Related papers: L1 penalized LAD estimator for high dimensional li…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
Many models for sparse regression typically assume that the covariates are known completely, and without noise. Particularly in high-dimensional applications, this is often not the case. This paper develops efficient OMP-like algorithms to…
Inference for high-dimensional logistic regression models using penalized methods has been a challenging research problem. As an illustration, a major difficulty is the significant bias of the Lasso estimator, which limits its direct…
The efficient estimation of an approximate model order is very important for real applications with multi-dimensional data if the observed low-rank data is corrupted by additive noise. In this paper, we present a novel robust method for…
We present a sparse analogue to stochastic gradient descent that is guaranteed to perform well under similar conditions to the lasso. In the linear regression setup with irrepresentable noise features, our algorithm recovers the support set…
Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the…
We propose Nodewise Loreg, a nodewise $L_0$-penalized regression method for estimating high-dimensional sparse precision matrices. We establish its asymptotic properties, including convergence rates, support recovery, and asymptotic…
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…
Recently, high dimensional vector auto-regressive models (VAR), have attracted a lot of interest, due to novel applications in the health, engineering and social sciences. The presence of temporal dependence poses additional challenges to…
This paper studies the statistical properties of the group Lasso estimator for high dimensional sparse quantile regression models where the number of explanatory variables (or the number of groups of explanatory variables) is possibly much…
Sparse linear regression is one of the most basic questions in machine learning and statistics. Here, we are given as input a design matrix $X \in \mathbb{R}^{N \times d}$ and measurements or labels ${y} \in \mathbb{R}^N$ where ${y} = {X}…
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…
We study functional regression with random subgaussian design and real-valued response. The focus is on the problems in which the regression function can be well approximated by a functional linear model with the slope function being…
Existing methods for sparse channel estimation typically provide an estimate computed as the solution maximizing an objective function defined as the sum of the log-likelihood function and a penalization term proportional to the l1-norm of…
Two important goals of high-dimensional modeling are prediction and variable selection. In this article, we consider regularization with combined $L_1$ and concave penalties, and study the sampling properties of the global optimum of the…
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…
The problem of finding the maximum likelihood estimates for the regression coefficients in generalised linear models with an L1 sparsity penalty is shown to be equivalent to minimising the unpenalised maximum log-likelihood function over a…
In this work, we propose an optimization framework for estimating a sparse robust one-dimensional subspace. Our objective is to minimize both the representation error and the penalty, in terms of the l1-norm criterion. Given that the…
The paper focuses on the automatic selection of the grouped explanatory variables in an high-dimensional model, when the model errors are asymmetric. After introducing the model and notations, we define the adaptive group LASSO expectile…
A Vector Auto-Regressive (VAR) model is commonly used to model multivariate time series, and there are many penalized methods to handle high dimensionality. However in terms of spatio-temporal data, most methods do not take the spatial and…