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We propose a novel class of time-varying nonparanormal graphical models, which allows us to model high dimensional heavy-tailed systems and the evolution of their latent network structures. Under this model, we develop statistical tests for…

Machine Learning · Statistics 2018-02-14 Junwei Lu , Mladen Kolar , Han Liu

This paper presents a novel method to make statistical inferences for both the model support and regression coefficients in a high-dimensional logistic regression model. Our method is based on the repro samples framework, in which we…

Methodology · Statistics 2024-03-18 Xiaotian Hou , Linjun Zhang , Peng Wang , Min-ge Xie

This paper studies inference in the high-dimensional linear regression model with outliers. Sparsity constraints are imposed on the vector of coefficients of the covariates. The number of outliers can grow with the sample size while their…

Statistics Theory · Mathematics 2021-02-08 Jad Beyhum

We consider the high-dimensional linear regression model and assume that a fraction of the measurements are altered by an adversary with complete knowledge of the data and the underlying distribution. We are interested in a scenario where…

Statistics Theory · Mathematics 2023-12-11 Stanislav Minsker , Mohamed Ndaoud , Lang Wang

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…

Machine Learning · Computer Science 2016-11-16 Hang Zhang , Fengyuan Zhu , Shixin Li

This paper focuses on the problem of determining as large a region as possible where a function exceeds a given threshold with high probability. We assume that we only have access to a noise-corrupted version of the function and that…

Machine Learning · Statistics 2018-11-27 Andrea Zanette , Junzi Zhang , Mykel J. Kochenderfer

Generalized linear models (GLMs) form one of the most popular classes of models in statistics. The gamma variant is used, for instance, in actuarial science for the modelling of claim amounts in insurance. A flaw of GLMs is that they are…

Methodology · Statistics 2024-02-12 Philippe Gagnon , Yuxi Wang

Sparse regression such as the Lasso has achieved great success in handling high-dimensional data. However, one of the biggest practical problems is that high-dimensional data often contain large amounts of missing values. Convex Conditioned…

Machine Learning · Statistics 2019-06-20 Masaaki Takada , Hironori Fujisawa , Takeichiro Nishikawa

The Gaussian kernel and its traditional normalizations (e.g., row-stochastic) are popular approaches for assessing similarities between data points. Yet, they can be inaccurate under high-dimensional noise, especially if the noise magnitude…

Statistics Theory · Mathematics 2023-07-12 Boris Landa , Xiuyuan Cheng

This paper addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing $L_1$-regularized estimation methods, including the…

Econometrics · Economics 2024-08-08 Zhan Gao , Hyungsik Roger Moon

We study efficient algorithms for linear regression and covariance estimation in the absence of Gaussian assumptions on the underlying distributions of samples, making assumptions instead about only finitely-many moments. We focus on how…

This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…

Methodology · Statistics 2023-11-27 Ying Jin , Dominik Rothenhäusler

Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a…

Statistics Theory · Mathematics 2026-04-21 Alejandro Cholaquidis , Emilien Joly , Leonardo Moreno

The success of the Lasso in the era of high-dimensional data can be attributed to its conducting an implicit model selection, i.e., zeroing out regression coefficients that are not significant. By contrast, classical ridge regression can…

Statistics Theory · Mathematics 2021-04-23 Yunyi Zhang , Dimitris N. Politis

Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…

Data Structures and Algorithms · Computer Science 2023-05-29 Jonathan Kelner , Frederic Koehler , Raghu Meka , Dhruv Rohatgi

This paper introduces a loss-based generalized Bayesian methodology for high-dimensional robust regression with serially correlated errors and predictors. The proposed framework employs a novel scaled pseudo-Huber (SPH) loss function, which…

Methodology · Statistics 2025-03-13 Saptarshi Chakraborty , Kshitij Khare , George Michailidis

Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…

Methodology · Statistics 2026-02-10 Teemu Härkönen , Simo Särkkä

Large Language Models (LLMs) have demonstrated remarkable in-context learning capabilities, enabling flexible utilization of limited historical information to play pivotal roles in reasoning, problem-solving, and complex pattern recognition…

Machine Learning · Computer Science 2025-03-31 Zhonglin Jiang , Qian Tang , Zequn Wang

We show that the two-stage adaptive Lasso procedure (Zou, 2006) is consistent for high-dimensional model selection in linear and Gaussian graphical models. Our conditions for consistency cover more general situations than those accomplished…

Statistics Theory · Mathematics 2009-03-17 Shuheng Zhou , Sara van de Geer , Peter Bühlmann

Finite mixture regression models are useful for modeling the relationship between response and predictors, arising from different subpopulations. In this article, we study high-dimensional predic- tors and high-dimensional response, and…

Statistics Theory · Mathematics 2016-01-07 Emilie Devijver