Probabilistic Information Retrieval Probability Ranking Principle Probability ranking principle(Prp Simple case: no selection costs or other utility concerns that would differentially weight errors BayesOptimal Decision Rule x is relevant iff p(rx)>p(nrx PRP in action: Rank all documents by p(rix Theorem Using the prp is optimal, in that it minimizes the loss (Bayes risk under 1/0 loss Provable if all probabilities correct, etc. [e. g ripley 1996]Probabilistic Information Retrieval 10 Probability Ranking Principle (PRP) ▪ Simple case: no selection costs or other utility concerns that would differentially weight errors ▪ Bayes’ Optimal Decision Rule ▪ x is relevant iff p(R|x) > p(NR|x) ▪ PRP in action: Rank all documents by p(R|x) ▪ Theorem: ▪ Using the PRP is optimal, in that it minimizes the loss (Bayes risk) under 1/0 loss ▪ Provable if all probabilities correct, etc. [e.g., Ripley 1996] Probability Ranking Principle