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June 2010 Statistical analysis of k-nearest neighbor collaborative recommendation
Gérard Biau, Benoît Cadre, Laurent Rouvière
Ann. Statist. 38(3): 1568-1592 (June 2010). DOI: 10.1214/09-AOS759


Collaborative recommendation is an information-filtering technique that attempts to present information items that are likely of interest to an Internet user. Traditionally, collaborative systems deal with situations with two types of variables, users and items. In its most common form, the problem is framed as trying to estimate ratings for items that have not yet been consumed by a user. Despite wide-ranging literature, little is known about the statistical properties of recommendation systems. In fact, no clear probabilistic model even exists which would allow us to precisely describe the mathematical forces driving collaborative filtering. To provide an initial contribution to this, we propose to set out a general sequential stochastic model for collaborative recommendation. We offer an in-depth analysis of the so-called cosine-type nearest neighbor collaborative method, which is one of the most widely used algorithms in collaborative filtering, and analyze its asymptotic performance as the number of users grows. We establish consistency of the procedure under mild assumptions on the model. Rates of convergence and examples are also provided.


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Gérard Biau. Benoît Cadre. Laurent Rouvière. "Statistical analysis of k-nearest neighbor collaborative recommendation." Ann. Statist. 38 (3) 1568 - 1592, June 2010.


Published: June 2010
First available in Project Euclid: 24 March 2010

zbMATH: 1189.62190
MathSciNet: MR2662352
Digital Object Identifier: 10.1214/09-AOS759

Primary: 62G05
Secondary: 62G20

Keywords: Collaborative recommendation , consistency , cosine-type similarity , nearest neighbor estimate , rate of convergence

Rights: Copyright © 2010 Institute of Mathematical Statistics

Vol.38 • No. 3 • June 2010
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