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Exact Block-Constant Rating Matrix Recovery from a Few Noisy Observations

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Stochastic Processes in Communication Sciences

Co-authors: Jiaming Xu (UIUC), Rui Wu (UIUC), Kai Zhu (Arizona State), Bruce Hajek (UIUC), Lei Ying (Arizona State)

We consider the problem of predicting ratings given by users to movies, for example, in the well-known Netflix-like problem scenario. We make some simplifying assumptions: users and movies are grouped in clusters, and users in the same cluster give identical ratings to movies in the same cluster. We also assume that the ratings are binary: +1 (thumbs up) and -1 (thumbs down). Most of the entries of this matrix are assumed to be erased, and the remaining entries may contain a lot of errors. We will present algorithms for recovering the entries of the matrix, and present sufficient conditions under which these algorithms recover the matrix exactly. We will also present a conjecture on the incoherence of a random binary matrix, which if true, will allow us to strengthen some of our results.

This talk is part of the Isaac Newton Institute Seminar Series series.

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