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Building higher-dimensional copulas is generally recognized as a difficult problem. Regular-vines using bivariate copulas provide a flexible class of high-dimensional dependency models. In large dimensions, the drawback of the model is the…

Statistics Theory · Mathematics 2012-06-07 Edith Kovacs , Tamas Szantai

High-dimensional compositional data arise naturally in many applications such as metagenomic data analysis. The observed data lie in a high-dimensional simplex, and conventional statistical methods often fail to produce sensible results due…

Methodology · Statistics 2016-01-19 Yuanpei Cao , Wei Lin , Hongzhe Li

Standard high-dimensional regression methods assume that the underlying coefficient vector is sparse. This might not be true in some cases, in particular in presence of hidden, confounding variables. Such hidden confounding can be…

Methodology · Statistics 2020-08-19 Domagoj Ćevid , Peter Bühlmann , Nicolai Meinshausen

A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To…

Methodology · Statistics 2011-01-19 Jianqing Fan , Yang Feng , Rui Song

We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…

Methodology · Statistics 2015-12-09 T. Tony Cai , Linjun Zhang

Finite order Markov models are theoretically well-studied models for dependent discrete data. Despite their generality, application in empirical work when the order is large is rare. Practitioners avoid using higher order Markov models…

Statistics Theory · Mathematics 2023-03-06 Guilherme Ost , Daniel Takahashi

The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…

Methodology · Statistics 2012-11-05 Cun-Hui Zhang , Stephanie S. Zhang

We study the classification problem for high-dimensional data with $n$ observations on $p$ features where the $p \times p$ covariance matrix $\Sigma$ exhibits a spiked eigenvalue structure and the vector $\zeta$, given by the difference…

Machine Learning · Statistics 2026-02-12 Yin-Jen Chen , Minh Tang

Finding an approximation of the inverse of the covariance matrix, also known as precision matrix, of a random vector with empirical data is widely discussed in finance and engineering. In data-driven problems, empirical data may be…

Statistics Theory · Mathematics 2026-03-10 Renjie Chen , Huifu Xu , Henryk Zähle

Sparse principal component analysis (sPCA) has become one of the most widely used techniques for dimensionality reduction in high-dimensional datasets. The main challenge underlying sPCA is to estimate the first vector of loadings of the…

Methodology · Statistics 2018-02-01 Jana Janková , Sara van de Geer

We introduce a new sparse sliced inverse regression estimator called Cholesky matrix penalization and its adaptive version for achieving sparsity in estimating the dimensions of the central subspace. The new estimators use the Cholesky…

Methodology · Statistics 2021-04-21 Linh Nghiem , Francis K. C. Hui , Samuel Mueller , A. H. Welsh

Training neural network models with discrete (categorical or structured) latent variables can be computationally challenging, due to the need for marginalization over large or combinatorial sets. To circumvent this issue, one typically…

Machine Learning · Computer Science 2020-12-29 Gonçalo M. Correia , Vlad Niculae , Wilker Aziz , André F. T. Martins

In many applications it is desirable to infer coarse-grained models from observational data. The observed process often corresponds only to a few selected degrees of freedom of a high-dimensional dynamical system with multiple time scales.…

Statistics Theory · Mathematics 2015-05-06 Serafim Kalliadasis , Sebastian Krumscheid , Grigorios A. Pavliotis

We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…

Statistics Theory · Mathematics 2016-07-21 Jana Janková , Sara van de Geer

We focus on the problem of estimating the change in the dependency structures of two $p$-dimensional Gaussian Graphical models (GGMs). Previous studies for sparse change estimation in GGMs involve expensive and difficult non-smooth…

Machine Learning · Computer Science 2018-05-24 Beilun Wang , Arshdeep Sekhon , Yanjun Qi

We propose a sparse regression method based on the non-concave penalized density power divergence loss function which is robust against infinitesimal contamination in very high dimensionality. Present methods of sparse and robust regression…

Methodology · Statistics 2021-05-18 Abhik Ghosh , Subhabrata Majumdar

Across a variety of scientific disciplines, sparse inverse covariance estimation is a popular tool for capturing the underlying dependency relationships in multivariate data. Unfortunately, most estimators are not scalable enough to handle…

In this paper, we study the problem of high-dimensional approximately low-rank covariance matrix estimation with missing observations. We propose a simple procedure computationally tractable in high-dimension and that does not require…

Statistics Theory · Mathematics 2012-05-14 Karim Lounici

We propose a novel, efficient approach for distributed sparse learning in high-dimensions, where observations are randomly partitioned across machines. Computationally, at each round our method only requires the master machine to solve a…

Machine Learning · Statistics 2016-05-26 Jialei Wang , Mladen Kolar , Nathan Srebro , Tong Zhang

This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. We consider a sparse projection of input variables and a general stationary covariance model that depends on the Euclidean distance…

Machine Learning · Computer Science 2020-08-26 Chiwoo Park , David J. Borth , Nicholas S. Wilson , Chad N. Hunter