Related papers: A Bayesian Approach for Noisy Matrix Completion: O…

We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…

We study the problem of matrix estimation and matrix completion under a general framework. This framework includes several important models as special cases such as the gaussian mixture model, mixed membership model, bi-clustering model and…

In this paper we consider the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We establish for the nuclear-norm penalized estimator of…

We address the new problem of estimating a piece-wise constant signal with the purpose of detecting its change points and the levels of clusters. Our approach is to model it as a nonparametric penalized least square model selection on a…

This paper considers the problem of matrix completion when the observed entries are noisy and contain outliers. It begins with introducing a new optimization criterion for which the recovered matrix is defined as its solution. This…

We develop a Bayesian methodology aimed at simultaneously estimating low-rank and row-sparse matrices in a high-dimensional multiple-response linear regression model. We consider a carefully devised shrinkage prior on the matrix of…

The paper deals with the non-parametric estimation in the regression with the multiplicative noise. Using the local polynomial fitting and the bayesian approach, we construct the minimax on isotropic H\"older class estimator. Next applying…

Matrix completion is a basic machine learning problem that has wide applications, especially in collaborative filtering and recommender systems. Simple non-convex optimization algorithms are popular and effective in practice. Despite recent…

We propose a novel sparse spectrum approximation of Gaussian process (GP) tailored for Bayesian optimization. Whilst the current sparse spectrum methods provide desired approximations for regression problems, it is observed that this…

This paper deals with the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We propose a new nuclear norm penalized estimator of $A_0$ and…

Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise.…

We consider the problem of noisy matrix completion, in which the goal is to reconstruct a structured matrix whose entries are partially observed in noise. Standard approaches to this underdetermined inverse problem are based on assuming…

Source separation is one of the signal processing's main emerging domain. Many techniques such as maximum likelihood (ML), Infomax, cumulant matching, estimating function, etc. have been used to address this difficult problem.…

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…

We extend the theory of low-rank matrix recovery and completion to the case when Poisson observations for a linear combination or a subset of the entries of a matrix are available, which arises in various applications with count data. We…

A general framework based on Gaussian models and a MAP-EM algorithm is introduced in this paper for solving matrix/table completion problems. The numerical experiments with the standard and challenging movie ratings data show that the…

Low-rank matrix completion is an important problem with extensive real-world applications. When observations are uniformly sampled from the underlying matrix entries, existing methods all require the matrix to be incoherent. This paper…

The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation methods non-negative matrix factorization. We derive an oracle inequality for an aggregated estimator. This result holds for a very general…

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

We obtain the optimal Bayesian minimax rate for the unconstrained large covariance matrix of multivariate normal sample with mean zero, when both the sample size, n, and the dimension, p, of the covariance matrix tend to infinity.…