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In this work, we propose a theory for information matching. It is motivated by the observation that retrieval is about the relevance matching between two sets of properties (features), namely, the information need representation and information item representation. However, many probabilistic retrieval models rely on fixing one representation and optimizing the other (e.g. fixing the single information need and tuning the document) but not both. Therefore, it is difficult to use the available related information on both the document and the query at the same time in calculating the probability of relevance. In this paper, we address the problem by hypothesizing the relevance as a logical relationship between the two sets of properties; the relationship is defined on two separate mappings between these properties. By using the hypothesis we develop a unified probabilistic relevance model which is capable of using all the available information. We validate the proposed theory by formulating and developing probabilistic relevance ranking functions for both ad-hoc text retrieval and collaborative filtering. Our derivation in text retrieval illustrates the use of the theory in the situation where no relevance information is available. In collaborative filtering, we show that the resulting recommender model unifies the user and item information into a relevance ranking function without applying any dimensionality reduction techniques or computing explicit similarity between two different users (or items), in contrast to the state-of-the-art recommender models.

In this paper, an Eliteness Hypothesis for information retrieval is proposed, where we define two generative processes to create information items and queries. By assuming the deterministic relationships between the eliteness of terms and relevance, we obtain a new theoretical retrieval framework. The resulting ranking function is a unified one as it is capable of using available relevance information on both the document and the query, which is otherwise unachievable by existing retrieval models. Our preliminary experiment on a simple ranking function has demonstrated the potential of the approach.