From bilinear regression to inductive matrix completion: a quasi-Bayesian analysis

Abstract

In this paper we study the problem of bilinear regression and we further address the case when the response matrix contains missing data that referred as the problem of inductive matrix completion. We propose a quasi-Bayesian approach first to the problem of bilinear regression where a quasi-likelihood is employed. Then, we adapt this approach to the context of inductive matrix completion. Under a low-rankness assumption and leveraging PAC-Bayes bound technique, we provide statistical properties for our proposed estimators and for the quasi-posteriors. We propose a Langevin Monte Carlo method to approximately compute the proposed estimators. Some numerical studies are conducted to demonstrated our methods.

arXiv admin note: substantial text overlap with arXiv:2206.08619

References in corpus (5)

• Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
• On the properties of variational approximations of Gibbs posteriors
• Learning with the Weighted Trace-norm under Arbitrary Sampling Distributions
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Cited by in corpus (2)

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