Related papers: Bayesian Matrix Completion via Adaptive Relaxed Sp…
In this paper, we propose a novel method for matrix completion under general non-uniform missing structures. By controlling an upper bound of a novel balancing error, we construct weights that can actively adjust for the non-uniformity in…
Techniques of matrix completion aim to impute a large portion of missing entries in a data matrix through a small portion of observed ones. In practice including collaborative filtering, prior information and special structures are usually…
We consider the matrix completion problem of recovering a structured matrix from noisy and partial measurements. Recent works have proposed tractable estimators with strong statistical guarantees for the case where the underlying matrix is…
We propose a novel approach to estimating the precision matrix of multivariate Gaussian data that relies on decomposing them into a low-rank and a diagonal component. Such decompositions are very popular for modeling large covariance…
Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix.…
Rank regularized minimization problem is an ideal model for the low-rank matrix completion/recovery problem. The matrix factorization approach can transform the high-dimensional rank regularized problem to a low-dimensional factorized…
Low-rank matrix estimation from incomplete measurements recently received increased attention due to the emergence of several challenging applications, such as recommender systems; see in particular the famous Netflix challenge. While the…
The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…
The problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However,…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…
The completion of low rank matrices from few entries is a task with many practical applications. We consider here two aspects of this problem: detectability, i.e. the ability to estimate the rank $r$ reliably from the fewest possible random…
We present a new sampling-based approach for enabling efficient computation of low-rank Bayesian matrix completion and quantifying the associated uncertainty. Firstly, we design a new prior model based on the singular-value-decomposition…
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…
This paper studies the problem of deterministic rank-one matrix completion. It is known that the simplest semidefinite programming relaxation, involving minimization of the nuclear norm, does not in general return the solution for this…
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…
Sparse signal reconstruction algorithms have attracted research attention due to their wide applications in various fields. In this paper, we present a simple Bayesian approach that utilizes the sparsity constraint and a priori statistical…
We consider the matrix completion problem where the aim is to esti-mate a large data matrix for which only a relatively small random subset of its entries is observed. Quite popular approaches to matrix completion problem are iterative…
Adaptive regularization methods pre-multiply a descent direction by a preconditioning matrix. Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive. We show how…
In many autonomous mapping tasks, the maps cannot be accurately constructed due to various reasons such as sparse, noisy, and partial sensor measurements. We propose a novel map prediction method built upon the recent success of Low-Rank…
In this paper we consider the low-rank matrix completion problem with specific application to forecasting in time series analysis. Briefly, the low-rank matrix completion problem is the problem of imputing missing values of a matrix under a…