Related papers: Iteratively Reweighted $\ell_1$-Penalized Robust R…
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…
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…
This paper presents a number of new findings about the canonical change point estimation problem. The first part studies the estimation of a change point on the real line in a simple stump model using the robust Huber estimating function…
We present a new method for high-dimensional linear regression when a scale parameter of the additive errors is unknown. The proposed estimator is based on a penalized Huber $M$-estimator, for which theoretical results on estimation error…
Heavy-tailed high-dimensional data are commonly encountered in various scientific fields and pose great challenges to modern statistical analysis. A natural procedure to address this problem is to use penalized quantile regression with…
We study the problem of linear regression where both covariates and responses are potentially (i) heavy-tailed and (ii) adversarially contaminated. Several computationally efficient estimators have been proposed for the simpler setting…
Robust estimation has played an important role in statistical and machine learning. However, its applications to functional linear regression are still under-developed. In this paper, we focus on Huber's loss with a diverging robustness…
In high-dimensional model selection problems, penalized simple least-square approaches have been extensively used. This paper addresses the question of both robustness and efficiency of penalized model selection methods, and proposes a…
Many problems in signal processing require finding sparse solutions to under-determined, or ill-conditioned, linear systems of equations. When dealing with real-world data, the presence of outliers and impulsive noise must also be accounted…
We investigate the high-dimensional properties of robust regression estimators in the presence of heavy-tailed contamination of both the covariates and response functions. In particular, we provide a sharp asymptotic characterisation of…
Longitudinal data often involve heterogeneity, sparse signals, and contamination from response outliers or high-leverage observations especially in biomedical science. Existing methods usually address only part of this problem, either…
We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are…
Iteratively reweighted $\ell_1$ algorithm is a popular algorithm for solving a large class of optimization problems whose objective is the sum of a Lipschitz differentiable loss function and a possibly nonconvex sparsity inducing…
Penalized regression estimators are a popular tool for the analysis of sparse and high-dimensional data sets. However, penalized regression estimators defined using an unbounded loss function can be very sensitive to the presence of…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…
We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…
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…
This paper proposes an adaptive penalized weighted mean regression for outlier detection of high-dimensional data. In comparison to existing approaches based on the mean shift model, the proposed estimators demonstrate robustness against…
Heavy-tailed errors impair the accuracy of the least squares estimate, which can be spoiled by a single grossly outlying observation. As argued in the seminal work of Peter Huber in 1973 [{\it Ann. Statist.} {\bf 1} (1973) 799--821], robust…
The explicit regularization and optimality of deep neural networks estimators from independent data have made considerable progress recently. The study of such properties on dependent data is still a challenge. In this paper, we carry out…