Modèles probabilistes pour les fréquences de mots et la recherche d'information. (Probabilistic Models of Document Collections)

The present study deals with word frequencies distributions and their relation to probabilistic Information Retrieval (IR) models. We examine the burstiness phenomenon (a rich get richer phenomenon) of word frequencies in textual collections. We propose to model this phenomenon as a property of probability distributions and we show that the Beta Negative Binomial distribution is a good statistical model for words frequencies. We then focus on probabilistic IR models and their fundamental properties. We then introduce a novel family of probabilistic models, based on Shannon information. These new models bridge the gap between significant properties of IR models and the burstiness phenomenon of word frequencies. These new models yield comparable performances to state of the art IR models and outperform them when Pseudo Relevance Feedback is used. Lastly, the better performances of our models for Pseudo Relevance Feedback (PRF) lead us to study empirically and theoretically PRF models. We propose a theoretical framework which explain well the empirical behaviour and performance of PRF models. Overall, this analysis highlights interesting properties for pseudo relevance feedback and shows that some state-of-the-art model are inadequate.