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Information Retrieval and Organisation Chapter 11 Probabilistic Information Retrieval Dell Zhang Birkbeck, University of London

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Why Probabilities in IR? User Information Need Documents Document Representation Query Representation Query Representation How to match? In IR systems, matching between each document and query is attempted in a semantically imprecise space of index terms. Probabilities provide a principled foundation for uncertain reasoning. Can we use probabilities to quantify our uncertainties? Uncertain guess of whether document has relevant content Understanding of user need is uncertain

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Why Probabilities in IR? Problems with vector space model Ad-hoc term weighting schemes Ad-hoc basis vectors Ad-hoc similarity measurement We need something more principled!

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Probability Ranking Principle The document ranking method is the core of an IR system We have a collection of documents. The user issues a query. A list of documents needs to be returned. In what order do we present documents to the user? We want the “best” document to be first, second best second, etc….

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Probability Ranking Principle “If a reference retrieval system's response to each request is a ranking of the documents in the collection in order of decreasing probability of relevance to the user who submitted the request, where the probabilities are estimated as accurately as possible on the basis of whatever data have been made available to the system for this purpose, the overall effectiveness of the system to its user will be the best that is obtainable on the basis of those data.” van Rijsbergen (1979: )

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Probability Ranking Principle Theorem. The PRP is optimal, in the sense that it minimizes the expected loss (also known as the Bayes risk) under 1/0 loss. Provable if all probabilities are known correctly.

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Binary Independence Model BIM is the model that has traditionally been used in conjunction with PRP “Binary” = Boolean: documents and queries are represented as binary incidence vectors of terms. “Independence”: terms occur in documents and queries independently. BIM = Bernoulli Naive Bayes model

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Binary Independence Model Use Bayes’ Rule

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Binary Independence Model Rank documents by their odds constant

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Binary Independence Model Make the Naïve Bayes conditional independence assumption

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Binary Independence Model Let

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Binary Independence Model Assume that constant useful

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Binary Independence Model Taking the logarithm function which is monotonic, we get the retrieval status value log odds ratio

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Binary Independence Model Assume that relevant documents are a very small percentage IDF

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Okapi BM25 Assume that Factor in the term frequencies ( tf ) and document length ( L d and L ave ) Practically good vales: 1.2 ≤ k 1 ≤ 2; b = 0.75 Ideally the parameters k 1, b should be tuned on a validation set.

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Appraisal Getting reasonable approximations of probabilities is possible, but requires restrictive assumptions. In the BIM, these are a Boolean representation of documents/queries/relevance term independence terms not in the query don’t affect the outcome document relevance values are independent Problem: either require partial relevance information or only can derive somewhat inferior term weights.

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Appraisal Probabilistic methods are one of the oldest but also one of the currently hottest topics in IR. Traditionally: neat ideas, but they’ve never won on performance. It may be different now. For example, the Okapi BM25 term weighting formulas have been very successful, especially in TREC evaluations.

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Okapi BM25 The parameters k 1, b should ideally be tuned on a validation set. The good values in practice are 1.2 ≤ k 1 ≤ 2; b = Retrieval Status Value IDF(t) The document length of d The average document length for the collection

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Well-Known UK Researchers Stephen Robertson Keith van Rijsbergen Karen Sparck Jones

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