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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…

Machine Learning · Statistics 2021-06-11 Jiayi Wang , Raymond K. W. Wong , Xiaojun Mao , Kwun Chuen Gary Chan

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…

Statistics Theory · Mathematics 2022-03-09 Ji Chen , Xiaodong Li , Zongming Ma

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…

Machine Learning · Statistics 2015-09-16 Suriya Gunasekar , Pradeep Ravikumar , Joydeep Ghosh

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…

Methodology · Statistics 2022-08-18 Noirrit Kiran Chandra , Peter Mueller , Abhra Sarkar

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.…

Machine Learning · Computer Science 2021-06-08 Amit Boyarski , Sanketh Vedula , Alex Bronstein

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…

Optimization and Control · Mathematics 2024-05-21 Wenjing Li , Wei Bian , Kim-Chuan Toh

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…

Machine Learning · Statistics 2014-10-23 Pierre Alquier , Vincent Cottet , Nicolas Chopin , Judith Rousseau

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…

Information Theory · Computer Science 2010-06-11 Wei Dai , Ely Kerman , Olgica Milenkovic

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,…

Machine Learning · Statistics 2018-06-27 Pierre Alquier

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…

Optimization and Control · Mathematics 2015-06-23 Weimin Miao , Shaohua Pan , Defeng Sun

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…

Disordered Systems and Neural Networks · Physics 2016-02-11 Alaa Saade , Florent Krzakala , Lenka Zdeborová

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…

Machine Learning · Statistics 2024-10-29 Tiangang Cui , Alex Gorodetsky

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…

Machine Learning · Statistics 2015-03-26 Yang Cao , Yao Xie

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…

Numerical Analysis · Mathematics 2018-01-03 Augustin Cosse , Laurent Demanet

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…

Machine Learning · Statistics 2017-09-04 Nihar B. Shah , Sivaraman Balakrishnan , Martin J. Wainwright

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…

Statistics Theory · Mathematics 2015-06-05 Ahmed A. Quadeer , Tareq Y. Al-Naffouri

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…

Statistics Theory · Mathematics 2015-02-03 Olga Klopp

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…

Machine Learning · Computer Science 2020-11-19 Naman Agarwal , Brian Bullins , Xinyi Chen , Elad Hazan , Karan Singh , Cyril Zhang , Yi Zhang

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…

Robotics · Computer Science 2021-11-02 Zheng Chen , Shi Bai , Lantao Liu

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…

Methodology · Statistics 2018-02-23 Jonathan Gillard , Konstantin Usevich