1. Probabilistic Model n Objective: to capture the IR problem using a probabilistic framework n Given a user query, there is an ideal answer set n Querying as specification of the properties of this ideal answer set (clustering) n But, what are these properties? n Guess at the beginning what they could be (i.e., guess initial description of ideal answer set) n Improve by iteration

2. Probabilistic Model n An initial set of documents is retrieved somehow n User inspects these docs looking for the relevant ones (in truth, only top 10-20 need to be inspected) n IR system uses this information to refine description of ideal answer set n By repeting this process, it is expected that the description of the ideal answer set will improve n Have always in mind the need to guess at the very beginning the description of the ideal answer set n Description of ideal answer set is modeled in probabilistic terms

3. Probabilistic Ranking Principle n Given a user query q and a document dj, the probabilistic model tries to estimate the probability that the user will find the document dj interesting (i.e., relevant). The model assumes that this probability of relevance depends on the query and the document representations only. Ideal answer set is referred to as R and should maximize the probability of relevance. Documents in the set R are predicted to be relevant. n But, u how to compute probabilities? u what is the sample space?

4. The Ranking n Probabilistic ranking computed as: u sim(q,dj) = P(dj relevant-to q) / P(dj non-relevant-to q) u This is the odds of the document dj being relevant u Taking the odds minimize the probability of an erroneous judgement n Definition: u wij  {0,1} u P(R | vec(dj)) : probability that given doc is relevant u P(  R | vec(dj)) : probability doc is not relevant

5. The Ranking n sim(dj,q) = P(R | vec(dj)) / P(  R | vec(dj)) = [P(vec(dj) | R) * P(R)] [P(vec(dj) |  R) * P(  R)] ~ P(vec(dj) | R) P(vec(dj) |  R) n P(vec(dj) | R) : probability of randomly selecting the document dj from the set R of relevant documents

6. The Ranking n sim(dj,q)~ P(vec(dj) | R) P(vec(dj) |  R) ~ [  P(ki | R)] * [  P(  ki | R)] [  P(ki |  R)] * [  P(  ki |  R)] n P(ki | R) : probability that the index term ki is present in a document randomly selected from the set R of relevant documents

7. The Ranking n sim(dj,q)~ log [  P(ki | R)] * [  P(  kj | R)] [  P(ki |  R)] * [  P(  kj |  R)] ~  wiq * wij * (log P(ki | R) + log P(ki |  R) ) P(  ki | R) P(  ki |  R) where P(  ki | R) = 1 - P(ki | R) P(  ki |  R) = 1 - P(ki |  R)

8. The Initial Ranking n Probabilities P(ki | R) and P(ki |  R) ? n Estimates based on assumptions: u P(ki | R) = 0.5 u P(ki |  R) = ni N where ni is the number of docs that contain ki u Use this initial guess to retrieve an initial ranking u Improve upon this initial ranking

9. Improving the Initial Ranking n Let u V : set of docs initially retrieved u Vi : subset of docs retrieved that contain ki n Reevaluate estimates: u P(ki | R) = Vi V u P(ki |  R) = ni - Vi N - V n Repeat recursively

10. Improving the Initial Ranking n To avoid problems with V=1 and Vi=0: u P(ki | R) = Vi + 0.5 V + 1 u P(ki |  R) = ni - Vi + 0.5 N - V + 1 n Also, u P(ki | R) = Vi + ni/N V + 1 u P(ki |  R) = ni - Vi + ni/N N - V + 1

11. Pluses and Minuses n Advantages: u Docs ranked in decreasing order of probability of relevance n Disadvantages: u need to guess initial estimates for P(ki | R) u method does not take into account tf and idf factors

12. Brief Comparison of Classic Models n Boolean model does not provide for partial matches and is considered to be the weakest classic model n Salton and Buckley did a series of experiments that indicate that, in general, the vector model outperforms the probabilistic model with general collections n This seems also to be the view of the research community