Related papers: Noisy Matrix Completion under Sparse Factor Models

We study the matrix completion problem when the observation pattern is deterministic and possibly non-uniform. We propose a simple and efficient debiased projection scheme for recovery from noisy observations and analyze the error under a…

In the present paper, we consider the problem of matrix completion with noise. Unlike previous works, we consider quite general sampling distribution and we do not need to know or to estimate the variance of the noise. Two new nuclear-norm…

We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…

This paper investigates statistical inference for noisy matrix completion in a semi-supervised model when auxiliary covariates are available. The model consists of two parts. One part is a low-rank matrix induced by unobserved latent…

We consider in this paper the problem of estimating a parameter matrix from observations which are affected by two types of noise components: (i) a sparse noise sequence which, whenever nonzero can have arbitrarily large amplitude (ii) and…

We develop a message-passing algorithm for noisy matrix completion problems based on matrix factorization. The algorithm is derived by approximating message distributions of belief propagation with Gaussian distributions that share the same…

The problem of low-rank matrix completion with heterogeneous and sub-exponential (as opposed to homogeneous and Gaussian) noise is particularly relevant to a number of applications in modern commerce. Examples include panel sales data and…

If learning methods are to scale to the massive sizes of modern datasets, it is essential for the field of machine learning to embrace parallel and distributed computing. Inspired by the recent development of matrix factorization methods…

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized…

We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…

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…

Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of…

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.…

We introduce a flexible framework for making inferences about general linear forms of a large matrix based on noisy observations of a subset of its entries. In particular, under mild regularity conditions, we develop a universal procedure…

The essence of distantly supervised relation extraction is that it is an incomplete multi-label classification problem with sparse and noisy features. To tackle the sparsity and noise challenges, we propose solving the classification…

We consider the statistical inference for noisy incomplete binary (or 1-bit) matrix. Despite the importance of uncertainty quantification to matrix completion, most of the categorical matrix completion literature focuses on point estimation…

Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce the…

This paper considers the problem of estimating linear dynamic system models when the observations are corrupted by random disturbances with nonstandard distributions. The paper is particularly motivated by applications where sensor…

An increasing number of applications is concerned with recovering a sparse matrix from noisy observations. In this paper, we consider the setting where each row of the unknown matrix is sparse. We establish minimax optimal rates of…

Matrix completion aims to predict missing elements in a partially observed data matrix which in typical applications, such as collaborative filtering, is large and extremely sparsely observed. A standard solution is matrix factorization,…