Less is More Probabilistic Models for Retrieving Fewer Relevant Documents

1. Less is MoreProbabilistic Models for Retrieving Fewer Relevant Documents Harr Chen, David R. Karger MIT CSAIL ACM SIGIR 2006 August 9, 2006

2. Outline • Motivations • Expected Metric Principle • Metrics • Bayesian Retrieval • Objectives • Heuristics • Experimental Results • Related Work • Future Work and Conclusions ACM SIGIR 2006

3. Motivation • In IR, we have formal models, and formal metrics • Models provide framework for retrieval • E.g.: Probabilistic • Metrics provide rigorous evaluation mechanism • E.g.: Precision and recall • Probability ranking principle (PRP) provably optimal for precision/recall • Ranking by probability of relevance • But other metrics capture other notions of result set quality  and PRP isn’t necessarily optimal ACM SIGIR 2006

4. Example: Diversity • User may be satisfied with one relevant result • Navigational queries, question/answering • In this case, we want to “hedge our bets” by retrieving for diversity in result set • Better to satisfy different users with different interpretations, than one user many times over • Reciprocal rank/search length metrics capture this notion • PRP is suboptimal ACM SIGIR 2006

5. IR System Design • Metrics define preference ordering on result sets • Metric[Result set 1] > Metric[Result set 2] Result set 1 preferred to Result set 2 • Traditional approach: Try out heuristics that we believe will improve relevance performance • Heuristics not directly motivated by metric • E.g. synonym expansion, psuedorelevance feedback • Observation: Given a model, we can try to directly optimize for some metric ACM SIGIR 2006

6. Expected Metric Principle (EMP) • Knowing which metric to use tells us what to maximize for – the expected value of the metric for each result set, given a model Corpus Result Sets Calculate E[Metric] using model Return set with max score 1, 2 Document 1 1, 3 2, 1 Document 2 2, 3 3, 1 Document 3 3, 2 ACM SIGIR 2006

7. Our Contributions • Primary: EMP – metric as retrieval goal • Metric designed to measure retrieval quality • Metrics we consider: precision/recall @ n, search length, reciprocal rank, instance recall, k-call • Build probabilistic model • Retrieve to maximize an objective: the expected value of metric • Expectations calculated according to our probabilistic model • Use computational heuristics to make optimization problem tractable • Secondary: retrieving for diversity (special case) • A natural side effect of optimizing for certain metrics ACM SIGIR 2006

8. Ad hoc approach Use heuristics that are believed to be correlated with good performance Heuristics used to improve relevance Heuristics (probably) make system slower Infinite number of possibilities, no formalism Model, heuristics intertwined Our approach Build model that directly optimizes for good performance Heuristics used to improve efficiency Heuristics (probably) make optimization worse Well-known space of optimization techniques Clean separation between model and heuristics Detour: What is a Heuristic? ACM SIGIR 2006

9. Our Contributions • Primary: EMP – metric as retrieval goal • Metric designed to measure retrieval quality • Metrics we consider: precision/recall @ n, search length, reciprocal rank, instance recall, k-call • Build probabilistic model • Retrieve to maximize an objective: the expected value of metric • Expectations calculated according to our probabilistic model • Use computational heuristics to make optimization problem tractable • Secondary: retrieving for diversity (special case) • A natural side effect of optimizing for certain metrics ACM SIGIR 2006

10. Search Length/Reciprocal Rank • (Mean) search length (MSL): number of irrelevant results until first relevant • (Mean) reciprocal rank (MRR): one over rank of first relevant } Search length = 2 Reciprocal rank = 1/3 ACM SIGIR 2006

11. Instance Recall • Each topic has multiple instances (subtopics, aspects) • Instance recall is how many instances covered (in union) over first n results } Instance recall @ 5 = 0.75 ACM SIGIR 2006

12. k-call @ n • Binary metric: 1 if top n results has k relevant, 0 otherwise • 1-call is (1 – %no) • See TREC robust track } 1-call @ 5 = 1 2-call @ 5 = 1 3-call @ 5 = 0 ACM SIGIR 2006

13. Motivation for k-call • 1-call: Want one relevant document • Many queries satisfied with one relevant result • Only need one relevant document, more room to explore  promotes result set diversity • n-call: Want all relevant documents • “Perfect precision” • Hone in on one interpretation and stick to it! • Intermediate k • Risk/reward tradeoff • Plus, easily modeled in our framework • Binary variable ACM SIGIR 2006

14. Our Contributions • Primary: EMP – metric as retrieval goal • Metric designed to measure retrieval quality • Metrics we consider: precision/recall @ n, search length, reciprocal rank, instance recall, k-call • Build probabilistic model • Retrieve to maximize an objective: the expected value of metric • Expectations calculated according to our probabilistic model • Use computational heuristics to make optimization problem tractable • Secondary: retrieving for diversity (special case) • A natural side effect of optimizing for certain metrics ACM SIGIR 2006

15. Bayesian Retrieval Model • There exists distributions that generate relevant documents, irrelevant documents • PRP: rank by • Remaining modeling questions: form of rel/irrel distributions and parameters for those distributions • In this paper, we assume multinomial models, and choose parameters by maximum a posteriori • Prior is background corpus word distribution ACM SIGIR 2006

16. Our Contributions • Primary: EMP – metric as retrieval goal • Metric designed to measure retrieval quality • Metrics we consider: precision/recall @ n, search length, reciprocal rank, instance recall, k-call • Build probabilistic model • Retrieve to maximize an objective: the expected value of metric • Expectations calculated according to our probabilistic model • Use computational heuristics to make optimization problem tractable • Secondary: retrieving for diversity (special case) • A natural side effect of optimizing for certain metrics ACM SIGIR 2006

17. Objective • Probability Ranking Principle (PRP): maximize at each step in ranking • Expected Metric Principle (EMP): maximize for complete result set • In particular for k-call, maximize: ACM SIGIR 2006

18. Our Contributions • Primary: EMP – metric as retrieval goal • Metric designed to measure retrieval quality • Metrics we consider: precision/recall @ n, search length, reciprocal rank, instance recall, k-call • Build probabilistic model • Retrieve to maximize an objective: the expected value of metric • Expectations calculated according to our probabilistic model • Use computational heuristics to make optimization problem tractable • Secondary: retrieving for diversity (special case) • A natural side effect of optimizing for certain metrics ACM SIGIR 2006

19. Optimization of Objective • Exact optimization of objective is usually NP-hard • E.g.: Exact optimization for k-call reducible to NP-hard maximum graph clique problem • Approximation heuristic: Greedy algorithm • Select documents successively in rank order • Hold previous documents fixed, optimize objective at each rank Maximize E[metric | d] d1 ACM SIGIR 2006

20. Optimization of Objective • Exact optimization of objective is usually NP-hard • E.g.: Exact optimization for k-call reducible to NP-hard maximum graph clique problem • Approximation heuristic: Greedy algorithm • Select documents successively in rank order • Hold previous documents fixed, optimize objective at each rank Fixed d1 Maximize E[metric | d, d1] d2 ACM SIGIR 2006

21. Optimization of Objective • Exact optimization of objective is usually NP-hard • E.g.: Exact optimization for k-call reducible to NP-hard maximum graph clique problem • Approximation heuristic: Greedy algorithm • Select documents successively in rank order • Hold previous documents fixed, optimize objective at each rank Fixed d1 Fixed d2 Maximize E[metric | d, d1, d2] d3 ACM SIGIR 2006

22. Greedy on 1-call and n-call • 1-greedy • Greedy algorithm reduces to ranking each successive document assuming all previous documents are irrelevant • Algorithm has “discovered” incremental negative pseudorelevance feedback • n-greedy: Assume all previous documents relevant ACM SIGIR 2006

23. Greedy on Other Metrics • Greedy with precision/recall  reduces to PRP! • Greedy on k-call for general k (k-greedy) • More complicated… • Greedy with MSL, MRR, instance recall works out to 1-greedy algorithm • Intuition: to make first relevant document appear earlier, we want to hedge our bets as to query interpretation (i.e., diversify) ACM SIGIR 2006

24. Experiments Overview • Experiments verify that optimizing for metric improves performance on metric • They do not tell us which metrics to use • Looked at ad hoc diversity examples • TREC topics/queries • Tuned weights on separate development set • Tested on: • Standard ad hoc (robust track) topics • Topics with multiple annotators • Topics with multiple instances ACM SIGIR 2006

25. Diversity on Google Results • Task: reranking top 1,000 Google results • In optimizing 1-call, our algorithm finds more diverse results than PRP, Google results ACM SIGIR 2006

26. Experiments: Robust Track • TREC 2003, 2004 robust tracks • 249 topics • 528,000 documents • 1-call, 10-call results statistically significant ACM SIGIR 2006

27. Experiments: Instance Retrieval • TREC-6,7,8 interactive tracks • 20 topics • 210,000 documents • 7 to 56 instances per topic • PRP baseline: instance recall @ 10 = 0.234 • Greedy 1-call: instance recall @ 10 = 0.315 ACM SIGIR 2006

28. Experiments: Multi-annotator • TREC-4,6 ad hoc retrieval • Independent annotators assessed same topics • TREC-4: 49 topics, 568,000 documents, 3 annotators • TREC-6: 50 topics, 556,000 documents, 2 annotators •  More annotators more satisfied using 1-greedy ACM SIGIR 2006

29. Related Work • Fits in risk minimization framework (objective as negative loss function) • Other approaches look at optimizing for metrics directly, with training data • Pseudorelevance feedback • Subtopic retrieval • Maximal marginal relevance • Clustering • See paper for references ACM SIGIR 2006

30. Future Work • General k-call (k = 2, etc.) • Determination if this is what users want • Better underlying probabilistic model • Our contribution is in the ranking objective, not the model  model can be arbitrarily sophisticated • Better optimization techniques • E.g., Local search would differentiate algorithms for MRR and 1-call • Other metrics • Preliminary work on mean average precision, precision @ recall • (Perhaps) surprisingly, these metrics are not optimized by PRP! ACM SIGIR 2006

31. Conclusions • EMP: Metric can motivate model – choosing and believing in a metric already gives us a reasonable objective, E[metric] • Can potentially apply EMP on top of a variety of different underlying probabilistic models • Diversity is one practical example of a natural side effect of using EMP with the right metric ACM SIGIR 2006

32. Acknowledgments • Harr Chen supported by the Office of Naval Research through a National Defense Science and Engineering Graduate Fellowship • Jaime Teevan, Susan Dumais, and anonymous reviewers provided constructive feedback • ChengXiang Zhai, William Cohen, and Ellen Voorhees provided code and data ACM SIGIR 2006