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Due to challenging applications such as collaborative filtering, the matrix completion problem has been widely studied in the past few years. Different approaches rely on different structure assumptions on the matrix in hand. Here, we focus…

In this paper we develop a theory of matrix completion for the extreme case of noisy 1-bit observations. Instead of observing a subset of the real-valued entries of a matrix M, we obtain a small number of binary (1-bit) measurements…

We consider the problem of noisy 1-bit matrix completion under an exact rank constraint on the true underlying matrix $M^*$. Instead of observing a subset of the noisy continuous-valued entries of a matrix $M^*$, we observe a subset of…

The problem of predicting unobserved entries in a binary matrix, known as 1-bit matrix completion, has found diverse applications in fields such as recommendation systems. In this study, we develop an empirical Bayes method for 1-bit matrix…

While Bayesian methods are extremely popular in statistics and machine learning, their application to massive datasets is often challenging, when possible at all. Indeed, the classical MCMC algorithms are prohibitively slow when both the…

We consider the problem of completing a matrix with categorical-valued entries from partial observations. This is achieved by extending the formulation and theory of one-bit matrix completion. We recover a low-rank matrix $X$ by maximizing…

Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral regularization…

The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…

We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with additive noise. We…

Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…

Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system.…

Matrix completion and robust principal component analysis have been widely used for the recovery of data suffering from missing entries or outliers. In many real-world applications however, the data is also time-varying, and the naive…

We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…

This study investigates the misclassification excess risk bound in the context of 1-bit matrix completion, a significant problem in machine learning involving the recovery of an unknown matrix from a limited subset of its entries. Matrix…

We extend the theory of matrix completion to the case where we make Poisson observations for a subset of entries of a low-rank matrix. We consider the (now) usual matrix recovery formulation through maximum likelihood with proper…

Inference on high-dimensional parameters in structured linear models is an important statistical problem. This paper focuses on the case of a piecewise polynomial Gaussian sequence model, and we develop a new empirical Bayes solution that…

This paper investigates the consistency of a posterior distribution in the single-measurement fractional Calder\'on problem with additive Gaussian noise. We consider a Bayesian framework with rescaled and Gaussian sieve priors, using a…

We explore the impact of coarse quantization on matrix completion in the extreme scenario of dithered one-bit sensing, where the matrix entries are compared with time-varying threshold levels. In particular, instead of observing a subset of…

We study the problem of matrix completion in this paper. A spectral scaled Student prior is exploited to favour the underlying low-rank structure of the data matrix. We provide a thorough theoretical investigation for our approach through…

We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is…