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For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called…

Optimization and Control · Mathematics 2025-08-04 Matteo Bergamaschi , Andrea Cristofari , Vyacheslav Kungurtsev , Francesco Rinaldi

The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a…

Statistics Theory · Mathematics 2008-06-26 Adam J. Rothman , Peter J. Bickel , Elizaveta Levina , Ji Zhu

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the…

Computer Vision and Pattern Recognition · Computer Science 2010-06-16 Guoshen Yu , Guillermo Sapiro , Stéphane Mallat

We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the…

Statistics Theory · Mathematics 2013-10-15 Tingni Sun , Cun-Hui Zhang

In this paper, we propose two new algorithms for maximum-likelihood estimation (MLE) of high dimensional sparse covariance matrices. Unlike most of the state of-the-art methods, which either use regularization techniques or penalize the…

Methodology · Statistics 2023-05-12 Ghania Fatima , Prabhu Babu , Petre Stoica

We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…

Artificial Intelligence · Computer Science 2007-07-06 Onureena Banerjee , Laurent El Ghaoui , Alexandre d'Aspremont

This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…

Methodology · Statistics 2021-09-13 Jason Xu , Kenneth Lange

Inverse optimization refers to the inference of unknown parameters of an optimization problem based on knowledge of its optimal solutions. This paper considers inverse optimization in the setting where measurements of the optimal solutions…

Optimization and Control · Mathematics 2017-12-27 Anil Aswani , Zuo-Jun Max Shen , Auyon Siddiq

AIMS. The maximum-likelihood method is the standard approach to obtain model fits to observational data and the corresponding confidence regions. We investigate possible sources of bias in the log-likelihood function and its subsequent…

Astrophysics · Physics 2009-11-11 J. Hartlap , P. Simon , P. Schneider

Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…

Methodology · Statistics 2023-06-13 Sunpeng Duan , Guo Yu , Juntao Duan , Yuedong Wang

We develop a method for estimating well-conditioned and sparse covariance and inverse covariance matrices from a sample of vectors drawn from a sub-gaussian distribution in high dimensional setting. The proposed estimators are obtained by…

Statistics Theory · Mathematics 2016-11-21 Ashwini Maurya

Inverse problems arise in a wide spectrum of applications in fields ranging from engineering to scientific computation. Connected with the rise of interest in inverse problems is the development and analysis of regularization methods, such…

Numerical Analysis · Mathematics 2025-05-12 Abinash Nayak

We propose a variant of the classical conditional gradient method for sparse inverse problems with differentiable measurement models. Such models arise in many practical problems including superresolution, time-series modeling, and matrix…

Optimization and Control · Mathematics 2015-07-07 Nicholas Boyd , Geoffrey Schiebinger , Benjamin Recht

In distributed systems, communication is a major concern due to issues such as its vulnerability or efficiency. In this paper, we are interested in estimating sparse inverse covariance matrices when samples are distributed into different…

Methodology · Statistics 2016-10-04 Jesús Arroyo , Elizabeth Hou

We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

Machine Learning · Computer Science 2019-05-31 Liu Liu , Yanyao Shen , Tianyang Li , Constantine Caramanis

A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…

Methodology · Statistics 2011-02-14 Tony Cai , Weidong Liu , Xi Luo

Sparse high dimensional graphical model selection is a popular topic in contemporary machine learning. To this end, various useful approaches have been proposed in the context of $\ell_1$-penalized estimation in the Gaussian framework.…

Computation · Statistics 2022-02-04 Sang-Yun Oh , Onkar Dalal , Kshitij Khare , Bala Rajaratnam

High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…

Methodology · Statistics 2016-06-28 Sang-Yun Oh , Bala Rajaratnam , Joong-Ho Won

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

We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call Iterative Conditional Fitting, for computing the maximum…

Statistics Theory · Mathematics 2010-03-04 Sanjay Chaudhuri , Mathias Drton , Thomas S. Richardson