Related papers: One-step sparse estimates in nonconcave penalized …
We construct an objective function that consists of a quadratic approximation term and a penalty term. Thanks to the quadratic approximation, we can deal with various kinds of loss functions into a unified way, and by taking advantage of…
Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least…
We consider the problem of sparse estimation via a lasso-type penalized likelihood procedure in a factor analysis model. Typically, the model estimation is done under the assumption that the common factors are orthogonal (uncorrelated).…
We provide theoretical analysis of the statistical and computational properties of penalized $M$-estimators that can be formulated as the solution to a possibly nonconvex optimization problem. Many important estimators fall in this…
We consider nonlinear mixed effects models including high-dimensional covariates to model individual parameters variability. The objective is to identify relevant covariates among a large set under sparsity assumption and to estimate model…
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…
In this paper, the high-dimensional sparse linear regression model is considered, where the overall number of variables is larger than the number of observations. We investigate the L1 penalized least absolute deviation method. Different…
This paper focuses on exploring the sparsity of the inverse covariance matrix $\bSigma^{-1}$, or the precision matrix. We form blocks of parameters based on each off-diagonal band of the Cholesky factor from its modified Cholesky…
We develop a penalized likelihood estimation framework to estimate the structure of Gaussian Bayesian networks from observational data. In contrast to recent methods which accelerate the learning problem by restricting the search space, our…
We propose a new class of nonconvex penalty functions, based on data depth functions, for multitask sparse penalized regression. These penalties quantify the relative position of rows of the coefficient matrix from a fixed distribution…
This paper provides an alternative to penalized estimators for estimation and vari- able selection in high dimensional linear regression models with measurement error or missing covariates. We propose estimation via bias corrected least…
This paper develops a general theory on rates of convergence of penalized spline estimators for function estimation when the likelihood functional is concave in candidate functions, where the likelihood is interpreted in a broad sense that…
The lasso is the most famous sparse regression and feature selection method. One reason for its popularity is the speed at which the underlying optimization problem can be solved. Sorted L-One Penalized Estimation (SLOPE) is a…
Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control…
Sparse parametric models are of great interest in statistical learning and are often analyzed by means of regularized estimators. Pathwise methods allow to efficiently compute the full solution path for penalized estimators, for any…
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…
We propose a sparse coefficient estimation and automated model selection procedure for autoregressive (AR) processes with heavy-tailed innovations based on penalized conditional maximum likelihood. Under mild moment conditions on the…
Sparse approximate solutions to linear equations are classically obtained via L1 norm regularized least squares, but this method often underestimates the true solution. As an alternative to the L1 norm, this paper proposes a class of…
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…
Mixed-effect models are very popular for analyzing data with a hierarchical structure, e.g. repeated observations within subjects in a longitudinal design, patients nested within centers in a multicenter design. However, recently, due to…