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Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

Machine Learning · Statistics 2012-06-22 Tingni Sun , Cun-Hui Zhang

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

Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight…

Optimization and Control · Mathematics 2007-06-13 Alexandre d'Aspremont , Onureena Banerjee , Laurent El Ghaoui

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

The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in…

Methodology · Statistics 2015-06-04 Viktoria Öllerer , Christophe Croux

A conditional independence graph is a concise representation of pairwise conditional independence among many variables. Graphical Random Forests (GRaFo) are a novel method for estimating pairwise conditional independence relationships among…

Sliced inverse regression is a popular tool for sufficient dimension reduction, which replaces covariates with a minimal set of their linear combinations without loss of information on the conditional distribution of the response given the…

Machine Learning · Statistics 2018-09-18 Kean Ming Tan , Zhaoran Wang , Tong Zhang , Han Liu , R. Dennis Cook

This paper studies model selection consistency for high dimensional sparse regression when data exhibits both cross-sectional and serial dependency. Most commonly-used model selection methods fail to consistently recover the true model when…

Methodology · Statistics 2018-09-12 Jianqing Fan , Yuan Ke , Kaizheng Wang

Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time,…

Methodology · Statistics 2025-07-29 Niloofar Ramezani , Martin Slawski

We provide a selected overview of methodology and theory for estimation and inference on the edge weights in high-dimensional directed and undirected Gaussian graphical models. For undirected graphical models, two main explicit…

Statistics Theory · Mathematics 2018-01-26 Jana Jankova , Sara van de Geer

This paper introduces a multi-way tensor generalization of the Bigraphical Lasso (BiGLasso), which uses a two-way sparse Kronecker-sum multivariate-normal model for the precision matrix to parsimoniously model conditional dependence…

Methodology · Statistics 2019-09-24 Kristjan Greenewald , Shuheng Zhou , Alfred Hero

This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…

Computation · Statistics 2011-05-31 F. Orieux , O. Féron , J. -F. Giovannelli

Identifying the Markov properties or conditional independencies of a collection of random variables is a fundamental task in statistics for modeling and inference. Existing approaches often learn the structure of a probabilistic graphical…

Machine Learning · Computer Science 2025-05-23 Sarah Liaw , Rebecca Morrison , Youssef Marzouk , Ricardo Baptista

We study the problem of prediction for evolving graph data. We formulate the problem as the minimization of a convex objective encouraging sparsity and low-rank of the solution, that reflect natural graph properties. The convex formulation…

Machine Learning · Statistics 2012-05-10 Emile Richard , Pierre-Andre Savalle , Nicolas Vayatis

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…

Machine Learning · Statistics 2011-06-28 Suvrit Sra , Dongmin Kim

In this paper, we are concerned with regression problems where covariates can be grouped in nonoverlapping blocks, and where only a few of them are assumed to be active. In such a situation, the group Lasso is an at- tractive method for…

Information Theory · Computer Science 2013-01-01 Samuel Vaiter , Charles Deledalle , Gabriel Peyré , Jalal Fadili , Charles Dossal

We consider the high-dimensional sparse linear regression problem of accurately estimating a sparse vector using a small number of linear measurements that are contaminated by noise. It is well known that the standard cadre of…

Statistics Theory · Mathematics 2014-02-25 Divyanshu Vats , Richard G. Baraniuk

Graphical modeling explores dependences among a collection of variables by inferring a graph that encodes pairwise conditional independences. For jointly Gaussian variables, this translates into detecting the support of the precision…

Methodology · Statistics 2018-02-16 Shota Katayama , Hironori Fujisawa , Mathias Drton

Gaussian Graphical Models (GGMs) are widely used in high-dimensional data analysis to synthesize the interaction between variables. In many applications, such as genomics or image analysis, graphical models rely on sparsity and clustering…

Machine Learning · Statistics 2026-03-25 Do Edmond Sanou , Christophe Ambroise , Geneviève Robin

Unsupervised feature selection is an important method to reduce dimensions of high dimensional data without labels, which is benefit to avoid ``curse of dimensionality'' and improve the performance of subsequent machine learning tasks, like…

Machine Learning · Computer Science 2020-12-29 Yanyong Huang , Zongxin Shen , Fuxu Cai , Tianrui Li , Fengmao Lv