Information Retrieval as Structured Prediction

1. Information Retrieval as Structured Prediction University of Massachusetts Amherst Machine Learning Seminar April 29th, 2009 Yisong Yue Cornell University Joint work with: Thorsten Joachims, Filip Radlinski, and Thomas Finley

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3. Examples of Complex Output Spaces Natural Language Parsing Given a sequence of words x, predict the parse tree y. Dependencies from structural constraints, since y has to be a tree. x The dog chased the cat y S NP VP NP Det N V Det N

4. Examples of Complex Output Spaces x The rain wet the cat y Det V Det N N • Part-of-Speech Tagging • Given a sequence of words x, predict sequence of tags y. • Dependencies from tag-tag transitions in Markov model. •  Similarly for other sequence labeling problems, e.g., RNA Intron/Exon Tagging.

5. Examples of Complex Output Spaces • Information Retrieval • Given a query x, predict a ranking y. • Dependencies between results (e.g. avoid redundant hits) • Loss function over rankings (e.g. Average Precision) y x • Kernel-Machines • SVM-Light • Learning with Kernels • SV Meppen Fan Club • Service Master & Co. • School of Volunteer Management • SV Mattersburg Online • … SVM

6. Goals of this Talk • Learning to Rank • Optimizing Average Precision • Diversified Retrieval • Structured Prediction • Complex Retrieval Goals • Structural SVMs (Supervised Learning)

7. Learning to Rank • At intersection of ML and IR • First generate input features

8. Learning to Rank • Design a retrieval function f(x) = wTx • (weighted average of features) • For each query q • Score all sq,d = wTxq,d • Sort by sq,d to produce ranking • Which weight vector w is best?

9. Conventional SVMs Input: x (high dimensional point) Target: y (either +1 or -1) Prediction: sign(wTx) Training: subject to: The sum of slacks smooth upper bound for 0/1 loss

10. Optimizing Pairwise Agreements • 2 pairwise disagreements

11. Pairwise Preferences SVM Such that: Large Margin Ordinal Regression [Herbrich et al., 1999] Can be reduced to time [Joachims, 2005] Pairs can be reweighted to more closely model IR goals [Cao et al., 2006]

12. Mean Average Precision Consider rank position of each relevant doc K1, K2, … KR Compute Precision@K for each K1, K2, … KR Average precision = average of P@K Ex: has AvgPrec of MAP is Average Precision across multiple queries/rankings

13. Optimization Challenges • Rank-based measures are multivariate • Cannot decompose (additively) into document pairs • Need to exploit other structure • Defined over rankings • Rankings do not vary smoothly • Discontinuous w.r.t model parameters • Need some kind of relaxation/approximation

14. [Yue & Burges, 2007]

15. Structured Prediction Let x be a structured input (candidate documents) Let y be a structured output (ranking) Use a joint feature map to encode the compatibility of predicting y for given x. Captures all the structure of the prediction problem Consider linear models: after learning w, we can make predictions via

16. Linear Discriminant for Ranking • Let x = (x1,…xn) denote candidate documents (features) • Let yjk = {+1, -1} encode pairwise rank orders • Feature map is linear combination of documents. • Prediction made by sorting on document scores wTxi

17. Structural SVM Let x denote a structured input (candidate documents) Let y denote a structured output (ranking) Standard objective function: Constraints are defined for each incorrect labeling y’ over the set of documents x. [Tsochantaridis et al., 2005]

18. Minimizing Hinge Loss Suppose for incorrect y’: Then: [Tsochantaridis et al., 2005]

19. Structural SVM for MAP Minimize subject to where ( yjk= {-1, +1} ) and Sum of slacks is smooth upper bound on MAP loss. [Yue et al., SIGIR 2007]

20. Too Many Constraints! For Average Precision, the true labeling is a ranking where the relevant documents are all ranked in the front, e.g., An incorrect labeling would be any other ranking, e.g., This ranking has Average Precision of about 0.8 with (y’) ¼ 0.2 Intractable number of rankings, thus an intractable number of constraints!

21. Original SVM Problem Exponential constraints Most are dominated by a small set of “important” constraints Structural SVM Approach Repeatedly finds the next most violated constraint… …until set of constraints is a good approximation. Cutting Plane Method [Tsochantaridis et al., 2005]

22. Original SVM Problem Exponential constraints Most are dominated by a small set of “important” constraints Structural SVM Approach Repeatedly finds the next most violated constraint… …until set of constraints is a good approximation. Cutting Plane Method [Tsochantaridis et al., 2005]

23. Original SVM Problem Exponential constraints Most are dominated by a small set of “important” constraints Structural SVM Approach Repeatedly finds the next most violated constraint… …until set of constraints is a good approximation. Cutting Plane Method [Tsochantaridis et al., 2005]

24. Original SVM Problem Exponential constraints Most are dominated by a small set of “important” constraints Structural SVM Approach Repeatedly finds the next most violated constraint… …until set of constraints is a good approximation. Cutting Plane Method [Tsochantaridis et al., 2005]

25. Finding Most Violated Constraint A constraint is violated when Finding most violated constraint reduces to Highly related to inference/prediction:

26. Finding Most Violated Constraint Observations MAP is invariant on the order of documents within a relevance class Swapping two relevant or non-relevant documents does not change MAP. Joint SVM score is optimized by sorting by document score, wTxj Reduces to finding an interleaving between two sorted lists of documents [Yue et al., SIGIR 2007]

27. Finding Most Violated Constraint Start with perfect ranking Consider swapping adjacent relevant/non-relevant documents ► [Yue et al., SIGIR 2007]

28. Finding Most Violated Constraint Start with perfect ranking Consider swapping adjacent relevant/non-relevant documents Find the best feasible ranking of the non-relevant document ► [Yue et al., SIGIR 2007]

29. Finding Most Violated Constraint Start with perfect ranking Consider swapping adjacent relevant/non-relevant documents Find the best feasible ranking of the non-relevant document Repeat for next non-relevant document ► [Yue et al., SIGIR 2007]

30. Finding Most Violated Constraint Start with perfect ranking Consider swapping adjacent relevant/non-relevant documents Find the best feasible ranking of the non-relevant document Repeat for next non-relevant document Never want to swap past previous non-relevant document ► [Yue et al., SIGIR 2007]

31. Finding Most Violated Constraint Start with perfect ranking Consider swapping adjacent relevant/non-relevant documents Find the best feasible ranking of the non-relevant document Repeat for next non-relevant document Never want to swap past previous non-relevant document Repeat until all non-relevant documents have been considered ► [Yue et al., SIGIR 2007]

33. Structural SVM for MAP • Treats rankings as structured objects • Optimizes hinge-loss relaxation of MAP • Provably minimizes the empirical risk • Performance improvement over conventional SVMs • Relies on subroutine to find most violated constraint • Computationally compatible with linear discriminant

34. Structural SVM Recipe • Joint feature map • Inference method • Loss function • Loss-augmented (most violated constraint)

35. Need for Diversity (in IR) Ambiguous Queries Users with different information needs issuing the same textual query “Jaguar” or “Apple” At least one relevant result for each information need Learning Queries User interested in “a specific detail or entire breadth of knowledge available” [Swaminathan et al., 2008] Results with high information diversity

36. Example • Choose K documents with maximal information coverage. • For K = 3, optimal set is {D1, D2, D10}

37. Diversity via Set Cover • Documents cover information • Assume information is partitioned into discrete units. • Documents overlap in the information covered. • Selecting K documents with maximal coverage is a set cover problem • NP-complete in general • Greedy has (1-1/e) approximation [Khuller et al., 1997]

38. Diversity via Subtopics Current datasets use manually determined subtopic labels E.g., “Use of robots in the world today” Nanorobots Space mission robots Underwater robots Manual partitioning of the total information Relatively reliable Use as training data

39. Weighted Word Coverage • Use words to represent units of information • More distinct words = more information • Weight word importance • Does not depend on human labeling • Goal: select K documents which collectively cover as many distinct (weighted) words as possible • Greedy selection yields (1-1/e) bound. • Need to find good weighting function (learning problem).

40. Example Document Word Counts Marginal Benefit

41. Example Document Word Counts Marginal Benefit

42. Related Work Comparison • Essential Pages[Swaminathan et al., 2008] • Uses fixed function of word benefit • Depends on word frequency in candidate set • Our goals • Automatically learn a word benefit function • Learn to predict set covers • Use training data • Minimize subtopic loss • No prior ML approach • (to our knowledge)

43. Linear Discriminant • x = (x1,x2,…,xn) - candidate documents • y – subset of x • V(y) – union of words from documents in y. • Discriminant Function: • (v,x) – frequency features (e.g., ¸10%, ¸20%, etc). • Benefit of covering word v is thenwT(v,x) [Yue & Joachims, ICML 2008]

44. Linear Discriminant • Does NOT reward redundancy • Benefit of each word only counted once • Greedy has (1-1/e)-approximation bound • Linear (joint feature space) • Allows for SVM optimization • (Used more sophisticated discriminant in experiments.) [Yue & Joachims, ICML 2008]

45. Weighted Subtopic Loss • Example: • x1 covers t1 • x2 covers t1,t2,t3 • x3 covers t1,t3 • Motivation • Higher penalty for not covering popular subtopics [Yue & Joachims, ICML 2008]

46. Finding Most Violated Constraint Encode each subtopic as an additional “word” to be covered. Use greedy algorithm: (1-1/e)-approximation

47. TREC Experiments TREC 6-8 Interactive Track Queries Documents labeled into subtopics. 17 queries used, considered only relevant docs decouples relevance problem from diversity problem 45 docs/query, 20 subtopics/query, 300 words/doc Trained using LOO cross validation

48. TREC 6-8 Interactive Track • Retrieving 5 documents

49. Can expect further benefit from having more training data.

50. Learning Set Cover Representations • Given: • Manual partitioning of a space • subtopics • Weighting for how items cover manual partitions • subtopic labels + subtopic loss • Automatic partitioning of the space • Words • Goal: • Weighting for how items cover automatic partitions • The (greedy) optimal covering solutions agree