1. Document Language Models, Query Models, and Risk Minimization for Information Retrieval
John Lafferty, Chengxiang Zhai
School of Computer Science
Carnegie Mellon University

2. LM Applied to IR First proposed in (Ponte & Croft, 98)
Also explored in (Miller et al., 99; Hiemstra et al. 99; Berger & Lafferty, 99; Song & Croft, 99; Hiemstra, 00 etc.)
A very promising approach
Good empirical performance
Statistical foundation
Re-use existing LM techniques
But,
Lack of understanding of the approach (lack of “relevance”)
Conceptual inconsistency in feedback (text + terms)
Real empirical advantage still needs to be demonstrated

3. Research Questions How can we extend the language modeling approach to
Allow modeling of both queries and documents
Exploit language modeling to perform natural and effective feedback
Estimate translation models without training data
(Berger & Lafferty 99)
What is the relationship between the language modeling approach and the traditional probabilistic retrieval models?
Can we go beyond the Probability Ranking Principle?

4. Outline A Risk Minimization Retrieval Framework Special Cases
Markov Chain Translation Model
Query Language Model Estimation
Evaluation

5. Risk Minimization Framework — Basic Idea
Utility/Risk as retrieval criterion
Retrieval as a sequence of presenting decisions
Application of Bayesian decision theory

6. Risk Minimization Framework — Features
Modeling utility-based retrieval (beyond binary relevance)
Modeling interactive retrieval (dynamic user model)
Covering many existing retrieval models
Fully probabilistic (language model + estimation)
Document language model + query language model
Feedback as query model estimation

7. Generative Model
inferred
observed U
User q
R  {0,1} d S
Source

8. Actions, Loss functions, and Bayes risk
Given C={d1,d2, …dk} from source S and query q from user U, which list of documents to present?
Action: a = “list of documents”
Loss: L(a,), (Q, D1, …,Dk ,R1, …, Rk)
Bayes risk:
a=di
L(a, Q , Di, Ri )
R(di;q) 
R(a=di|U,q,S,C)
def 
R(a|U,q,S,C) =
L(a, ) p( |U, q, S, C) d
Bayes optimal decision (risk minimization)
a* = argmin R(a|U,q,S,C)
d* = argmin R(d;q) d a

9. Risk Minimization Ranking Function
posterior distribution
Loss function
Query model
Doc model
“Relevance” model

10. Special Cases Loss function L(Q, D ,R)=? Prob. Relevance Model
L(Q, D ,R)=L(R)
Prob. Relevance Model
p(R=1|q,d)
L(Q, D ,R)=(Q, D)
Prob. Similarity Model
Generative Model?
Classical
prob. Model
Doc
generation
“Generalized” LM
approach
Unigram + D ||
TF-IDF + cosine
Vector space Model
Query
generation LM
approach
(Lafferty & Zhai 01)

11. A Markov Chain Method for Estimating Query Model
“Browsing” 
p(w|U)
User
q=q1,q2, …, qm
Query w1 w2 … wn w1 w2 … wn
doc
source
Markov chain “translation” channel
t,D(q|w)
query model = (posterior) prob. dist. over initial terms
prior
Markov chain
Restrict D for pseudo feedback

12. Markov Chain Translation Probabilities
1-
stop
1-
stop
1-
stop w0
p(w1|d0) w1 w2
p(w2|d2)
... d0
p(d0|w0)  d1
p(d1|w1)  A B
Matrix Formulation:

13. Sample Query Probabilities
q=star wars (TREC8)
Political sense
Movie sense
q=star wars
(feedback on TREC8)
Political sense

14. Evaluation KL-divergence Unigram Retrieval Model
Fixed linear interpolation smoothing for
Comparing two methods for estimating
Maximum likelihood (= query likelihood, simple LM)
Markov chain on top 50 docs
Three testing collections
AP89 (~250MB + 50 queries)
TREC8 ad hoc (~2GB + 50 queries)
TREC8 web track (~2GB + 50 queries)

15. Results: Simple LM vs. Markov Chain
AP89
TREC8
Web

16. Results: Rocchio vs. Markov Chain
AP89
TREC8
Web

17. Rocchio vs. Markov Chain: TREC8

18. Rocchio vs. Markov Chain : Web

19. Conclusions and Future Work
Risk minimization as a new general retrieval framework
Goes beyond the Probability Ranking Principle (PRR)
Recovers existing models
Extends existing work on language modeling
Markov chain model expansion
Efficient “translation” model
Applicable to both query model and document model
Empirically effective
Future Work
Explore utility-based ranking criterion (e.g., MMR)
Explore new models and new estimation methods