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Bayesian sequential design in matrix factorisation models

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SNAW05 - Bayesian methods for networks

Co-author: Annie Marsden (University of Cambridge)

Many problems in high-dimensional statistics rely on low-rank decompositions of matrices. Examples include matrix completion, recommender systems or collaborative filtering, and graph clustering or community detection. Most commonly, estimates are obtained by solving an optimisation problem through SDP relaxations, expectation maximisation, or projected gradient descent algorithms. Bayesian analogs of these procedures provide estimates of uncertainty, but these are rarely exploited in practice. In this talk, we explore how the posterior distribution in matrix factorisation models can be put to use in sequential design problems. Bayesian procedures such as Thompson sampling and the Bayesian UCB have been shown to achieve optimal regret in Multi-Arm Bandit problems. We present a simulation study supporting similar strategies in recommender systems.

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

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