Retrieval constraints and word frequency distributions: a log-logistic model for IR

We first present in this paper an analytical view of heuristic retrieval constraints which yields simple tests to determine whether a retrieval function satisfies the constraints or not. We then review empirical findings on word frequency distributions and the central role played by burstiness in this context. This leads us to propose a formal definition of burstiness which can be used to characterize probability distributions wrt this phenomenon. We then introduce the family of information-based IR models which naturally captures heuristic retrieval constraints when the underlying probability distribution is bursty and propose a new IR model within this family, based on the log-logistic distribution. The experiments we conduct on three different collections illustrate the good behavior of the log-logistic IR model: it significantly outperforms the Jelinek-Mercer and Dirichlet prior language models on all three collections, with both short and long queries and for both the MAP and the precision at 10 documents. It also outperforms the InL2 DFR model for the MAP, and yields results on a par with it for the precision at 10.