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Gaussian graphical models (GGM) have been widely used in many high-dimensional applications ranging from biological and financial data to recommender systems. Sparsity in GGM plays a central role both statistically and computationally.…

Machine Learning · Statistics 2014-06-12 Zhaoshi Meng , Brian Eriksson , Alfred O. Hero

We consider high-dimensional generalized linear models when the covariates are contaminated by measurement error. Estimates from errors-in-variables regression models are well-known to be biased in traditional low-dimensional settings if…

Computation · Statistics 2020-01-06 Michael Byrd , Monnie McGee

A popular regularized (shrinkage) covariance estimator is the shrinkage sample covariance matrix (SCM) which shares the same set of eigenvectors as the SCM but shrinks its eigenvalues toward its grand mean. In this paper, a more general…

Methodology · Statistics 2020-02-13 Esa Ollila , Daniel P. Palomar , Frederic Pascal

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

Methodology · Statistics 2013-10-22 Hua Zhou , Lexin Li

For a high-dimensional linear model with a finite number of covariates measured with error, we study statistical inference on the parameters associated with the error-prone covariates, and propose a new corrected decorrelated score test and…

Methodology · Statistics 2020-01-29 Mengyan Li , Runze Li , Yanyuan Ma

We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…

Machine Learning · Computer Science 2014-08-12 Vikas Sindhwani , Ha Quang Minh , Aurelie Lozano

We propose a general matrix-valued multiple kernel learning framework for high-dimensional nonlinear multivariate regression problems. This framework allows a broad class of mixed norm regularizers, including those that induce sparsity, to…

Machine Learning · Statistics 2013-03-11 Vikas Sindhwani , Minh Ha Quang , Aurelie C. Lozano

For high dimensional data, some of the standard statistical techniques do not work well. So modification or further development of statistical methods are necessary. In this paper, we explore these modifications. We start with the important…

Statistical Finance · Quantitative Finance 2024-05-29 Arnab Chakrabarti , Rituparna Sen

We perform a finite sample analysis of the detection levels for sparse principal components of a high-dimensional covariance matrix. Our minimax optimal test is based on a sparse eigenvalue statistic. Alas, computing this test is known to…

Statistics Theory · Mathematics 2014-01-30 Quentin Berthet , Philippe Rigollet

In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in…

Machine Learning · Statistics 2017-10-19 Mathurin Massias , Olivier Fercoq , Alexandre Gramfort , Joseph Salmon

This paper gives a theoretical analysis of high dimensional linear discrimination of Gaussian data. We study the excess risk of linear discriminant rules. We emphasis on the poor performances of standard procedures in the case when…

Statistics Theory · Mathematics 2010-02-19 Robin Girard

In this paper, we present a sharp analysis for a class of alternating projected gradient descent algorithms which are used to solve the covariate adjusted precision matrix estimation problem in the high-dimensional setting. We demonstrate…

Information Theory · Computer Science 2022-01-13 Xiao Lv , Wei Cui , Yulong Liu

Generalization theory has been established for sparse deep neural networks under high-dimensional regime. Beyond generalization, parameter estimation is also important since it is crucial for variable selection and interpretability of deep…

Machine Learning · Statistics 2024-06-27 Dongya Wu , Xin Li

High-dimensional statistical learning (HDSL) has wide applications in data analysis, operations research, and decision-making. Despite the availability of multiple theoretical frameworks, most existing HDSL schemes stipulate the following…

Statistics Theory · Mathematics 2021-10-25 Hongcheng Liu , Yinyu Ye , Hung Yi Lee

The classic Hettmansperger-Randles Estimator has found extensive use in robust statistical inference. However, it cannot be directly applied to high-dimensional data. In this paper, we propose a high-dimensional Hettmansperger-Randles…

Methodology · Statistics 2025-05-06 Guowei Yan , Long Feng , Xiaoxu Zhang

This paper aims at achieving a simultaneously sparse and low-rank estimator from the semidefinite population covariance matrices. We first benefit from a convex optimization which develops $l_1$-norm penalty to encourage the sparsity and…

Statistics Theory · Mathematics 2014-08-08 Shenglong Zhou , Naihua Xiu , Ziyan Luo , Lingchen Kong

In this paper we study the asymptotic normality in high-dimensional linear regression. We focus on the case where the covariance matrix of the regression variables has a KMS structure, in asymptotic settings where the number of predictors,…

Statistics Theory · Mathematics 2022-05-17 Saulius Jokubaitis , Remigijus Leipus

Several new estimation methods have been recently proposed for the linear regression model with observation error in the design. Different assumptions on the data generating process have motivated different estimators and analysis. In…

Statistics Theory · Mathematics 2014-12-24 Alexandre Belloni , Mathieu Rosenbaum , Alexandre B. Tsybakov

We study the parameter estimation problem for a varying index coefficient model in high dimensions. Unlike the most existing works that iteratively estimate the parameters and link functions, based on the generalized Stein's identity, we…

Machine Learning · Statistics 2019-10-29 Sen Na , Zhuoran Yang , Zhaoran Wang , Mladen Kolar

Estimating some mathematical expectations from partially observed data and in particular missing outcomes is a central problem encountered in numerous fields such as transfer learning, counterfactual analysis or causal inference. Matching…

Statistics Theory · Mathematics 2025-05-01 Simon Viel , Lionel Truquet , Ikko Yamane