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 commentarXiv admin note: substantial text overlap with arXiv:2206.08619

References in corpus (15)

• Restricted strong convexity and weighted matrix completion: Optimal bounds with noise
• A General Framework for Updating Belief Distributions
• User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient
• Noisy low-rank matrix completion with general sampling distribution
• Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity
• Sparse Regression Learning by Aggregation and Langevin Monte-Carlo
• On the properties of variational approximations of Gibbs posteriors
• Fast Low-Rank Bayesian Matrix Completion with Hierarchical Gaussian Prior Models
• Sparse Estimation by Exponential Weighting
• Learning with the Weighted Trace-norm under Arbitrary Sampling Distributions
• 1-bit Matrix Completion: PAC-Bayesian Analysis of a Variational Approximation
• A Bayesian Approach for Noisy Matrix Completion: Optimal Rate under General Sampling Distribution
• Pseudo-Bayesian Quantum Tomography with Rank-adaptation
• Exponential weights in multivariate regression and a low-rankness favoring prior
• Inductive Matrix Completion: No Bad Local Minima and a Fast Algorithm

Cited by in corpus (2)

• A reduced-rank approach to predicting multiple binary responses through machine learning
• Concentration properties of fractional posterior in 1-bit matrix completion