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Less is More Probabilistic Model for Retrieving Fewer Relevant Docuemtns Harr Chen and David R. Karger MIT CSAIL SIGIR2006 4/30/2007

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Abstract Probability Ranking Priciple (PRP) – Rank documents in decreasing order of probability of relevance. Propose a greedy algorithm that approximately optimizes the following objectives – %no metric: the percentages of queries for which no relevant documents are retrieved. – The diversity of results. 4/30/2007

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Introduction Probability Ranking Principle – Rule of thumb: “optimal”. TREC robust track – %no metric – Question answering and finding a homepage. Diversity – For example, “Trojan horse” – PRP-based method may choose one “most likely” interpretation. Greedy algorithm – Fill each position in the ranking by assuming that all previous documents in the ranking are not relevant. 4/30/2007

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Introduction (Cont.) Other measures – Search length (SL) – Reciprocal rank (RR) – Instance recall: the number of difference subtopics in a given result set. Retrieving for Diversity – The diversity automatically arises as a consequence of the objective function. 4/30/2007

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Related Work Algorithm – Zhai and Lafferty: a risk minimization framework – Bookstein: a sequential learning retrieval system Diversity – Zhai et al.: novelty and redundancy – Clustering is an approach to quickly cover a diverse range of query interpretations. 4/30/2007

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Evaluation Metrics MSL (mean search length) MRR (mean reciprocal rank) %no – k-call at n: 1 if at least k of the top n docs returned by system for the given query are deemed relevant; otherwise 0. – mean 1-call: one minus the %no metric – n-call at n: perfect precision Instance recall at rank n 4/30/2007

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Bayesian Retrieval Standard Bayesian Information Retrival – The documents in a corpus should be ranked by Pr[r|d] – By a monotonic transformation – Focus on the objective function, so use Naïve Bayes framework with multinomial models (θ i ) as the family of distributions. – Determine the parameters (training) – Dirichlet prior: prior probability distribution over the parameters (θ i ). – Estimate the probability of parameters of the relevant distribution (i.e., Pr[d|r]). 4/30/2007

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Object Function Considering optimizing for the k-call at n metric. – k=1: the probability that at least one of the first n relevance variables be true – For arbitrary k: the probability that at least k docs are relevant 4/30/2007

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Optimization Methods NP-hard Problem – To perfectly optimize the k-call of any specific set of n docs objective function from a corpus of m docs, because Greedy algorithm (approximately optimize it) – Successively select each result of the result set. 1.Select first result by applying the conventional PRP. 2.For the ith result, we hold results 1 throught i-1 to their already selected value, and consider all remaining corpus documents as a possibility for document i. 3.Pick the document with highest k-call score as the ith result. 4/30/2007

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Applying the Greedy Approach k=1 – First, choose the doc d 0 maximizing Pr[r 0 |d 0 ]. – Wish to choose d 1 maximizing the below quantity: – Choose d2 by maximizing – In general, select the optimal d i that maximizes 4/30/2007

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Applying the Greedy Approach (Cont.) k=n (perfect precision) – Select the ith document according to: 1

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Optimizing for Other Metrics Optimizing 1-call – Choose greedily conditioned on there being no previous document relevant. – Equal to minimize expected search length and maximize expected reciprocal rank. – Also optimize instance recall metric, which measures the number of distinct subtopics retrieved. If a query has t subtopics, then instance recall is 4/30/2007

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Google Examples Two ambiguous queries: “Trojan horse” and “virus” – Usd the titles, summaries, and snippets of Google’s results to form a corpus of 1000 docs for each query. 4/30/2007

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Experiments Methods – 1-greedy, 10-greedy, and conventional PRP Datasets – ad hoc topics from TREC-1, TREC-2, and TREC-3 to set the weight parameters of model appropriately. – TREC2004 robust track – TREC-6,7,8 interactive track – TREC-4 and TREC-6 ad hoc tracks 4/30/2007

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Tuning the Weights Key weight – For the proposed model, the key weights are the strength of the relevant distribution and irrelevant distribution priors with respect to the strength of the docs. TRECs 1, 2, and 3 – Consisting about 724,000 docs, and 150 topics (topics ) – Used for tuning weight 4/30/2007

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Robust Track Experiments TREC2004 robust track – 249 topics in total, about 528,000 docs – 50 topics were selected by TREC as being “difficult” queries. 4/30/2007

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Instance Retrieval Experiments TREC-6, 7, and 8 interactive track – Test the performance of diversity – Total 20 topics with between 7 and 56 aspects each, and about 210,000 docs. – Zhai et al’s LM approach is better for aspect retrieval. 4/30/2007

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Multiple Annotator Experiments TREC-4 and TREC-6 – Multiple independent annotators are asked to make relevant judgments for the same topics over the same corpus. – TREC-6 had three annotators, TREC-6 had two. 4/30/2007

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Query Analysis A specific topic 100 – The description is: 4/30/2007

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Conclusions and Future Work Conclusions – Identify the PRP is not optimal, and given an approach to directly optimize other desired objective. – The approach is algorithmically feasible. Future work – Other objective functions – More sophisticated techniques, such as local search alg. – The likelihood of relevance collections of docs Two-Poisson model Language model 4/30/2007

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