statistics
University of Illinois, Urbana-Champaign
http://www-faculty.cs.uiuc.edu/~czhai, czhai@cs.uiuc.edu
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
1
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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
2
More about statistical
language models in general
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
3
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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
4
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)
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
5
Source-Channel Framework
(Model of Communication System [Shannon 48] )
Source
X
Noisy
Channel
Transmitter
(encoder)
P(X)
Y
Receiver
(decoder)
Destination
X’
P(X|Y)=?
P(Y|X)
Xˆ  arg max p( X | Y )  arg max p(Y | X ) p( X ) (Bayes Rule)
X
X
When X is text, p(X) is a language model
Many Examples:
Speech recognition:
Machine translation:
OCR Error Correction:
Information Retrieval:
Summarization:
X=Word sequence
X=English sentence
X=Correct word
X=Document
X=Summary
2008 © ChengXiang Zhai
Y=Speech signal
Y=Chinese sentence
Y= Erroneous word
Y=Query
Y=Document
Dragon Star Lecture at Beijing University, June 21-30, 2008
6
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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
7
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(w )+…+p(w )=1 (N is voc. size)
• Essentially a multinomial distribution over words
• A piece of text can be regarded as a sample
1
N
drawn according to this word distribution
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
8
Text Generation with Unigram LM
(Unigram) Language Model 
p(w| )
Sampling
Document d
…
Topic 1:
Text mining
text 0.2
mining 0.1
assocation 0.01
clustering 0.02
…
food 0.00001
…
Text mining
paper
Given , p(d| ) varies according to d
…
Topic 2:
Health
food 0.25
nutrition 0.1
healthy 0.05
diet 0.02
Food nutrition
paper
…
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
9
Estimation of Unigram LM
(Unigram) Language Model  Estimation
Document
p(w| )=?
…
10/100
5/100
3/100
3/100
1/100
text 10
mining 5
association 3
database 3
algorithm 2
…
query 1
efficient 1
text ?
mining ?
assocation ?
database ?
…
query ?
…
Total #words
=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…
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
10
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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
11
Zipf’s Law
• rank * frequency  constant
Word
Freq.
F ( w) 
C
r ( w)
  1, C  0.1
Most useful words (Luhn 57)
Is “too rare” a problem?
Biggest
data structure
(stop words)
Word Rank (by Freq)
Generalized Zipf’s law:
C
F ( w) 
[r ( w)  B]
2008 © ChengXiang Zhai
Applicable in many domains
Dragon Star Lecture at Beijing University, June 21-30, 2008
12
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]
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
13
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 ...
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
14
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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
15
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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
16
Systematic Review of
Language Models for IR
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
17
Representative LMs for IR (up to 2006)
1998
1999
2000
2001
2002
2003
2004
2005 -
Smoothing examined
Bayesian Query likelihood
Zhai & Lafferty 01a
Zaragoza et al. 03.
Ponte & Croft 98
Hiemstra & Kraaij 99; Parameter Theoretical justification URL prior
Time prior
sensitivity Lafferty & Zhai 01a,01b Kraaij et al. 02
Miller et al. 99
Li & Croft 03
Two-stage LMs
Ng 00
Zhai & Lafferty 02
Query likelihood scoring
Basic LM (Query Likelihood)
Improved
Basic LM
Beyond unigram
Song & Croft 99
Translation model
Berger & Lafferty 99
Relevance LM
Parsimonious LM
Rel. Query FB Hiemstra et al. 04
Lavrenko & Croft 01
Nallanati et al 03
Model-based FB
Zhai & Lafferty 01b
Markov-chain query model
Lafferty & Zhai 01b
Query/Rel
Model &
Feedback
Special
IR tasks
Term-specific smoothing
Cluster LM
Cluster smoothing
Hiemstra 02
Kurland & Lee 04 Liu & Croft 04; Tao et al. 06
Title LM
Concept Likelihood Dependency LM Thesauri
Jin et al. 02
Srikanth & Srihari 03
Cao et al. 05
Gao et al. 04
Xu & Croft 99
Dissertations
Ponte 98
Lavrenko et al. 02 Ogilvie & Callan 03
Xu et al. 01
Zhang et al. 02
Zhai et al. 03
Cronen-Townsend et al. 02
Si et al. 02
Hiemstra 01
Berger 01
2008 © ChengXiang Zhai
Zhai 02
Pesudo Query
Kurland et al. 05
Query expansion
Bai et al. 05
Rebust Est.
Tao & Zhai 06
Shen et al. 05
Tan et al. 06
Kurland & Lee 05
Lavrenko 04
Kraaij 04
Srikanth 04
Dragon Star Lecture at Beijing University, June 21-30, 2008
Tao 06
Kurland 06
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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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
19
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….
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
20
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]
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
21
Review of LM for IR:
Part 1. Basic Language Modeling
Approach
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
22
The Basic LM Approach
[Ponte & Croft 98]
Document
Language Model
…
Text mining
paper
text ?
mining ?
assocation ?
clustering ?
…
food ?
…
Food nutrition
paper
…
Query =
“data mining algorithms”
?
Which model would most
likely have generated
this query?
food ?
nutrition ?
healthy ?
diet ?
…
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
23
Ranking Docs by Query Likelihood
Doc LM
Query likelihood
d1
 d1
p(q| d1)
d2
 d2
p(q| d2)
q
p(q| dN)
dN
dN
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
24
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
|V |
p(q  ( x1 ,..., x|V | ) | d )  p( wi  xi | d ) 
i 1
•
|V |

i 1, xi 1
– Parameters: {p(wi=1|d), p(wi=0|d)}
p( wi  1| d )
|V |

i 1, xi  0
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
|V |
m a query word
p(q  q1...qm | d )  p(q j | d )   p ( wi | d )c ( wi ,q )
j 1
i 1
– c(wi,q) is the count of word wi in query q
– Parameters: {p(wi|d)}
p(w1|d)+… p(w|v||d) = 1
[Ponte & Croft 98] uses Multi-Bernoulli; most other work uses multinomial
Multinomial seems to work better [Song & Croft 99, McCallum & Nigam 98,Lavrenko 04]
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
25
Retrieval as LM Estimation
• Document ranking based on query likelihood
m
|V |
i 1
i 1
log p(q | d )   log p(qi | d )   c( wi , q) log p( wi | d )
where, q  q1q2 ...qm
Document language model
• Retrieval problem  Estimation of p(wi|d)
• Smoothing is an important issue, and
distinguishes different approaches
• Many smoothing methods are available
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
26
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 exist
See [Chen & Goodman 98] and other publications in speech recognition…
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
27
Comparison of Three Methods
[Zhai & Lafferty 01a]
Query T yp e
Title
Long
Jelinek- M ercer
0.228
0 .2 78
D irichlet
0 .2 56
0.276
A b s. D isco unt ing
0.237
0.260
Relative performance of JM, Dir. and AD
precision
0.3
TitleQuery
0.2
LongQuery
0.1
0
JM
DIR
AD
Method
Comparison is performed on a variety of test collections
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
28
The Dual-Role of Smoothing [Zhai & Lafferty 02]
long
Verbose
queries
Keyword
queries
long
short
short
Why does query type affect smoothing sensitivity?
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
29
Another Reason for Smoothing
Content words
Query = “the
pDML(w|d1):
0.04
pDML(w|d2):
0.02
algorithms
0.001
0.001
for
0.02
0.01
p( “algorithms”|d1) = p(“algorithm”|d2)
p( “data”|d1) < p(“data”|d2)
p( “mining”|d1) < p(“mining”|d2)
data
0.002
0.003
mining”
0.003
0.004
Intuitively, d2 should
have a higher score,
but p(q|d1)>p(q|d2)…
So we should make p(“the”) and p(“for”) less different for all docs,
and smoothing helps achieve this goal…
After smoothing with p( w | d )  0.1 pDML ( w | d )  0.9 p( w | REF ), p(q | d1)  p(q | d 2)!
Query
P(w|REF)
Smoothed p(w|d1):
Smoothed p(w|d2):
= “the
0.2
0.184
0.182
algorithms
for
0.00001
0.000109
0.000109
0.2
0.182
0.181
2008 © ChengXiang Zhai
data
mining”
0.00001
0.000209
0.000309
0.00001
0.000309
0.000409
Dragon Star Lecture at Beijing University, June 21-30, 2008
30
Two-stage Smoothing [Zhai & Lafferty 02]
Stage-1
Stage-2
-Explain unseen words
-Explain noise in query
-Dirichlet prior(Bayesian) -2-component mixture


Collection LM
P(w|d) = (1-)
c(w,d) +p(w|C)
|d|
+ p(w|U)
+
User background model
Can be approximated by p(w|C)
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
31
Estimating  using leave-one-out
[Zhai & Lafferty 02]
w1
P(w1|d- w1)
log-likelihood
N
l1 (  | C )   c( w, di ) log(
w2
i 1 wV
P(w2|d- w2)
Leave-one-out
c( w, di )  1  p( w | C )
)
| di | 1  
Maximum Likelihood Estimator
...
μˆ  argmax l 1 (μ | C)
μ
wn
Newton’s Method
P(wn|d- wn)
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
32
Why would “leave-one-out” work?
20 word by author1
abc abc ab c d d
abc cd d d
abd ab ab ab ab
cd d e cd e
20 word by author2
abc abc ab c d d
abe cb e f
acf fb ef aff abef
cdc 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…
 doesn’t have to be big
20 1


p(" e " | REF )
20   19 20  
20 0

psmooth (" e " | author 2) 

p(" e " | REF )
20   19 20  
1
19
0
pml (" e " | author 2)
19
pml (" e " | author1) 
psmooth (" e " | author1) 
 must be big! more smoothing
The amount of smoothing is closely related to
the underlying vocabulary size
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
33
Estimating  using Mixture Model
[Zhai & Lafferty 02]
Stage-2
Stage-1
d1

P(w|d1)

(1-)p(w|d1)+ p(w|U)
...
… ...
dN

N

P(w|dN)
1
Query
Q=q1…qm
(1-)p(w|dN)+ p(w|U)
Estimated in stage-1
p (q j | di ) 
c(q j , di )  ˆ p(q j | C )
| di |  ˆ
Maximum Likelihood Estimator
Expectation-Maximization (EM) algorithm
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
34
Automatic 2-stage results
 Optimal 1-stage results [Zhai & Lafferty 02]
Average precision (3 DB’s + 4 query types, 150 topics)
* Indicates significant difference
Collection
AP88-89
WSJ87-92
ZIFF1-2
query
SK
LK
SV
LV
SK
LK
SV
LV
SK
LK
SV
LV
Optimal-JM
20.3%
36.8%
18.8%
28.8%
19.4%
34.8%
17.2%
27.7%
17.9%
32.6%
15.6%
26.7%
Optimal-Dir
23.0%
37.6%
20.9%
29.8%
22.3%
35.3%
19.6%
28.2%
21.5%
32.6%
18.5%
27.9%
Auto-2stage
22.2%*
37.4%
20.4%
29.2%
21.8%*
35.8%
19.9%
28.8%*
20.0%
32.2%
18.1%
27.9%*
Completely automatic tuning of parameters IS POSSIBLE!
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
35
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]
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
36
Review of LM for IR:
Part 2. Advanced Language Modeling
Approaches
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
37
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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
38
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]
Basic translation model p (Q | D, R ) 
m
  p (q | w ) p( w
i 1 w j V
t
i
Translation model
2008 © ChengXiang Zhai
j
j
| D)
Regular doc LM
Dragon Star Lecture at Beijing University, June 21-30, 2008
39
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]
p(Q | D, R) 

p(Q | C ) p(C | D)
CClusters
How likely doc D
belongs to cluster C
Likelihood of Q
given C
Only effective when interpolated with the basic LM scores
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
40
Feedback and Doc/Query Generation
Rel. doc model
Classic Prob. Model O( R  1| Q, D)  P( D | Q, R  1)
P( D | Q, R  0)
NonRel. doc model
Query likelihood
(“Language Model”) O( R  1| Q, D)  P(Q | D, R  1)
(q1,d1,1)
(q1,d2,1)
(q1,d3,1)
(q1,d4,0)
Parameter (q1,d5,0)
Estimation
(q3,d1,1)
(q4,d1,1)
(q5,d1,1)
(q6,d2,1)
(q6,d3,0)
P(D|Q,R=1)
P(D|Q,R=0)
P(Q|D,R=1)
“Rel. query” model
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
Query-based feedback
2008 © ChengXiang Zhai
Doc-based feedback
Dragon Star Lecture at Beijing University, June 21-30, 2008
41
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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
42
•
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])
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
43
Two Alternative Ways of Using LMs
• Classic Probabilistic Model :Doc-Generation as opposed to
Query-generation
O( R  1| Q, D) 
P( D | Q, R  1) P( D | Q, R  1)

P( D | Q, R  0)
P( D)
– 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
score(Q, D)   D(Q ||  D ), essentially  p( w | Q ) log p( w |  D )
wV
– Retrieval is now to estimate query & doc models and feedback
is treated as query LM updating [Lafferty & Zhai 01b; Zhai &
Lafferty 01b]
Both methods outperform the basic LM significantly
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
44
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)
p( w | Q, R)   p( w |  ) p( | Q, R)d   p( w |  ) p( | R) p(Q |  )d
D
D
D



DC
D
D
D
D

m
p( w |  D ) p( D | R) p(Q |  D )   p( w |  D ) p(q j | D )
DC
j 1
– Conditional sampling: p(w,Q)=p(w)p(Q|w)
m
p ( w | Q, R  1)  p( w) p(Q | w)  p( w)  p(qi | D) p( D | w)
i 1 DC
p ( w) 
 p( w | D) p( D)
DC
p( D | w) 
p( w | D) p( D)
p ( w)
2008 © ChengXiang Zhai
Original formula in [Lavranko &Croft 01]
p( D | w) 
p( w | D) p( w)
p ( D)
Dragon Star Lecture at Beijing University, June 21-30, 2008
45
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 cooccurrence 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 pseudofeedback documents [ Tao & Zhai 06]
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
46
Review of LM for IR:
Part 3. KL-divergence retrieval model
and feedback
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
47
Kullback-Leibler (KL) Divergence
Retrieval Model
•
Unigram similarity model
query entropy
(ignored for ranking)
Sim(d ; q)   D(ˆQ || ˆD )
  p( w | ˆQ ) log p(w | ˆD )  ( p( w | ˆQ ) log p(w | ˆQ ))
•
w
w
Retrieval  Estimation of Q and D
sim(q; d )

wi  d
p ( wi |Q ) 0
•
pseen ( wi | d )
ˆ
[ p( wi | Q ) log
]  log  d
 d p( wi | C )
Special case: ˆQ = empirical distribution of q
“query-likelihood”
2008 © ChengXiang Zhai
recovers
Dragon Star Lecture at Beijing University, June 21-30, 2008
48
Feedback as Model Interpolation
(Rocchio for Language Models)
Document D
D
D( Q ||  D )
Query Q
Q
 Q '  (1   ) Q  F
=0
Q '  Q
No feedback
Results
=1
Q '   F
F
Feedback Docs
F={d1, d2 , …, dn}
Generative model
Full feedback
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
49
Generative Mixture Model
Background words

P(w| C)
w
F={d1, …, dn}
P(source)
Topic words
1-
P(w|  )
w
log p( F |  )   c( w; di ) log[(1   ) p( w |  )   p( w | C )]
i
w
Maximum Likelihood
 F  arg max log p(F |  )

 = Noise in feedback documents
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
50
How to Estimate F?
Known
Background
p(w|C)
the 0.2
a 0.1
we 0.01
to 0.02
…
text 0.0001
mining 0.00005
=0.7
…
Unknown
query topic
p(w|F)=?
…
“Text mining”
…
Observed
Doc(s)
ML
Estimator
text =?
mining =?
association =?
word =?
=0.3
Suppose,
we know
the identity of each word ...
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
51
Can We Guess the Identity?
Identity (“hidden”) variable: zi {1 (background), 0(topic)}
zi
the
paper
presents
a
text
mining
algorithm
the
paper
...
1
1
1
1
0
0
0
1
0
...
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?)
p ( zi  1| wi ) 

p
new
( wi |  F ) 
p( zi  1) p( wi | zi  1)
p ( zi  1) p ( wi | zi  1)  p ( zi  0) p ( wi | zi  0)
 p( wi | C )
 p( wi | C )  (1   ) p( wi |  F )
E-step
c( wi , F )(1  p ( n ) ( zi  1 | wi ))
 c(w j , F )(1  p (n) ( z j  1 | w j )) M-step
w j vocabulary
Initially, set p(w| F) to some random value, then iterate …
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
52
An Example of EM Computation
Expectation-Step:
Augmenting data by guessing hidden variables
p( wi | C )
p ( zi  1 | wi ) 
p( wi | C )  (1   ) p ( n ) ( wi |  F )
(n)
p
( n 1)
c( wi , F )(1  p ( n ) ( zi  1 | wi ))
 c(w j , F )(1  p ( n) ( z j  1 | w j ))
( wi |  F ) 
w j vocabulary
Maximization-Step
With the “augmented data”, estimate parameters
using maximum likelihood
Assume =0.5
Word
#
P(w|C)
The
4
0.5
Paper
2
0.3
Text
4
0.1
Mining
2
0.1
Log-Likelihood
Iteration 1
P(w|F) P(z=1)
0.67
0.25
0.55
0.25
0.29
0.25
0.29
0.25
-16.96
2008 © ChengXiang Zhai
Iteration 2
P(w|F) P(z=1)
0.71
0.20
0.68
0.14
0.19
0.44
0.31
0.22
-16.13
Iteration 3
P(w|F) P(z=1)
0.74
0.18
0.75
0.10
0.17
0.50
0.31
0.22
-16.02
Dragon Star Lecture at Beijing University, June 21-30, 2008
53
Example of Feedback Query Model
Trec topic 412: “airport security”
=0.9
W
security
airport
beverage
alcohol
bomb
terrorist
author
license
bond
counter-terror
terror
newsnet
attack
operation
headline
Mixture model approach
p(W|  F )
0.0558
0.0546
0.0488
0.0474
0.0236
0.0217
0.0206
0.0188
0.0186
0.0173
0.0142
0.0129
0.0124
0.0121
0.0121
Web database
Top 10 docs
2008 © ChengXiang Zhai
=0.7
W
the
security
airport
beverage
alcohol
to
of
and
author
bomb
terrorist
in
license
state
by
p(W|  F )
0.0405
0.0377
0.0342
0.0305
0.0304
0.0268
0.0241
0.0214
0.0156
0.0150
0.0137
0.0135
0.0127
0.0127
0.0125
Dragon Star Lecture at Beijing University, June 21-30, 2008
54
Model-based feedback
Improves over Simple LM [Zhai & Lafferty 01b]
collection
AvgPr
0.21
0.296
InitPr
0.617
0.591
3067/4805
3888/4805
AvgPr
0.256
0.282
InitPr
0.729
0.707
2853/4728
3160/4728
AvgPr
0.281
0.306
InitPr
0.742
0.732
Recall
1755/2279
1758/2279
AP88-89 Recall
TREC8 Recall
WEB
Simple LM Mixture
Improv.
pos +41%
pos -4%
pos +27%
pos +10%
pos -3%
pos +11%
pos +9%
pos -1%
pos +0%
Div.Min.
Improv.
0.295
pos +40%
0.617
pos +0%
3665/4805 pos +19%
0.269
pos +5%
0.705
pos -3%
3129/4728 pos +10%
0.312
pos +11%
0.728
pos -2%
1798/2279 pos +2%
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)
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
55
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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
56
Review of LM for IR:
Part 4. Language models for special
retrieval tasks
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
57
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]
English
m
p(Q | D, R)   [ p(qi | REF )  (1   )
i 1
English

cVChinese
Chinese word
p(c | D) ptrans (qi | c)]
Translation
model
Chinese
• Cross-lingual p(D|Q,R) [Lavrenko et al 02]
p (c, q1...qm )
p (c | Q , R ) 
p (q1...qm )
Method 1:
Method 2:
p (c, q1...qm ) 
p (c, q1...qm ) 

( M E , M C )M

M C M
Estimate with a
bilingual lexicon
Or
Parallel corpora
Estimate with parallel corpora
m
p ( M E , M C ) p (c | M c ) p (qi | M E )
i 1
m
p ( M C ) p (c | M c ) p (qi | M C )
i 1
2008 © ChengXiang Zhai
p (qi | M C ) 

cVChinese
ptrans (qi | c) p (c | M C )
Dragon Star Lecture at Beijing University, June 21-30, 2008
58
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)
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
59
Structured Document Retrieval
[Ogilvie & Callan 03]
-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
Select Dj and generate a
query word using Dj
D
Title
D1
Abstract
D2
Body-Part1
D3
Body-Part2
Q  q1q2 ...qm
m
p (Q | D, R  1)   p(qi | D, R  1)
…
i 1
m
k
   s ( D j | D, R  1) p(qi | D j , R  1)
i 1 j 1
Dk
“part selection” prob. Serves as weight for Dj
Can be trained using EM
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
60
Personalized/Context-Sensitive
Search
• User information and search context can be used to
[Shen et al. 05, Tan et al. 06]
estimate a better query model
Context-independent Query LM:
ˆQ  arg max p( | Query, Collection)
Context-sensitive Query LM:
ˆQ  arg max p( | Query, User, SearchContext , Collection)
Refinement of this model leads to specific retrieval formulas
Simple 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]
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
61
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]
log p ( D1 |  ,  D2 )   c( w, D1 ) log[ p( w |  D2 )  (1   ) p( w | REF )]
wV
 *  arg max  log p( D1 |  , D )
2
Maximum Likelihood estimator
EM algorithm
•
•
LM for D2
Reference LM
Measure of
redundancy
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]
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
62
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
p( w |  )
clarity (Q)   p(w | Q ) log
w
•
Q
p( w | Collection)
– 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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
63
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:
Rank
O( R  1 | Tmodel:
, C )   p(C | D, R  1)  p( D | T , R  1)
Topic generation
DS
Rank
O( R  1 | T , C ) 
 p(T | D, R  1) 
DS
p(C | D, R  1)
p(C | R  1)

 p(C | D' , R  1) p(C | R  0)
D 'S
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
64
Summary
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
65
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 fullfledged traditional methods (at least, no evidence for beating them)
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
66
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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
67
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
Can LMs consistently (convincingly) outperform traditional methods
without sacrificing efficiency?
•
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 we do much better by going beyond unigram LMs?
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
68
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
How can we learn effectively from past relevance judgments?
•
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 break the document unit in a principled way?
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
69
Challenges and Future Directions (cont.)
• 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
How can we exploit user information and search context to improve search?
•
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
What role can LMs play when combining text with relational data?
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
70
Challenges and Future Directions (cont.)
• Challenge 7: Develop LMs for hypertext retrieval
– Combine LMs with link information
– Modeling and exploiting anchor text
– Develop a unified LM for hypertext search
How can we develop an effective unified retrieval model for Web 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?
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
71
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
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
72
References
[Agichtein & Cucerzan 05] E. Agichtein and S. Cucerzan, Predicting accuracy of extracting information from
unstructured text collections, Proceedings of ACM CIKM 2005. pages 413-420.
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2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
79
Roadmap
• This lecture: systematic review of language models
for IR
• Next lecture: formal retrieval frameworks
2008 © ChengXiang Zhai
Dragon Star Lecture at Beijing University, June 21-30, 2008
80