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Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…

The sparse-group lasso performs both variable and group selection, simultaneously using the strengths of the lasso and group lasso. It has found widespread use in genetics, a field that regularly involves the analysis of high-dimensional…

Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…

Sparse linear regression methods including the well-known LASSO and the Dantzig selector have become ubiquitous in the engineering practice, including in medical imaging. Among other tasks, they have been successfully applied for the…

This paper examines LASSO, a widely-used $L_{1}$-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors…

Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of…

In high dimensional regression, feature clustering by their effects on outcomes is often as important as feature selection. For that purpose, clustered Lasso and octagonal shrinkage and clustering algorithm for regression (OSCAR) are used…

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…

In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…

This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…

Irregularly sampled AR(1) processes appear in many computationally demanding applications. This text provides an analytical expression for the precision matrix of such a process, and gives efficient algorithms for density evaluation and…

We suggest a new method, called Functional Additive Regression, or FAR, for efficiently performing high-dimensional functional regression. FAR extends the usual linear regression model involving a functional predictor, $X(t)$, and a scalar…

The parallel alternating direction method of multipliers (ADMM) algorithms have gained popularity in statistics and machine learning due to their efficient handling of large sample data problems. However, the parallel structure of these…

Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…

In this article, we analyze the SPICE method developed in [1], and establish its connections with other standard sparse estimation methods such as the Lasso and the LAD-Lasso. This result positions SPICE as a computationally efficient…

We compare alternative computing strategies for solving the constrained lasso problem. As its name suggests, the constrained lasso extends the widely-used lasso to handle linear constraints, which allow the user to incorporate prior…

Asg is a Python package that solves penalized linear regression and quantile regression models for simultaneous variable selection and prediction, for both high and low dimensional frameworks. It makes very easy to set up and solve…

This paper presents an innovative approach to dimensionality reduction and feature extraction in high-dimensional datasets, with a specific application focus on wood surface defect detection. The proposed framework integrates sparse…

The LASSO is a recent technique for variable selection in the regression model \bean y & = & X\beta + z, \eean where $X\in \R^{n\times p}$ and $z$ is a centered gaussian i.i.d. noise vector $\mathcal N(0,\sigma^2I)$. The LASSO has been…

We study the high-dimensional linear regression problem with categorical predictors that have many levels. We propose a new estimation approach, which performs model compression via two mechanisms by simultaneously encouraging (a)…