A 1

Report
Towards a Game-Theoretic Framework
for Information Retrieval
ChengXiang Zhai
翟成祥
Department of Computer Science
University of Illinois at Urbana-Champaign
http://www.cs.uiuc.edu/homes/czhai
Email: [email protected]
CCIR 2014, Aug. 10, 2014, Kunming, China
1
Search is everywhere,
and part of everyone’s life
Web Search
Desk Search
Enterprise Search
Social Media Search
Site Search
……
2
Search is also important for big data:
make big data small, but more useful
Information Retrieval
Big
Raw Data
Text Mining
Decision Support
Small
Relevant Data
3
Search accuracy matters!
# Queries /Day
X 1 sec
X 10 sec
4,700,000,000
~1,300,000 hrs ~13,000,000 hrs
1,600,000,000
~440,000 hrs ~4,400,000 hrs
2,000,000
……
~550 hrs
~5,500 hrs
How can we optimize all search engines in a general way?
Sources:
Google, Twitter: http://www.statisticbrain.com/
PubMed: http://www.ncbi.nlm.nih.gov/About/tools/restable_stat_pubmed.html
4
How can we optimize all search engines in a general way?
However, this is an ill-defined
question!
What is a search engine?
What is an optimal search engine?
What should be the objective function to optimize?
5
Current-generation search engines
number of queries
k search engines
Document collection
Query
Q
Retrieval task = rank documents for a query
Interface = ranked list
( “10 blue links”)
Ranked
list 
Score(Q,D)
Optimal Search Engine=optimal score(q,d)
D
Machine Learning
Retrieval
Model
Objective = ranking accuracy on training data
Minimum NLP
6
Current search engines are well justified
• Probability ranking principle [Robertson 77]:returning a
ranked list of documents in descending order of
probability that a document is relevant to the query is
the optimal strategy under two assumptions:
– The utility of a document (to a user) is independent of
the utility of any other document
– A user would browse the results sequentially
7
Two Justifications of PRP
• Optimization of traditional retrieval effectiveness measures
– Given an expected level of recall, ranking based on PRP maximizes
the precision
– Given a fixed rank cutoff, ranking based on PRP maximizes precision
and recall
• Optimal decision making
– Regardless the tradeoffs (e.g., favoring high precision vs. high recall),
ranking based on PRP optimizes the expected utility of a binary
(independent) retrieval decision (i.e., to retrieve or not to retrieve a
document)
• Intuition: if a user sequentially examines one doc at each
time, we’d like the user to see the very best ones first
8
Success of Probability Ranking Principle
• Vector Space Models: [Salton et al. 1975], [Singhal et al. 1996], …
• Classic Probabilistic Models: [Maron & Kuhn 1960], [Harter 1975],
[Robertson & Sparck Jones 1976], [van Rijsbergen 1977], [Robertson
1977], [Robertson et al. 1981], [Robertson & Walker 1994], …
• Language Models: [Ponte & Croft 1998], [Hiemstra & Kraaij 1998], [Zhai
& Lafferty 2001], [Lavrenko & Croft 2001], [Kurland & Lee 2004], …
• Non-Classic Logic Models: [van Rijsbergen 1986], [Wong & Yao 1995],
…
• Divergence from Randomness: [Amati & van Rijsbergen 2002], [He &
Ounis 2005], …
• Learning to Rank: [Fuhr 1989], [Gey 1994], ...
• Axiomatic retrieval framework [Fang et al. 2004], [Fang et al. 2011], …
• …
Most information retrieval models are to optimize score(Q,D)
9
Limitations of PRP 
Limitations of optimizing Score(Q,D)
• Assumptions made by PRP don’t hold in practice
– Utility of a document depends on others
– Users don’t strictly follow sequential browsing
• As a result
– Redundancy can’t be handled (duplicated docs have
the same score!)
– Collective relevance can’t be modeled
– Heuristic post-processing of search results is
inevitable
10
Improvement: instead of scoring one
document, score a whole ranked list
• Instead of scoring an individual document, score an
entire candidate ranked list of documents [Zhai 02; Zhai &
Lafferty 06]
– A list with redundant documents on the top can be
penalized
– Collective relevance can be captured also
• Powerful machine learning techniques can be used
[Cao et al. 07]
• However, scoring is still for just one query: score(Q, )
Optimal SE = optimal score(Q, )
Objective = Ranking accuracy on training data
11
Limitations of single query scoring
•
•
•
•
No consideration of past queries and history
No modeling of users
Can’t optimize the utility over an entire session
…
12
Heuristic solutions  emerging topics in IR
• No consideration of past queries and history
 Implicit feedback (e.g, [Shen et al. 05] ), personalized search
(see, e.g., [Teevan et al. 10])
• No modeling of users
 intent modeling (see, e.g. , [Shen et al. 06]), task inference
(see, e.g., [Wang et al. 13])
• Can’t optimize the utility over an entire session
 Active feedback (e.g., [Shen & Zhai 05]), exploration-exploitation
tradeoff (e.g., [Agarwal et al. 09], [Karimzadehgan & Zhai 13])
Can we solve all these problems in a more principled way with
a unified formal framework?
13
Going back to the basic questions…
•
•
•
•
What is a search engine?
What is an optimal search engine?
What should be the objective function to optimize?
How can we solve such an optimization problem?
14
Proposed Solution:
A Game-Theoretic Framework for IR
• Retrieval process = cooperative game-playing
• Players: Player 1= search engine; Player 2= user
• Rules of game:
–
–
–
–
Each player takes turns to make “moves”
User makes the first move; system makes the last move
For each move of the user, the system makes a response move
Current search engine:
• User’s moves= {query, click}; system’s moves = {ranked list, show doc}
• Objective: multiple possibilities
– satisfying the user’s information need with minimum effort of user and
minimum resource overhead of the system.
– Given a constant effort of a user, subject to constraints of system resources,
maximize the utility of delivered information to the user
– Given a fixed “budget” for system resources, and an upper bound of user
effort, maximize the utility of delivered information
15
Search as a Sequential Game
(Satisfy an information need
with minimum effort)
User
A1 : Enter a query
Which items
to view?
A2 : View item
View more?
(Satisfy an information need
with minimum user effort, minimum resource)
System
Which information items to present?
How to present them?
Ri: results (i=1, 2, 3, …)
Which aspects/parts of the item
to show? How?
R’: Item summary/preview
A3 : Scroll down or click on
“Back”/”Next” button
16
Retrieval Task = Sequential Decision-Making
Given U, C, At , and H, choose
the best Rt from all possible
responses to At
History H={(Ai,Ri)}
i=1, …, t-1
Query=“light laptop”
User U:
A1 A2 … … At-1
System:
R1 R2 … … Rt-1
C
Info Item
Collection
Click on “Next” button
At
Rt =?
The best ranking for the query
The best ranking of unseen items
Rt  r(At)
All possible rankings of items in C
All possible rankings of unseen items
17
Formalization based on Bayesian Decision
Theory : Risk Minimization Framework
[Zhai & Lafferty 06, Shen et al. 05]
Observed
User Model
User:
U
Interaction history: H
Current user action: At
Document collection: C
Seen items
M=(S, U,… )
Information need
All possible responses:
r(At)={r1, …, rn}
L(ri,At,M)
Loss Function
Optimal response: r* (minimum loss)
Rt  arg min rr ( At )  L(r , At , M ) P( M | U , H , At , C )dM
M
Bayes risk
Inferred
Observed
18
A Simplified Two-Step
Decision-Making Procedure
• Approximate the Bayes risk by the loss at the
mode of the posterior distribution
Rt  arg min rr ( At )  L(r , At , M ) P( M | U , H , At , C )dM
M
 arg min rr ( At ) L(r , At , M *) P( M * | U , H , At , C )
 arg min rr ( At ) L(r , At , M *)
where M *  arg max M P( M | U , H , At , C )
• Two-step procedure
– Step 1: Compute an updated user model M* based on
the currently available information
– Step 2: Given M*, choose a response to minimize the
loss function
19
Optimal Interactive Retrieval
User
A1
Many possible actions:
-type in a query character
- scroll down a page
A
- click on any 2button
-…
U
M*1
C
Collection
P(M1|U,H,A1,C)
Many possible responses:
L(r,A1,M*1)
-query completion
R1
-display adaptive summaries
-recommendation/advertising
-clarification
M*2
P(M2|U,H,A
-…2,C)
L(r,A2,M*2)
…
R2
M can be regarded as states
in an MDP or POMDP.
3
ThusAreinforcement
learning will
be very useful!
IR system
(see SIGIR’14 tutorial on dynamic IR modeling [Yang et al. 14])
20
Refinement of Risk Minimization
Framework
• r(At): decision space (At dependent)
–
–
–
–
–
r(At) = all possible rankings of items in C
r(At) = all possible rankings of unseen items
r(At) = all possible summarization strategies
r(At) = all possible ways to diversify top-ranked items
r(At) = all possible ways to mix results with query suggestions (or topic map)
–
–
–
–
Essential component: U = user information need
S = seen items
n = “new topic?” (or “Never purchased such a product before”?)
t = user’s task?
• M: user model
• L(Rt ,At,M): loss function
– Generally measures the utility of Rt for a user modeled as M
– Often encodes relevance criteria, but may also capture other preferences
– Can be based on long-term gain (i.e., “winning the whole “game” of info service)
• P(M|U, H, At, C): user model inference
– Often involves estimating the information need U
– May involve inference of other variables also (e.g., task, exploratory vs. fixed item
search)
21
Case 1: Context-Insensitive IR
–
–
–
–
At=“enter a query Q”
r(At) = all possible rankings of docs in C
M= U, unigram language model (word distribution)
p(M|U,H,At,C)=p(U |Q)
L(ri , At , M )  L((d1 ,..., d N ), U )
N
  p (viewed | d i )D (U ||  di )
i 1
Since p (viewed | d1 )  p (viewed | d 2 )  ....
the optimal ranking Rt is given by ranking documents by D (U ||  di )
22
Optimal Ranking for Independent Loss
 *  arg min

 L( , ) p( | q,U , C, S )d

N
i
i 1
j 1
N
i
L( ,  )   si  l ( j |1... j 1 )
  si  l ( j )
i 1
j 1
N
N  j 1
j 1
i 1
 (

N
 *  arg min   (

 j 1
Sequential browsing
Independent loss
si )l ( j )
N  j 1

i 1
N
N  j 1
j 1
i 1
 arg min  (

Decision space = {rankings}

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
Independent risk
= independent scoring

 *  Ranking based on r (d k | q,U , C , S )
“Risk ranking principle”
[Zhai 02, Zhai & Lafferty 06]
23
Case 2: Implicit Feedback
–
–
–
–
–
At=“enter a query Q”
r(At) = all possible rankings of docs in C
M= U, unigram language model (word distribution)
H={previous queries} + {viewed snippets}
p(M|U,H,At,C)=p(U |Q,H)
L(ri , At , M )  L((d1 ,..., d N ), U )
N
  p (viewed | d i )D (U ||  di )
i 1
Since p (viewed | d1 )  p (viewed | d 2 )  ....
the optimal ranking Rt is given by ranking documents by D (U ||  di )
24
Case 3: General Implicit Feedback
–
–
–
–
–
At=“enter a query Q” or “Back” button, “Next” button
r(At) = all possible rankings of unseen docs in C
M= (U, S), S= seen documents
H={previous queries} + {viewed snippets}
p(M|U,H,At,C)=p(U |Q,H)
L(ri , At , M )  L((d1 ,..., d N ), U )
N
  p (viewed | d i )D (U ||  di )
i 1
Since p (viewed | d1 )  p (viewed | d 2 )  ....
the optimal ranking Rt is given by ranking documents by D (U ||  di )
25
Case 4: User-Specific Result Summary
–
–
–
–
At=“enter a query Q”
r(At) = {(D,)}, DC, |D|=k, {“snippet”,”overview”}
M= (U, n), n{0,1} “topic is new to the user”
p(M|U,H,At,C)=p(U, n|Q,H), M*=(*, n*)
L( i , n*)
L(ri , At , M )  L( Di ,  i ,  *, n*)
n*=1 n*=0
 L( Di ,  *)  L( i , n*)

 D( * || 
d Di
Choose k most relevant docs
d
)  L( i , n*)
i=snippet
i=overview
1
0
0
1
If a new topic (n*=1),
give an overview summary;
otherwise, a regular snippet summary
26
Case 5: Modeling Different Notions of
Diversification
• Redundancy reduction  reduce user effort
• Diverse information needs (e.g., overview,
subtopic retrieval)  increase the immediate
utility
• Active relevance feedback  increase future
utility
27
Risk Minimization for Diversification
• Redundancy reduction: Loss function includes a
redundancy measure
– Special case: list presentation + MMR [Zhai et al. 03]
• Diverse information needs: loss function defined
on latent topics
– Special case: PLSA/LDA + topic retrieval [Zhai 02]
• Active relevance feedback: loss function considers
both relevance and benefit for feedback
– Special case: hard queries + feedback only [Shen & Zhai 05]
28
Subtopic Retrieval [Zhai et al. 03]
Query: What are the applications of robotics in the world today?
Find as many DIFFERENT applications as possible.
Example subtopics:
A1: spot-welding robotics
A2: controlling inventory
A3: pipe-laying robots
A4: talking robot
A5: robots for loading & unloading
memory tapes
A6: robot [telephone] operators
A7: robot cranes
……
Subtopic judgments
d1
d2
d3
….
dk
A1 A2 A3 … ...
Ak
1 1 0 0… 0 0
0 1 1 1… 0 0
0 0 0 0… 1 0
1 0 1 0 ... 0 1
This is a non-traditional retrieval task …
29
5.1 Diversify = Remove Redundancy
N  N


 *  arg min  L( , ) p( | q, U , C , S )d  arg min    si  r (d j | d1 ,..., d j1 )


j 1  i  j



r (d k | d1 ,..., d k 1 )   r (d k | d1 ,..., d k 1 ,  ) p ( | q, U , C , S )d

Greedy Algorithm for Ranking: Maximal Marginal Relevance (MMR)
l (d k | d1 ,..., d k 1 ,  Q , { i }ik11 )  c2 p(Re l | d k )(1  p ( New | d k ))  c3 (1  p (Re l | d k ))
Cost
REL
NON-REL
NEW
0
C3
where,  
NOT-NEW
C2
C3
c3
1
c2
Rank


Rank
p(Re l | d k )(1    p( New | d k ))
p(q | d k ) (1    p( New | d k ))
“Willingness to tolerate redundancy”
C2<C3, since a redundant relevant doc is
better than a non-relevant doc
30
5.2 Diversity = Satisfy Diverse Info. Need
[Zhai 02]
• Need to directly model latent aspects and then
optimize results based on aspect/topic matching
• Reducing redundancy doesn’t ensure complete
coverage of diverse aspects
31
Aspect Loss Function: Illustration
perfect
redundant
Desired coverage“Already covered”
p(a|Q)
p(a|1)... p(a|k -1)
non-relevant
New candidate
p(a|k)
Combined coverage
p(a|k)
32
5.3 Diversify = Active Feedback [Shen & Zhai 05]
Decision problem:
Decide subset of documents for relevance judgment
D  arg min  L( D, ) p( | U , q, C)d
*

D


L ( D,  )   l ( D , j ,  ) p ( j | D ,  , U )

j

k
  l ( D, j , ) p ( ji | di , ,U )

j
i 1
33
Independent Loss

k
L( D,  )   l ( D, j ,  ) p( ji | di ,  , U )

i 1
j
Independent Loss
k
l ( D, j, )   l (di , ji ,  )
k
k
L( D,  )   l (di , ji ,  ) p( ji | d i ,  ,U )
i 1
i 1

j
i 1
k
D*  arg min   l (di , ji , ) p( ji | di , ,U ) p( | U , q, C )d
D
i 1
ji

r (di )    l (di , ji , ) p( ji | di ,  ,U ) p( | U , q, C )d
ji

34
Independent Loss (cont.)
r (di )    l (d i , ji ,  ) p ( ji | d i ,  , U ) p ( | U , q, C ) d 
ji

di  C , l (di ,1, )  C1 ,
l (di , 0, )  C0 , C1  C0
l (di ,1, )  log p( R  1| di , ) di  C
l (di ,0, )  log p( R  0 | di , ) di  C
r (di )  C0  (C1  C0 )  p( ji  1| di , ,U ) p( | U , q, C )d

Top K
r (di )    H ( R | di ,  ) p( | U , q, C )d

Uncertainty
Sampling
35
Dependent Loss
k
L( D,U , )   p( ji  1| di ,  ,U )  ( D,  )
i 1
Heuristics: consider relevance
first, then diversity
Select Top N documents
…
N  (G  1) K Cluster N docs into K clusters
K Cluster Centroid
Gapped Top K
MMR
36
Illustration of Three AF Methods
Gapped
Top-K
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
…
Top-K
(normal feedback)
K-cluster centroid
Experiment results show that Top-K is worse
than all others [Shen & Zhai 05]
37
Suggested answers to the basic questions
• Search Engine = Game System
• Optimal Search Engine = Optimal Game Plan/Strategy
• Objective function: based on 3 factors and at the session level
– Utility of information delivered to the user
– Effort needed from the user
– System resource overhead
• How can we solve such an optimization problem?
– Bayesian decision theory in general, partially observable Markov
decision process (POMDP) [Luo et al. 14]
– Reinforcement learning
– ...
38
Major benefits of IR as game playing
• Naturally optimize performance on an entire
session instead of that on a single query
(optimizing the chance of winning the entire
game)
• It optimizes the collaboration of machines and
users (maximizing collective intelligence)
• It opens up many interesting new research
directions (e.g., crowdsourcing + interactive IR)
39
An interesting new problem: Crowdsourcing to users
for relevance judgments collection
• Assumption: Approximate relevance judgments
with clickthroughs
• Question: how to optimize the explorationexploitation tradeoff when leveraging users to
collect clicks on lowly-ranked (“tail”) documents?
– Where to insert a candidate ?
– Which user should get this “assignment”?
• Potential solution must include a model for a
user’s behavior
40
General Research Questions Suggested by
the Game-Theoretic Framework
• How should we design an IR game?
– How to design “moves” for the user and the system?
– How to design the objective of the game?
– How to go beyond search to support access and task
completion?
• How to formally define the optimization problem
and compute the optimal strategy for the IR system?
– To what extent can we directly apply existing game
theory? Does Nash equilibrium matter?
– What new challenges must be solved?
• How to evaluate such a system? MOOC?
41
Some Relevant Challenges in NLP
• How can we turn partial understanding into additional
dimension of scoring ?
– Readability
– Trustworthiness
• How can we perform syntactic and semantic analysis of
queries?
• How can we generate adaptive explanatory summaries of
documents?
• How can we generate coherent preview of search results ?
• How can we generate a topic map to enable users to
browse freely?
42
Intelligent IR System in the Future:
Optimizing multiple games simultaneously
Game 2
Game 1
Learning engine
(MOOC)
Mobile service
search
Intelligent
IR System
Game k
Medical advisor
–Support whole workflow of a user’s task (multimodel
info access, info analysis, decision support, task support)
–Minimize user effort (maximum relevance, natural
dialogue)
–Minimize system resource overhead
–Learn to adapt & improve over time from all users/data
Log
Documents
43
Action Item: future research requires
integration of multiple fields
Psychology
User action
Human-Computer Interactive Service
Game
Theory
(Economics)
(Search,
Browsing,
Recommend…)
Interaction
System response
Document
Collection
Traditional Information Retrieval
User
Understanding
User
Model
Natural Language Processing
Document
Representation
Document
Understanding
Natural Language Processing
Machine Learning
(particularly reinforcement learning)
External User
External Doc
User interaction Log
Info (social network)
Info (structures)
44
References
Note: the references are inevitably incomplete due to
the breadth of the topic;
if you know of any important missing references, please email me at [email protected]
•
•
•
•
•
•
•
[Salton et al. 1975] A theory of term importance in automatic text analysis. G. Salton,
C.S. Yang and C. T. Yu. Journal of the American Society for Information Science, 1975.
[Singhal et al. 1996] Pivoted document length normalization. A. Singhal, C. Buckley and
M. Mitra. SIGIR 1996.
[Maron&Kuhn 1960] On relevance, probabilistic indexing and information retrieval. M. E.
Maron and J. L. Kuhns. Journal o fhte ACM, 1960.
[Harter 1975] A probabilistic approach to automatic keyword indexing. S. P. Harter.
Journal of the American Society for Information Science, 1975.
[Robertson&Sparck Jones 1976] Relevance weighting of search terms. S. Robertson and
K. Sparck Jones. Journal of the American Society for Information Science, 1976.
[van Rijsbergen 1977] A theoretical basis for the use of co-occurrence data in
information retrieval. C. J. van Rijbergen. Journal of Documentation, 1977.
[Robertson 1977] The probability ranking principle in IR. S. E. Robertson. Journal of
Documentation, 1977.
45
References (cont.)
•
•
•
•
•
•
•
•
•
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