English
Related papers

Related papers: High dimensional matrix estimation with unknown va…

200 papers

The estimation of high dimensional precision matrices has been a central topic in statistical learning. However, as the number of parameters scales quadratically with the dimension $p$, many state-of-the-art methods do not scale well to…

Computation · Statistics 2019-07-10 Cheng Wang , Binyan Jiang

Estimating conditional dependence graphs and precision matrices are some of the most common problems in modern statistics and machine learning. When data are fully observed, penalized maximum likelihood-type estimators have become standard…

Machine Learning · Statistics 2019-04-09 Roger Fan , Byoungwook Jang , Yuekai Sun , Shuheng Zhou

In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the…

Statistics Theory · Mathematics 2011-10-26 Jérémie Bigot , Rolando Biscay , Jean-Michel Loubes , Lilian Muniz Alvarez

Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating…

Machine Learning · Statistics 2019-10-29 Cheng Mao , Ashwin Pananjady , Martin J. Wainwright

In this paper, we consider the problem of identifying a linear map from measurements which are subject to intermittent and arbitarily large errors. This is a fundamental problem in many estimation-related applications such as fault…

Systems and Control · Computer Science 2016-08-09 Laurent Bako , Henrik Ohlsson

Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…

Computer Vision and Pattern Recognition · Computer Science 2020-03-23 Huu Le , Christopher Zach

Many important problems are characterized by the eigenvalues of a large matrix. For example, the difficulty of many optimization problems, such as those arising from the fitting of large models in statistics and machine learning, can be…

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

Methodology · Statistics 2025-02-07 Neil K. Chada , Ajay Jasra , Mohamed Maama , Raul Tempone

We propose a new method of estimation in high-dimensional linear regression model. It allows for very weak distributional assumptions including heteroscedasticity, and does not require the knowledge of the variance of random errors. The…

Statistics Theory · Mathematics 2013-04-16 Eric Gautier , Alexandre Tsybakov

We study the matrix denoising problem of estimating the singular vectors of a rank-$1$ signal corrupted by noise with both column and row correlations. Existing works are either unable to pinpoint the exact asymptotic estimation error or,…

Statistics Theory · Mathematics 2024-10-29 Yihan Zhang , Marco Mondelli

This work addresses the issue of large covariance matrix estimation in high-dimensional statistical analysis. Recently, improved iterative algorithms with positive-definite guarantee have been developed. However, these algorithms cannot be…

Information Theory · Computer Science 2016-07-29 Fei Wen , Yuan Yang , Peilin Liu , Robert C. Qiu

In this paper we propose new approaches to estimating large dimensional monotone index models. This class of models has been popular in the applied and theoretical econometrics literatures as it includes discrete choice, nonparametric…

Econometrics · Economics 2023-02-22 Shakeeb Khan , Xiaoying Lan , Elie Tamer , Qingsong Yao

We consider a structured estimation problem where an observed matrix is assumed to be generated as an $s$-sparse linear combination of $N$ given $n\times n$ positive-semidefinite matrices. Recovering the unknown $N$-dimensional and…

Information Theory · Computer Science 2020-03-27 Fabian Jaensch , Peter Jung

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

Information Theory · Computer Science 2026-05-12 Frédéric Zheng , Yassir Jedra , Alexandre Proutiere

Estimation of low-rank matrices is of significant interest in a range of contemporary applications. In this paper, we introduce a rank-one projection model for low-rank matrix recovery and propose a constrained nuclear norm minimization…

Statistics Theory · Mathematics 2014-12-10 T. Tony Cai , Anru Zhang

We propose methodology for statistical inference for low-dimensional parameters of sparse precision matrices in a high-dimensional setting. Our method leads to a non-sparse estimator of the precision matrix whose entries have a Gaussian…

Statistics Theory · Mathematics 2015-08-13 Jana Jankova , Sara van de Geer

The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…

Methodology · Statistics 2019-07-22 Guo Yu , Jacob Bien

We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…

Machine Learning · Computer Science 2020-05-05 Yu Cheng , Ilias Diakonikolas , Rong Ge , Mahdi Soltanolkotabi

This article explores the estimation of precision matrices in high-dimensional Gaussian graphical models. We address the challenge of improving the accuracy of maximum likelihood-based precision estimation through penalization.…

Methodology · Statistics 2023-12-27 A. Bekker , A. Kheyri , M. Arashi

Precision matrix estimation is a fundamental topic in multivariate statistics and modern machine learning. This paper proposes an adversarially perturbed precision matrix estimation framework, motivated by recent developments in adversarial…

Methodology · Statistics 2026-03-25 Yiling Xie