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Abstract: Collaborative recommendation is an information-filtering technique thatattempts to present information items that are likely of interest to anInternet user. Traditionally, collaborative systems deal with situations withtwo types of variables, users and items. In its most common form, the problemis framed as trying to estimate ratings for items that have not yet beenconsumed by a user. Despite wide-ranging literature, little is known about thestatistical properties of recommendation systems. In fact, no clearprobabilistic model even exists which would allow us to precisely describe themathematical forces driving collaborative filtering. To provide an initialcontribution to this, we propose to set out a general sequential stochasticmodel for collaborative recommendation. We offer an in-depth analysis of theso-called cosine-type nearest neighbor collaborative method, which is one ofthe most widely used algorithms in collaborative filtering, and analyze itsasymptotic performance as the number of users grows. We establish consistencyof the procedure under mild assumptions on the model. Rates of convergence andexamples are also provided.

Autor: Gérard Biau, Benoît Cadre, Laurent Rouvière


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