Transcript ACM SIGIR 2005 Tutorial - University of Illinois at Urbana

Statistical Language Models
for Information Retrieval
Tutorial at NAACL HLT 2007
April 22, 2007
ChengXiang Zhai
Department of Computer Science
University of Illinois, Urbana-Champaign
http://www-faculty.cs.uiuc.edu/~czhai
[email protected]
Goal of the Tutorial
• Introduce the emerging area of applying statistical
language models (SLMs) to information retrieval
(IR).
• Targeted audience:
– IR practitioners who are interested in acquiring
advanced modeling techniques
– IR researchers who are looking for new research
problems in IR models
– SLM experts who are interested in applying SLMs to
IR
• Accessible to anyone with basic knowledge of
probability and statistics
© ChengXiang Zhai, 2007
2
Scope of the Tutorial
• What will be covered
– Brief background on IR and SLMs
– Review of recent applications of unigram SLMs in IR
– Details of some specific methods that are either empirically
effective or theoretically important
– A framework for systematically exploring SLMs in IR
– Outstanding research issues in applying SLMs to IR
• What will not be covered
–
–
–
–
See any IR textbook
e.g., [Baeza-Yates & Ribeiro-Neto 99,
Traditional IR methods
Grossman & Frieder 04, Manning et al. 07]
Implementation of IR systems
See [Witten et al. 99]
Discussion of high-order or other complex SLMs
Application of SLMs in supervised learning
See [Manning & Schutze 99]
E.g., TDT, Text Categorization….
and [Jelinek 98]
See publications in Machine Learning, Information Retrieval, and Natural Language Processing
© ChengXiang Zhai, 2007
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Tutorial Outline
1. Introduction
2. The Basic Language Modeling Approach
3. More Advanced Language Models
4. Language Models for Special Retrieval Tasks
5. A General Framework for Applying SLMs to IR
6. Summary
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Part 1: Introduction
1. Introduction
We are here
-
Information Retrieval (IR)
-
Statistical Language Models (SLMs)
-
Applications of SLMs to IR
2. The Basic Language Modeling Approach
3. More Advanced Language Models
4. Language Models for Special Retrieval Tasks
5. A General Framework for Applying SLMs to IR
6. Summary
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What is Information Retrieval (IR)?
• Narrow sense (= ad hoc text retrieval)
– Given a collection of text documents (information items)
– Given a text query from a user (information need)
– Retrieve relevant documents from the collection
• A broader sense of IR may include
– Retrieving non-textual information (e.g., images)
– Other tasks (e.g., filtering, categorization or summarization)
• In this tutorial, IR  ad hoc text retrieval
• Ad hoc text retrieval is fundamental to IR and has
many applications (e.g., search engines, digital
libraries, …)
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Formalization of IR Tasks
• Vocabulary V={w1, w2, …, wN} of language
• Query q = q1,…,qm, where qi  V
• Document di = di1,…,dimi, where dij  V
• Collection C= {d1, …, dk}
• Set of relevant documents R(q)  C
– Generally unknown and user-dependent
– Query is a “hint” on which doc is in R(q)
• Task =
compute R’(q), an “approximate R(q)”
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Computing R’(q): Doc Selection vs. Ranking
R(q)={dC|f(d,q)=1}, where f(d,q) {0,1}
is an indicator function (classifier)
True R(q)
+ +- - + - + +
--- ---
1
Doc Selection
f(d,q)=?
0
Doc Ranking
f(d,q)=?
R(q) = {dC|f(d,q)>}, where f(d,q)  is a
ranking function;  is a cutoff implicitly set by the user
© ChengXiang Zhai, 2007
+ +- + ++
R’(q)
- -- - - + - 0.98 d1 +
0.95 d2 +
0.83 d3 0.80 d4 +
0.76 d5 0.56 d6 0.34 d7 0.21 d8 +
0.21 d9 -
R’(q)
=0.77
8
Problems with Doc Selection
• The classifier is unlikely accurate
– “Over-constrained” query (terms are too specific):
no relevant documents found
– “Under-constrained” query (terms are too general):
over delivery
– It is extremely hard to find the right position
between these two extremes
• Even if it is accurate,
all relevant documents are
not equally relevant
• Relevance is a matter of degree!
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Ranking is often preferred
•
A user can stop browsing anywhere, so the
boundary/cutoff is controlled by the user
– High recall users would view more items
•
•
•
•
– High precision users would view only a few
Theoretical justification: Probability Ranking Principle
[Robertson 77], Risk Minimization [Zhai 02, Zhai & Lafferty 06]
The retrieval problem is now reduced to defining a
ranking function f, such that, for all q, d1, d2,
f(q,d1) > f(q,d2) iff p(Relevant|q,d1) >p(Relevant|q,d2)
Function f is an operational definition of relevance
Most IR research is centered on finding a good f…
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Two Well-Known Traditional
Retrieval Formulas [Singhal 01]
Key retrieval heuristics:
TF (Term Frequency)
IDF (Inverse Doc Freq.)
+
Length normalization
[Sparck Jones 72, Salton & Buckley 88,
Singhal et al. 96, Robertson & Walker 94,
Fang et al. 04]
[
]
Other heuristics:
Stemming
Stop word removal
Phrases
Typo
(k1  1)tf
dl
k1 (1  b  b
)  tf
avdl
© ChengXiang Zhai, 2007
Similar quantities will
occur in the LMs…
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Feedback in IR
Query
Updated
query
Retrieval
Engine
Results:
d1 3.5
d2 2.4
…
dk 0.5
...
User
Judgments:
Document
d1 +
collection
d2 +
d3 +
Assume top 10 docs …
dk are relevant
...
Pseudo feedback
Judgments:
top 10 d +
1
d2 d3 +
…
dk ...
Feedback
Learn from
Examples
Relevance feedback
© ChengXiang Zhai, 2007
User judges documents
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Feedback in IR (cont.)
• An essential component in any IR method
• Relevance feedback is always desirable, but a user
may not be willing to provide explicit judgments
• Pseudo/automatic feedback is always possible, and
often improves performance on average through
– Exploiting word co-occurrences
– Enriching a query with additional related words
– Indirectly addressing issues such as ambiguous
words and synonyms
• Implicit feedback is a good compromise
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Evaluation of Retrieval Performance
Total # relevant docs = 8
As a SET of results
1. d1 
2. d2 
3. d3 
4. d4 
5. d5 
6. d6 
7. d7 
8. d8 
9. d9 
10. d10 
precision
As a ranked list
PR-curve
1.0
x
x
x
How do we compare different rankings?
A
A>C
B>C
But is A>B?
C
B
0.0
x
recall
1.0
Summarize a ranking with a single number
Which is the best?
0.0
# relret
4

 0.4
# retrieved 10
# relret
4
recall 
  0.5
# relevant 8
precision 
1 k
AvgPrec   pi
k i 1
k is the total # of rel docs
pi = prec at the rank where the i-th rel doc is retrieved
pi=0 if the i-th rel doc is not retrieved
AvgPrec = (1/1+2/2+3/4+4/10+0+0+0+0)/8=0.394
Avg. Prec. is sensitive to the position of each rel doc!
Alternatives: cumulated gains [Jarvelin & Kekalainen 02]
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Part 1: Introduction (cont.)
1. Introduction
-
Information Retrieval (IR)
-
Statistical Language Models (SLMs)
-
Application of SLMs to IR
We are here
2. The Basic Language Modeling Approach
3. More Advanced Language Models
4. Language Models for Special Retrieval Tasks
5. A General Framework for Applying SLMs to IR
6. Summary
© ChengXiang Zhai, 2007
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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
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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)
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Source-Channel Framework
(Model of Communication System [Shannon 48] )
Source
X
Transmitter
(encoder)
P(X)
Noisy
Channel
Y
Receiver
(decoder)
Destination
X’
P(X|Y)=?
P(Y|X)
Xˆ  argmax p( X | Y )  argmax 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
© ChengXiang Zhai, 2007
Y=Speech signal
Y=Chinese sentence
Y= Erroneous word
Y=Query
Y=Document
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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
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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
…
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Estimation of Unigram LM
(Unigram) Language Model  Estimation
Document
p(w| )=?
…
10/100
5/100
3/100
3/100
1/100
text ?
mining ?
assocation ?
database ?
…
query ?
…
text 10
mining 5
association 3
database 3
algorithm 2
…
query 1
efficient 1
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…
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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 tutorial. If
interested, read [Jelinek 98, Manning & Schutze 99, Rosenfeld 00]
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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 ...
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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
© ChengXiang Zhai, 2007
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Part 1: Introduction (cont.)
1. Introduction
-
Information Retrieval (IR)
-
Statistical Language Models (SLMs)
-
Application of SLMs to IR
We are here
2. The Basic Language Modeling Approach
3. More Advanced Language Models
4. Language Models for Special Retrieval Tasks
5. A General Framework for Applying SLMs to IR
6. Summary
© ChengXiang Zhai, 2007
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Representative LMs for IR
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
Query/Rel
Model &
Feedback
Special
IR tasks
Xu & Croft 99
Dissertations
Ponte 98
Cluster smoothing
Term-specific smoothing
Cluster LM
04; Tao et al. 06
Hiemstra 02
Kurland & Lee 04 Liu & Croft
Thesauri
Title LM
Concept Likelihood Dependency LM Cao et al. 05
LDA
Jin et al. 02
Srikanth & Srihari 03
Gao et al. 04
Wei & Croft 06
Relevance LM
Parsimonious LM
Pesudo Query
Rel. Query FB Hiemstra et al. 04
Lavrenko & Croft 01
Kurland et al. 05
Nallanati et al 03
Model-based FB
Query expansion
Zhai & Lafferty 01b
Bai et al. 05
Markov-chain query model
Rebust Est.
Lafferty & Zhai 01b
Tao & Zhai 06
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
© ChengXiang Zhai, 2007
Zhai 02
Shen et al. 05
Tan et al. 06
Kurland & Lee 05
Lavrenko 04
Kraaij 04
Srikanth 04
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
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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….
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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,
Wei & Croft 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]
© ChengXiang Zhai, 2007
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Part 2: The Basic LM Approach
1. Introduction
2. The Basic Language Modeling Approach
-
3.
4.
5.
6.
Query Likelihood Document Ranking
Smoothing of Language Models
Why does it work?
Variants of the basic LM
We are here
More Advanced Language Models
Language Models for Special Retrieval Tasks
A General Framework for Applying SLMs to IR
Summary
© ChengXiang Zhai, 2007
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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 ?
…
© ChengXiang Zhai, 2007
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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
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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
p(wi  1| d )
– Parameters: {p(wi=1|d), p(wi=0|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 a query word
|V |
m
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]
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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
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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 …
© ChengXiang Zhai, 2007
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Part 2: The Basic LM Approach (cont.)
1. Introduction
2. The Basic Language Modeling Approach
-
3.
4.
5.
6.
Query Likelihood Document Ranking
Smoothing of Language Models
We are here
Why does it work?
Variants of the basic LM
More Advanced Language Models
Language Models for Special Retrieval Tasks
A General Framework for Applying SLMs to IR
Summary
© ChengXiang Zhai, 2007
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Language Model Smoothing
(Illustration)
P(w)
Max. Likelihood Estimate
pML ( w ) 
count of w
count of all words
Smoothed LM
Word w
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How to Smooth?
•
All smoothing methods try to
– discount the probability of words seen in a document
– re-allocate the extra counts so that unseen words will
have a non-zero count
•
Method 1 Additive smoothing [Chen & Goodman 98]: Add
a constant  to the counts of each word, e.g.,
“add 1”
Counts of w in d
c( w, d )  1
p( w | d ) 
| d |  |V |
“Add one”, Laplace
Vocabulary size
Length of d (total counts)
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Improve Additive Smoothing
• Should all unseen words get equal
probabilities?
• We can use a reference model
unseen words
to discriminate
Discounted ML estimate
if w is seen in d
 pDML ( w | d )
p( w | d )  
 d p( w | REF ) otherwise
Reference language model
1
d 


pDML ( w | d )
w is seen
p ( w | REF )
Normalizer
Prob. Mass for unseen words
w is unseen
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Other Smoothing Methods
•
Method 2 Absolute discounting [Ney et al. 94]: Subtract a
constant  from the counts of each word
# unique words
p (w | d ) 
•
max( c ( w, d )  ,0)  |d |u p ( w| REF )
|d |
Method 3 Linear interpolation [Jelinek-Mercer 80]: “Shrink”
uniformly toward p(w|REF)
c( w, d )
p( w | d )  (1   )
  p( w | REF )
|d |
ML estimate
© ChengXiang Zhai, 2007
parameter
40
Other Smoothing Methods (cont.)
•
Method 4 Dirichlet Prior/Bayesian [MacKay & Peto 95, Zhai &
Lafferty 01a, Zhai & Lafferty 02]: Assume pseudo counts
p(w|REF)
parameter
c( w, d )   p( w | REF )
| d | c( w, d )

p (w | d ) 


p( w | REF )
| d | 
| d |  | d |
| d | 
•
Method 5 Good Turing [Good 53]: Assume total # unseen
events to be n1 (# of singletons), and adjust the seen
events in the same way
p (w | d ) 
c*( w, d )
|d |
; c *( w, d ) 
n
2* n2
c( w, d )  1
nc ( w,d ) 1;0*  1 ,1* 
,.....
nc ( w,d )
n0
n1
nr  the number of words with count r
What if nc ( w,d )  0? What about p  w | REF  ?
© ChengXiang Zhai, 2007
Heuristics needed
41
So, which 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…
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
© ChengXiang Zhai, 2007
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Part 2: The Basic LM Approach (cont.)
1. Introduction
2. The Basic Language Modeling Approach
-
3.
4.
5.
6.
Query Likelihood Document Ranking
Smoothing of Language Models
Why does it work?
We are here
Variants of the basic LM
More Advanced Language Models
Language Models for Different Retrieval Tasks
A General Framework for Applying SLMs to IR
Summary
© ChengXiang Zhai, 2007
44
Understanding Smoothing
Retrieval formula using
the general smoothing
scheme
The general smoothing scheme
Discounted ML estimate
if w is seen in d
 pDML ( w | d )
p( w | d )  
 d p( w | REF ) otherwise
log p(q | d )   c( w, q) log p( w | d )
Reference language model
wV


c( w, q) log pDML ( w | d ) 

c( w, q) log pDML ( w | d )   c( w, q) log  d p( w | REF ) 

c( w, q) log
wV ,c ( w, d )  0

wV ,c ( w, d )  0

wV ,c ( w, d )  0
c ( w, q )  0

wV ,c ( w, d ) 0
c( w, q) log  d p( w | REF )
wV

wV ,c ( w, d ) 0
c( w, q) log  d p( w | REF )
pDML ( w | d )
 | q | log  d   c( w, q) p( w | REF )
 d p( w | REF )
wV
The key rewriting step
Similar rewritings are very common when using LMs for IR…
© ChengXiang Zhai, 2007
45
Smoothing & TF-IDF Weighting
[Zhai & Lafferty 01a]
•
Plug in the general smoothing scheme to the query
likelihood retrieval formula, we obtain
TF weighting
Doc length normalization
(long doc is expected to have a smaller d)
pDML ( w | d )
log p(q | d ) 
c( w, q) log
 | q | log  d   c( w, q) p( w | REF )

 d p( w | REF )
wV ,c ( w, d )  0
wV
c ( w, q )  0
Words in both query
and doc
•
•
IDF-like weighting
Ignore for ranking
Smoothing with p(w|C)  TF-IDF + length norm.
Smoothing implements traditional retrieval heuristics
LMs with simple smoothing can be computed as
efficiently as traditional retrieval models
© ChengXiang Zhai, 2007
46
The Dual-Role of Smoothing [Zhai & Lafferty 02]
long
Verbose
queries
Keyword
queries
long
short
short
Why does query type affect smoothing sensitivity?
© ChengXiang Zhai, 2007
47
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 smoothingwith p(w | d )  0.1pDML (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
© ChengXiang Zhai, 2007
data
mining”
0.00001
0.000209
0.000309
0.00001
0.000309
0.000409
48
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)
© ChengXiang Zhai, 2007
49
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)
© ChengXiang Zhai, 2007
50
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
1
19
0
pml (" e " | author 2)
19
pml (" e " | author1) 
20 1


p (" e " | REF )
20   19 20  
20 0

psmooth (" e " | author 2) 

p (" e " | REF )
20   19 20  
psmooth (" e " | author1) 
 must be big! more smoothing
The amount of smoothing is closely related to
the underlying vocabulary size
© ChengXiang Zhai, 2007
51
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
© ChengXiang Zhai, 2007
52
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!
© ChengXiang Zhai, 2007
53
The Notion of Relevance
Relevance
(Rep(q), Rep(d))
Similarity
Different
rep & similarity
P(d q) or P(q d)
Probabilistic inference
P(r=1|q,d) r {0,1}
Probability of Relevance
Regression
Model
(Fox 83)
Generative
Model
Doc
generation
…
Vector space
Prob. distr.
model
model
(Salton et al., 75) (Wong & Yao, 89)
Query
generation
Different
inference system
Prob. concept
space model
(Wong & Yao, 95)
Classical
Basic LM
prob. Model
approach
(Robertson &
(Ponte & Croft, 98)
Sparck Jones, 76)
Later, LMs are used along these lines too
© ChengXiang Zhai, 2007
Inference
network
model
(Turtle & Croft, 91)
Initially, LMs are applied
to IR in this way
54
Justification of Query Likelihood
[Lafferty & Zhai 01a]
•
The General Probabilistic Retrieval Model
– Define P(Q,D|R)
– Compute P(R|Q,D) using Bayes’ rule
– Rank documents by O(R|Q,D)
O( R  1 | Q , D ) 
•
P (Q, D | R  1) P ( R  1)
P ( Q , D | R  0 ) P ( R  0)
Ignored for ranking D
Special cases
– Document “generation”: P(Q,D|R)=P(D|Q,R)P(Q|R)
– Query “generation”: P(Q,D|R)=P(Q|D,R)P(D|R)
Doc generation leads to the classic Robertson-Sparck Jones model
Query generation leads to the query likelihood LM approach
© ChengXiang Zhai, 2007
55
Query Generation [Lafferty & Zhai 01a]
P (Q , D | R  1)
P (Q , D | R  0 )
P (Q | D, R  1) P ( D | R  1)

P (Q | D , R  0 ) P ( D | R  0 )
P ( D | R  1)
 P (Q | D, R  1)
( Assume P (Q | D, R  0)  P (Q | R  0))
P ( D | R  0)
O( R  1 | Q , D ) 
Query likelihood p(q| d)
Document prior
Assuming uniform prior, we have
O( R  1 | Q, D)  P (Q | D, R  1)
Computing P(Q|D, R=1) generally involves two steps:
(1) estimate a language model based on D
(2) compute the query likelihood according to the estimated model
P(Q|D)=P(Q|D, R=1)! Prob. that a user who likes D would pose query Q
Relevance-based interpretation of the so-called
“document language model”
© ChengXiang Zhai, 2007
56
Part 2: The Basic LM Approach (cont.)
1. Introduction
2. The Basic Language Modeling Approach
-
3.
4.
5.
6.
Query Likelihood Document Ranking
Smoothing of Language Models
Why does it work?
Variants of the basic LM
We are here
More Advanced Language Models
Language Models for Special Retrieval Tasks
A General Framework for Applying SLMs to IR
Summary
© ChengXiang Zhai, 2007
57
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]
© ChengXiang Zhai, 2007
58
Part 3: More Advanced LMs
1. Introduction
2. The Basic Language Modeling Approach
3. More Advanced Language Models
We are here
-
Improving the basic LM approach
-
Feedback and alternative ways of using LMs
4. Language Models for Special Retrieval Tasks
5. A General Framework for Applying SLMs to IR
6. Summary
© ChengXiang Zhai, 2007
59
•
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
© ChengXiang Zhai, 2007
60
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
© ChengXiang Zhai, 2007
j
j
| D)
Regular doc LM
61
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
© ChengXiang Zhai, 2007
62
Part 3: More Advanced LMs (cont.)
1. Introduction
2. The Basic Language Modeling Approach
3. More Advanced Language Models
-
-
We are
Improving the basic LM approach
here
Feedback and Alternative ways of using LMs
4. Language Models for Special Retrieval Tasks
5. A General Framework for Applying SLMs to IR
6. Summary
© ChengXiang Zhai, 2007
63
Feedback and Doc/Query Generation
Classic Prob. Model O( R  1| Q, D) 
P( D | Q, R  1)
P( D | Q, R  0)
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. doc model
NonRel. doc model
“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
© ChengXiang Zhai, 2007
Doc-based feedback
64
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])
© ChengXiang Zhai, 2007
65
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
© ChengXiang Zhai, 2007
66
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)
© ChengXiang Zhai, 2007
Original formula in [Lavranko &Croft 01]
p( D | w) 
p( w | D) p( w)
p ( D)
67
Kernel-based Allocation [Lavrenko 04]
• A general generative model for text
 n

p( w1...wn )     p( wi |  )  p(d )

  i 1
1
p( d )   K w (d )
N wT
T= training data
An infinite mixture model
Kernel-based density function
Kernel function kw ( )  similarity(w, )
• Choices of the kernel function
– Delta kernel:
1
p( w1...wn ) 
N
n
 p(w | w)
wT i 1
i
Average probability of w1…wn over all training points
– Dirichlet kernel: allow a training point to “spread”
its influence
© ChengXiang Zhai, 2007
68
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]
© ChengXiang Zhai, 2007
69
Feedback as Model Interpolation
[Zhai & Lafferty 01b]
Document D
D
D( Q ||  D )
Query Q
Q
 Q '  (1   ) Q  F
=0
Q '  Q
No feedback
Results
=1
Q '   F
Full feedback
© ChengXiang Zhai, 2007
F
Feedback Docs
F={d1, d2 , …, dn}
Generative model
Divergence minimization
70
F Estimation Method I:
Generative Mixture Model
Background words

P(w| C)
w
F={D1, …, Dn}
P(source)
Topic words
1-
log p( F |  ) 
P(w|  )
w
  c(w; D) log((1   ) p(w | )   p(w | C ))
DF wD
Maximum Likelihood
 F  arg max log p(F |  )

The learned topic model is called a “parsimonious language model” in [Hiemstra et al. 04]
© ChengXiang Zhai, 2007
71
F Estimation Method II:
Empirical Divergence Minimization
Background model
C
C
d
close

far ()
F={D1, …, Dn}
d
Empirical divergence D ( , F , C ) 
Divergence minimization
D1
1
n
Dn
n
1
|F |
 D( || 
i 1
Dj
)   D( || C ))
 F  arg min D ( , F ,C )
© ChengXiang Zhai, 2007

72
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
© ChengXiang Zhai, 2007
=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
73
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)
© ChengXiang Zhai, 2007
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Part 4: LMs for Special Retrieval Tasks
1.
2.
3.
4.
5.
6.
Introduction
The Basic Language Modeling Approach
More Advanced Language Models
Language Models for Special Retrieval Tasks
-
Cross-lingual IR
Distributed IR
Structured document retrieval
-
Personalized/context-sensitive search
Modeling redundancy
Predicting query difficulty
Expert finding
Subtopic retrieval
We are
here
A General Framework for Applying SLMs to IR
Summary
© ChengXiang Zhai, 2007
75
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
© ChengXiang Zhai, 2007
p(qi | M C ) 

cVChinese
ptrans (qi | c) p (c | M C )
76
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)
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Structured Document Retrieval
[Ogilvie & Callan 03]
D
Title
D1
Abstract
D2
Body-Part1
D3
Body-Part2
-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
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
© ChengXiang Zhai, 2007
78
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
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]
© ChengXiang Zhai, 2007
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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]
© ChengXiang Zhai, 2007
80
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
© ChengXiang Zhai, 2007
81
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 | T , C ) 
•
 p(C | D, R  1)  p( D | T , R  1)
DS
Topic generation model:
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
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82
Subtopic Retrieval [Zhai 02, Zhai et al 03]
•
•
Subtopic retrieval: Aim at retrieving as many distinct
subtopics of the query topic as possible
– E.g., retrieve “different applications of robotics”
– Need to go beyond independent relevance
Two methods explored in [Zhai 02]
– Maximal Marginal Relevance:
• Maximizing subtopic coverage indirectly through redundancy
elimination
• LMs can be used to model redundancy
– Maximal Diverse Relevance:
• Maximizing subtopic coverage directly through subtopic modeling
• Define a retrieval function based on subtopic representation of
query and documents
• Mixture LMs can be used to model subtopics (essentially
clustering)
© ChengXiang Zhai, 2007
83
Unigram Mixture Models
•
•
•
•
•
Each subtopic is modeled with one unigram LM
A document is treated as observations from a mixture
model involving many subtopic LMs
Two different sampling strategies to generate a document
– Strategy 1 (Document Clustering): Choose a subtopic model
and generate all the words in a document using the same
model
– Strategy 2 (Aspect Models [Hofmann 99; Blei et al 02])Use a
(potentially) different subtopic model when generating each
word in a document, so two words in a document may be
generated using different LMs
For subtopic retrieval, we assume a document may have
multiple subtopics, so strategy 2 is more appropriate
Many other applications…
© ChengXiang Zhai, 2007
84
Aspect/Topic Models
Subtopic 1
k
p( w | 1 ,..., k , 1 ,..., k )   i p( w |  i )
P(w|1)
i 1

Subtopic 2
w
Document
D=d1 … dn
P(w|2)
Prob. LSI [Hofmann 99]:
Different D has a different set of ’s
Subtopic k
P(w|k)
n
A
p( D | 1 ,..., k ,  ,...,  )     p(di |  a )
D
1
D
k
i 1 a 1
D
a
Flexible aspect distr.
Need regularization
Latent Dirichlet Allocation [Blei et al 02, Lafferty & Minka 03]
’s are drawn fromn a Acommon Dirichlet distribution
p( D |  1 ,..., k , 1 ,...,  k )   [  p( di |  a ) p( a |  )]Dir ( | 1,...,  k ) d 

i 1 a 1
© ChengXiang Zhai, 2007
 is now regularized
85
Topic Models for Text Mining
•
•
•
Many variants of topic mixture models have recently been proposed for
theme-based text mining
In the line of PLSI [Hofmann 99]
–
–
–
–
–
Comparative text mining [Zhai et al. 04]
Temporal text mining [Mei & Zhai 05]
Spatiotemporal text mining [Mei et al. 06]
Contextual text mining [Mei & Zhai 06]
Sentiment analysis [Mei et al. 07]
In the line of LDA [Blei et al. 02]
– Author-topic models [Steyvers et al. 04]
– Modeling annotated data [Blei & Jordan 03]
– Dynamic topic models [Blei & Lafferty 06b]
– Correlated topic models [Blei & Lafferty 06a]
– Pachinko allocation [Li & McCallum 06]
– Topics over time [Wang & McCallum 06]
© ChengXiang Zhai, 2007
86
Part 5: A General Framework for
Applying SLMs to IR
1. Introduction
2. The Basic Language Modeling Approach
3. More Advanced Language Models
4. Language Models for Special Retrieval Tasks
5. A General Framework for Applying SLMs to IR
-
Risk minimization framework
-
Special cases
We are
here
6. Summary
© ChengXiang Zhai, 2007
87
Risk Minimization: Motivation
• Long-standing IR Challenges
– Improve IR theory
• Develop theoretically sound and empirically effective models
• Go beyond the limited traditional notion of relevance
(independent, topical relevance)
– Improve IR practice
• Optimize retrieval parameters automatically
• SLMs are very promising tools …
– How can we systematically exploit SLMs in IR?
– Can SLMs offer anything hard/impossible to
achieve in traditional IR?
© ChengXiang Zhai, 2007
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Idea 1: Retrieval as Decision-Making
(A more general notion of relevance)
Given a query,
- Which documents should be selected? (D)
- How should these docs be presented to the user? ()
Choose: (D,)
?
Query
?
?
© ChengXiang Zhai, 2007
Unordered subset
…
Ranked list
1 2 3 4
Clustering
89
Idea 2: Systematic Language Modeling
QUERY MODELING
Query
Language Model
Query
USER MODELING
Retrieval Decision:
Documents
?
Loss Function
User
Document
Language Models
DOC MODELING
© ChengXiang Zhai, 2007
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Generative Model of
Document & Query [Lafferty & Zhai 01b]
User
U
p( Q | U )
Partially
observed
Source
Q
p ( R | Q ,  D )
S
p( D | S )
D
p (q |  Q , U )
q
observed
R
p(d |  D ,S )
Query
d
Document
inferred
© ChengXiang Zhai, 2007
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Applying Bayesian Decision Theory
[Lafferty & Zhai 01b, Zhai 02, Zhai & Lafferty 06]
Loss
Choice: (D1,1)
L
Choice: (D2,2)
L
query q
user U
q
1
...
L
Choice: (Dn,n)
doc set C
source S
N
( D*, *)  arg min  L( D,  , ) p( | q,U , C , S )d
D ,
RISK MINIMIZATION

loss
hidden observed
Bayes risk for choice (D, )
© ChengXiang Zhai, 2007
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Special Cases
• Set-based models (choose D)
• Ranking models (choose )
Boolean model
– Independent loss
Probabilistic relevance model
Generative Relevance Theory
Vector-space Model
Two-stage LM
KL-divergence model
• Relevance-based loss
• Distance-based loss
– Dependent loss
• MMR loss
• MDR loss
Subtopic retrieval model
© ChengXiang Zhai, 2007
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Optimal Ranking for Independent Loss
 *  arg min

 L( , ) p( | q,U , C, S )d
Decision space = {rankings}

N
i
i 1
j 1
N
i
L( ,  )   si  l ( j |1... j 1 )
Sequential browsing
  si  l ( j )
i 1
j 1
N
N  j 1
j 1
i 1
 (

N
 *  arg min   (

 j 1

si )l ( j )
N  j 1

i 1
N
N  j 1
j 1
i 1
 arg min  (
Independent loss

si )l ( j ) p( | q, U , C , S ) d
si )  l ( j ) p( j | q, U , C , S )d j

r (d k | q, U , C , S )   l ( k ) p( k | q, U , C , S )d k

 *  Ranking based on r (d k | q,U , C , S )
Independent risk
= independent scoring
“Risk ranking principle”
[Zhai 02]
© ChengXiang Zhai, 2007
94
Automatic Parameter Tuning
•
Retrieval parameters are needed to
– model different user preferences
– customize a retrieval model to specific queries and documents
•
Retrieval parameters in traditional models
– EXTERNAL to the model, hard to interpret
– Parameters are introduced heuristically to implement “intuition”
– No principles to quantify them, must set empirically through
many experiments
– Still no guarantee for new queries/documents
•
Language models make it possible to estimate parameters…
© ChengXiang Zhai, 2007
95
Parameter Setting in Risk Minimization
Estimate
Query
Estimate
Documents
Query model parameters
Query
Language Model
User model parameters
Loss
Function
Set
User
Doc model parameters
Document
Language Models
© ChengXiang Zhai, 2007
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Generative Relevance Hypothesis
[Lavrenko 04]
•
•
•
Generative Relevance Hypothesis:
– For a given information need, queries expressing that need and
documents relevant to that need can be viewed as independent
random samples from the same underlying generative model
A special case of risk minimization when document models
and query models are in the same space
Implications for retrieval models: “the same underlying
generative model” makes it possible to
– Match queries and documents even if they are in different
languages or media
– Estimate/improve a relevant document model based on example
queries or vice versa
© ChengXiang Zhai, 2007
97
Risk Minimization: Summary
•
Risk minimization is a general probabilistic retrieval
framework
– Retrieval as a decision problem (=risk min.)
– Separate/flexible language models for queries and docs
•
Advantages
– A unified framework for existing models
– Automatic parameter tuning due to LMs
– Allows for modeling complex retrieval tasks
•
•
Lots of potential for exploring LMs…
For more information, see [Zhai 02]
© ChengXiang Zhai, 2007
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Part 6: Summary
1. Introduction
2. The Basic Language Modeling Approach
3. More Advanced Language Models
4. Language Models for Special Retrieval Tasks
5. A General Framework for Applying SLMs to IR
6. Summary
We are here
–
SLMs vs. traditional methods: Pros & Cons
–
What we have achieved so far
–
Challenges and future directions
© ChengXiang Zhai, 2007
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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)
© ChengXiang Zhai, 2007
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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
© ChengXiang Zhai, 2007
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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?
© ChengXiang Zhai, 2007
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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?
© ChengXiang Zhai, 2007
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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?
© ChengXiang Zhai, 2007
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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 & topical text mining
– Readability constrained retrieval
– Entity retrieval (e.g. expert search)
How can we exploit LMs to develop models for complex retrieval tasks?
© ChengXiang Zhai, 2007
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