Related papers: The BerHu penalty and the grouped effect
The ordinary least squares estimate in linear regression is sensitive to the influence of errors with large variance, which reduces its robustness, especially when dealing with heavy-tailed errors or outliers frequently encountered in…
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 investigates tradeoffs among optimization errors, statistical rates of convergence and the effect of heavy-tailed errors for high-dimensional robust regression with nonconvex regularization. When the additive errors in linear…
We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…
In this paper, we propose a novel method to select significant variables and estimate the corresponding coefficients in multiple-index models with a group structure. All existing approaches for single-index models cannot be extended…
Penalization schemes like Lasso or ridge regression are routinely used to regress a response of interest on a high-dimensional set of potential predictors. Despite being decisive, the question of the relative strength of penalization is…
Penalized logistic regression is extremely useful for binary classification with large number of covariates (higher than the sample size), having several real life applications, including genomic disease classification. However, the…
Many estimators of the average effect of a treatment on an outcome require estimation of the propensity score, the outcome regression, or both. It is often beneficial to utilize flexible techniques such as semiparametric regression or…
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…
We introduce a novel method to simultaneously perform variable selection and estimation in the joint frailty model of recurrent and terminal events using the Broken Adaptive Ridge Regression penalty. The BAR penalty can be summarized as an…
High-dimensional sparse modeling via regularization provides a powerful tool for analyzing large-scale data sets and obtaining meaningful, interpretable models. The use of nonconvex penalty functions shows advantage in selecting important…
The $\ell_1$-penalized method, or the Lasso, has emerged as an important tool for the analysis of large data sets. Many important results have been obtained for the Lasso in linear regression which have led to a deeper understanding of…
We consider the problem of simultaneous variable selection and estimation of the corresponding regression coefficients in an ultra-high dimensional linear regression models, an extremely important problem in the recent era. The adaptive…
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…
High-dimensional data subject to heavy-tailed phenomena and heterogeneity are commonly encountered in various scientific fields and bring new challenges to the classical statistical methods. In this paper, we combine the asymmetric square…
In high-dimensional data settings, additional information on the features is often available. Examples of such external information in omics research are: (a) p-values from a previous study, (b) a summary of prior information, and (c) omics…
This paper studies the asymptotic properties of the penalized least squares estimator using an adaptive group Lasso penalty for the reduced rank regression. The group Lasso penalty is defined in the way that the regression coefficients…
Penalized least squares estimation is a popular technique in high-dimensional statistics. It includes such methods as the LASSO, the group LASSO, and the nuclear norm penalized least squares. The existing theory of these methods is not…
We consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a…
This paper introduces a new regularized version of the robust $\tau$-regression estimator for analyzing high-dimensional datasets subject to gross contamination in the response variables and covariates. The resulting estimator, termed…