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We analyze the statistical consistency of robust estimators for precision matrices in high dimensions. We focus on a contamination mechanism acting cellwise on the data matrix. The estimators we analyze are formed by plugging appropriately…

Statistics Theory · Mathematics 2015-09-25 Po-Ling Loh , Xin Lu Tan

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

Covariance matrix estimation is a fundamental statistical task in many applications, but the sample covariance matrix is sub-optimal when the sample size is comparable to or less than the number of features. Such high-dimensional settings…

Methodology · Statistics 2022-06-06 Huiqin Xin , Sihai Dave Zhao

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

This paper tackles the problem of robust covariance matrix estimation when the data is incomplete. Classical statistical estimation methodologies are usually built upon the Gaussian assumption, whereas existing robust estimation ones assume…

We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…

Methodology · Statistics 2021-08-17 Shev Macnamara , Erik Schlögl , Zdravko I. Botev

CoVariance Neural Networks (VNNs) perform convolutions on the graph determined by the covariance matrix of the data, which enables expressive and stable covariance-based learning. However, covariance matrices are typically dense, fail to…

Machine Learning · Computer Science 2026-01-21 Andrea Cavallo , Samuel Rey , Antonio G. Marques , Elvin Isufi

The pattern of zero entries in the inverse covariance matrix of a multivariate normal distribution corresponds to conditional independence restrictions between variables. Covariance selection aims at estimating those structural zeros from…

Statistics Theory · Mathematics 2016-08-16 Nicolai Meinshausen , Peter Bühlmann

This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine…

Data Analysis, Statistics and Probability · Physics 2023-02-22 Krasymyr Tretiak , Georg Schollmeyer , Scott Ferson

Fitting high-dimensional data involves a delicate tradeoff between faithful representation and the use of sparse models. Too often, sparsity assumptions on the fitted model are too restrictive to provide a faithful representation of the…

Machine Learning · Statistics 2013-12-17 Majid Janzamin , Animashree Anandkumar

The precision matrix that encodes conditional linear dependency relations among a set of variables forms an important object of interest in multivariate analysis. Sparse estimation procedures for precision matrices such as the graphical…

Methodology · Statistics 2023-03-09 Gaëtan Louvet , Jakob Raymaekers , Germain Van Bever , Ines Wilms

Missing data occur frequently in a wide range of applications. In this paper, we consider estimation of high-dimensional covariance matrices in the presence of missing observations under a general missing completely at random model in the…

Methodology · Statistics 2016-05-17 T. Tony Cai , Anru Zhang

Precision matrix, which is the inverse of covariance matrix, plays an important role in statistics, as it captures the partial correlation between variables. Testing the equality of two precision matrices in high dimensional setting is a…

Methodology · Statistics 2018-10-23 Mingjuan Zhang , Yong He , Cheng Zhou , Xinsheng Zhang

Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…

Methodology · Statistics 2026-03-03 Rakheon Kim , Irina Gaynanova

This paper studies the covariance matrix estimation for high-dimensional time series within a new framework that combines low-rank factor and latent variable-specific cluster structures. The popular methods based on assuming the sparse…

Methodology · Statistics 2025-02-25 Dong Li , Xinghao Qiao , Cheng Yu

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

High-dimensional time series data exist in numerous areas such as finance, genomics, healthcare, and neuroscience. An unavoidable aspect of all such datasets is missing data, and dealing with this issue has been an important focus in…

Machine Learning · Statistics 2018-02-27 Amin Jalali , Rebecca Willett

The real-life data have a complex and non-linear structure due to their nature. These non-linearities and the large number of features can usually cause problems such as the empty-space phenomenon and the well-known curse of dimensionality.…

Machine Learning · Computer Science 2025-03-13 Kadir Özçoban , Murat Manguoğlu , Emrullah Fatih Yetkin

Precision matrix is of significant importance in a wide range of applications in multivariate analysis. This paper considers adaptive minimax estimation of sparse precision matrices in the high dimensional setting. Optimal rates of…

Statistics Theory · Mathematics 2012-12-13 T. Tony Cai , Weidong Liu , Harrison H. Zhou

This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…

Information Theory · Computer Science 2015-06-03 Jianfeng Yao , Abla Kammoun , Jamal Najim