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We study ridge estimation of the precision matrix in the high-dimensional setting where the number of variables is large relative to the sample size. We first review two archetypal ridge estimators and note that their utilized penalties do…

Methodology · Statistics 2016-06-17 Wessel N. van Wieringen , Carel F. W. Peeters

We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…

Machine Learning · Statistics 2025-05-13 Samuel Erickson , Tobias Rydén

We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…

Statistics Theory · Mathematics 2016-04-20 Ilya Soloveychik , Ami Wiesel

In this paper, we consider testing the correlation coefficient matrix between two subsets of high-dimensional variables. We produce a test statistic by using the extended cross-data-matrix (ECDM) methodology and show the unbiasedness of…

Methodology · Statistics 2015-03-24 Kazuyoshi Yata , Makoto Aoshima

We consider the problem of precision matrix estimation where, due to extraneous confounding of the underlying precision matrix, the data are independent but not identically distributed. While such confounding occurs in many scientific…

Machine Learning · Statistics 2019-07-01 Sinong Geng , Mladen Kolar , Oluwasanmi Koyejo

We consider a graphical model where a multivariate normal vector is associated with each node of the underlying graph and estimate the graphical structure. We minimize a loss function obtained by regressing the vector at each node on those…

Machine Learning · Statistics 2017-09-19 Xingqi Du , Subhashis Ghosal

We study the accuracy of estimating the covariance and the precision matrix of a $D$-variate sub-Gaussian distribution along a prescribed subspace or direction using the finite sample covariance. Our results show that the estimation…

Statistics Theory · Mathematics 2021-01-14 Zeljko Kereta , Timo Klock

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

Machine Learning · Statistics 2010-09-07 Mehryar Mohri , Ameet Talwalkar

We consider the problem of estimating a sparse precision matrix of a multivariate Gaussian distribution, including the case where the dimension $p$ is large. Gaussian graphical models provide an important tool in describing conditional…

Statistics Theory · Mathematics 2014-04-08 Sayantan Banerjee , Subhashis Ghosal

In the realm of high-dimensional data analysis, the estimation of covariance matrices is a fundamental task, and this holds true for interval-valued data as well. However, there is no unified definition for the covariance matrix of…

Methodology · Statistics 2026-04-02 Wan Tian , Wenhao Cui , Rui Zhang , Bingyi Jing , Yang Liu , Yijie Peng

Estimation of Markov Random Field and covariance models from high-dimensional data represents a canonical problem that has received a lot of attention in the literature. A key assumption, widely employed, is that of {\em sparsity} of the…

Optimization and Control · Mathematics 2018-05-16 Davoud Ataee Tarzanagh , George Michailidis

The geometric median covariation matrix is a robust multivariate indicator of dispersion which can be extended without any difficulty to functional data. We define estimators, based on recursive algorithms, that can be simply updated at…

Statistics Theory · Mathematics 2016-07-12 Hervé Cardot , Antoine Godichon-Baggioni

Estimation of a sparse spectral precision matrix, the inverse of a spectral density matrix, is a canonical problem in frequency-domain analysis of high-dimensional time series (HDTS), with applications in neurosciences and environmental…

Methodology · Statistics 2025-11-11 Navonil Deb , Amy Kuceyeski , Sumanta Basu

We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…

Machine Learning · Computer Science 2023-10-24 Jian-Feng Cai , José Vinícius de M. Cardoso , Daniel P. Palomar , Jiaxi Ying

We consider the estimation and inference of graphical models that characterize the dependency structure of high-dimensional tensor-valued data. To facilitate the estimation of the precision matrix corresponding to each way of the tensor, we…

Machine Learning · Statistics 2019-02-27 Xiang Lyu , Will Wei Sun , Zhaoran Wang , Han Liu , Jian Yang , Guang Cheng

The variance--covariance matrix plays a central role in the inferential theories of high-dimensional factor models in finance and economics. Popular regularization methods of directly exploiting sparsity are not directly applicable to many…

Methodology · Statistics 2012-03-15 Jianqing Fan , Yuan Liao , Martina Mincheva

Because of the advance in technologies, modern statistical studies often encounter linear models with the number of explanatory variables much larger than the sample size. Estimation and variable selection in these high-dimensional problems…

Statistics Theory · Mathematics 2012-06-06 Jun Shao , Xinwei Deng

In this manuscript a unified framework for conducting inference on complex aggregated data in high dimensional settings is proposed. The data are assumed to be a collection of multiple non-Gaussian realizations with underlying undirected…

Applications · Statistics 2013-10-14 Fang Han , Han Liu , Brian Caffo

We develop a new estimator of the inverse covariance matrix for high-dimensional multivariate normal data using the horseshoe prior. The proposed graphical horseshoe estimator has attractive properties compared to other popular estimators,…

Methodology · Statistics 2019-01-08 Yunfan Li , Bruce A. Craig , Anindya Bhadra

Estimation of the precision matrix (or inverse covariance matrix) is of great importance in statistical data analysis and machine learning. However, as the number of parameters scales quadratically with the dimension $p$, computation…

Computation · Statistics 2022-11-02 Qian LI , Binyan Jiang , Defeng Sun