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Matrix completion algorithms recover a low rank matrix from a small fraction of the entries, each entry contaminated with additive errors. In practice, the singular vectors and singular values of the low rank matrix play a pivotal role for…

Methodology · Statistics 2016-05-03 Juhee Cho , Donggyu Kim , Karl Rohe

An incoherent low-rank matrix can be efficiently reconstructed after observing a few of its entries at random, and then solving a convex program that minimizes the nuclear norm. In many applications, in addition to these entries,…

Information Theory · Computer Science 2018-03-14 Armin Eftekhari , Dehui Yang , Michael B. Wakin

Theoretical guarantees are established for a standard estimator in a semi-parametric finite mixture model, where each component density is modeled as a product of univariate densities under a conditional independence assumption. The focus…

Statistics Theory · Mathematics 2025-11-07 Marie Du Roy de Chaumaray , Michael Levine , Matthieu Marbac

The linear regression model with a random variable (RV) measurement matrix, where the mean of the random measurement matrix has full column rank, has been extensively studied. In particular, the quasiconvexity of the maximum likelihood…

Signal Processing · Electrical Eng. & Systems 2025-07-16 Ruohai Guo , Jiang Zhu , Xing Jiang , Fengzhong Qu

This paper studies the stability of some reconstruction algorithms for compressed sensing in terms of the bit precision. Considering the fact that practical digital systems deal with discretized signals, we motivate the importance of the…

Information Theory · Computer Science 2009-01-16 Ehsan Ardestanizadeh , Mahdi Cheraghchi , Amin Shokrollahi

In this paper, we introduce the Maximum Matrix Contraction problem, where we aim to contract as much as possible a binary matrix in order to maximize its density. We study the complexity and the polynomial approximability of the problem.…

Computational Complexity · Computer Science 2023-06-05 Dimitri Watel , Pierre-Louis Poirion

We study the problem of estimating a low-rank positive semidefinite (PSD) matrix from a set of rank-one measurements using sensing vectors composed of i.i.d. standard Gaussian entries, which are possibly corrupted by arbitrary outliers.…

Information Theory · Computer Science 2016-12-21 Yuanxin Li , Yue Sun , Yuejie Chi

We prove various theorems on approximation using polynomials with integer coefficients in the Bernstein basis of any given order. In the extreme, we draw the coefficients from $\{ \pm 1\}$ only. A basic case of our results states that for…

Information Theory · Computer Science 2022-12-08 C. Sinan Güntürk , Weilin Li

We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…

Machine Learning · Computer Science 2009-11-04 Raghunandan H. Keshavan , Andrea Montanari , Sewoong Oh

A completion of an m-by-n matrix A with entries in {0,1,*} is obtained by setting all *-entries to constants 0 or 1. A system of semi-linear equations over GF(2) has the form Mx=f(x), where M is a completion of A and f:{0,1}^n --> {0,1}^m…

Computational Complexity · Computer Science 2012-04-18 S. Jukna , G. Schnitger

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

This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power…

Optimization and Control · Mathematics 2020-06-09 Yajing Liu , April Sagan , Andrey Bernstein , Rui Yang , Xinyang Zhou , Yingchen Zhang

It is generally believed that ensemble approaches, which combine multiple algorithms or models, can outperform any single algorithm at machine learning tasks, such as prediction. In this paper, we propose Bayesian convex and linear…

Statistics Theory · Mathematics 2014-03-07 Yun Yang , David B. Dunson

This work considers detecting the presence of a band-limited random radio source using an antenna array featuring a low-complexity digitization process with single-bit output resolution. In contrast to high-resolution analog-to-digital…

Information Theory · Computer Science 2018-02-21 Manuel S. Stein

Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem---e.g., in determining the relationship between genetics and the presence or absence of a disease---or they…

Information Theory · Computer Science 2014-08-01 Richard Baraniuk , Simon Foucart , Deanna Needell , Yaniv Plan , Mary Wootters

Minimum Bayes Risk (MBR) decoding optimizes output selection by maximizing the expected utility value of an underlying human distribution. While prior work has shown the effectiveness of MBR decoding through empirical evaluation, few…

Computation and Language · Computer Science 2025-06-23 Yuki Ichihara , Yuu Jinnai , Kaito Ariu , Tetsuro Morimura , Eiji Uchibe

Tensor completion is a fundamental tool for incomplete data analysis, where the goal is to predict missing entries from partial observations. However, existing methods often make the explicit or implicit assumption that the observed entries…

Machine Learning · Statistics 2022-03-18 Yuning Qiu , Guoxu Zhou , Qibin Zhao , Shengli Xie

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…

Statistics Theory · Mathematics 2017-07-10 Olga Klopp , Yu Lu , Alexandre B. Tsybakov , Harrison H. Zhou

This paper considers the problem of estimating a low-rank matrix from the observation of all or a subset of its entries in the presence of Poisson noise. When we observe all entries, this is a problem of matrix denoising; when we observe…

Machine Learning · Statistics 2024-04-22 Andrew D. McRae , Mark A. Davenport

We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…

Machine Learning · Statistics 2015-06-15 Zhaoshi Meng , Dennis Wei , Ami Wiesel , Alfred O. Hero