Related papers: High dimensional thresholded regression and shrink…

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 provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…

We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…

Simultaneous feature selection and non-linear function estimation is challenging in modeling, especially in high-dimensional settings where the number of variables exceeds the available sample size. In this article, we investigate the…

This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset…

Covariance regression offers an effective way to model the large covariance matrix with the auxiliary similarity matrices. In this work, we propose a sparse covariance regression (SCR) approach to handle the potentially high-dimensional…

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…

Penalized likelihood approaches are widely used for high-dimensional regression. Although many methods have been proposed and the associated theory is now well-developed, the relative efficacy of different approaches in finite-sample…

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…

Logistic regression is commonly used for modeling dichotomous outcomes. In the classical setting, where the number of observations is much larger than the number of parameters, properties of the maximum likelihood estimator in logistic…

In this paper, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop $\ell_1$-penalized estimators of both regression coefficients and the threshold…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

The paper considers a linear regression model in high-dimension for which the predictive variables can change the influence on the response variable at unknown times (called change-points). Moreover, the particular case of the heavy-tailed…

$\ell_p$-norm penalization, notably the Lasso, has become a standard technique, extending shrinkage regression to subset selection. Despite aiming for oracle properties and consistent estimation, existing Lasso-derived methods still rely on…

Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. They were first dedicated to linear variable selection but numerous extensions have now emerged such as structured sparsity or kernel…

Feature subset selection arises in many high-dimensional applications of statistics, such as compressed sensing and genomics. The $\ell_0$ penalty is ideal for this task, the caveat being it requires the NP-hard combinatorial evaluation of…

This paper develops a new scalable sparse Cox regression tool for sparse high-dimensional massive sample size (sHDMSS) survival data. The method is a local $L_0$-penalized Cox regression via repeatedly performing reweighted $L_2$-penalized…

We consider high-dimensional generalized linear models with Lipschitz loss functions, and prove a nonasymptotic oracle inequality for the empirical risk minimizer with Lasso penalty. The penalty is based on the coefficients in the linear…

A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty,…

This paper discusses a class of thresholding-based iterative selection procedures (TISP) for model selection and shrinkage. People have long before noticed the weakness of the convex $l_1$-constraint (or the soft-thresholding) in wavelets…