Active multiple matrix completion with adaptive confidence sets

Andrea Locatelli 1 Alexandra Carpentier 1 Michal Valko 2, 3
2 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : In this work, we formulate a new multi-task active learning setting in which the learner's goal is to solve multiple matrix completion problems simultaneously. At each round, the learner can choose from which matrix it receives a sample from an entry drawn uniformly at random. Our main practical motivation is market segmentation, where the matrices represent different regions with different preferences of the customers. The challenge in this setting is that each of the matrices can be of a different size and also of a different rank which is unknown. We provide and analyze a new algorithm, MALocate that is able to adapt to the unknown ranks of the different matrices. We then give a lower-bound showing that our strategy is minimax-optimal and demonstrate its performance with synthetic experiments.
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Submitted on : Friday, November 29, 2019 - 6:00:38 PM
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Andrea Locatelli, Alexandra Carpentier, Michal Valko. Active multiple matrix completion with adaptive confidence sets. International Conference on Artificial Intelligence and Statistics, 2019, Okinawa, Japan. ⟨hal-02387468⟩

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