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Linear models that contain a time-dependent response and explanatory variables have attracted much interest in recent years. The most general form of the existing approaches is of a linear regression model with autoregressive moving average…

We consider a class of sparse learning problems in high dimensional feature space regularized by a structured sparsity-inducing norm which incorporates prior knowledge of the group structure of the features. Such problems often pose a…

The popularity of penalized regression in high-dimensional data analysis has led to a demand for new inferential tools for these models. False discovery rate control is widely used in high-dimensional hypothesis testing, but has only…

Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…

In this paper, we study the ratio of the $L_1 $ and $L_2 $ norms, denoted as $L_1/L_2$, to promote sparsity. Due to the non-convexity and non-linearity, there has been little attention to this scale-invariant model. Compared to popular…

In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…

We discuss two new methods of recovery of sparse signals from noisy observation based on $\ell_1$- minimization. They are closely related to the well-known techniques such as Lasso and Dantzig Selector. However, these estimators come with…

The Lasso has been widely used as a method for variable selection, valued for its simplicity and empirical performance. However, Lasso's selection stability deteriorates in the presence of correlated predictors. Several approaches have been…

This article introduces lassopack, a suite of programs for regularized regression in Stata. lassopack implements lasso, square-root lasso, elastic net, ridge regression, adaptive lasso and post-estimation OLS. The methods are suitable for…

LASSO regularization is a popular regression tool to enhance the prediction accuracy of statistical models by performing variable selection through the $\ell_1$ penalty, initially formulated for the linear model and its variants. In this…

Sparse linear (or generalized linear) models combine a standard likelihood function with a sparse prior on the unknown coefficients. These priors can conveniently be expressed as a maximization over zero-mean Gaussians with different…

We investigate problems in penalized $M$-estimation, inspired by applications in machine learning debugging. Data are collected from two pools, one containing data with possibly contaminated labels, and the other which is known to contain…

Lasso is a celebrated method for variable selection in linear models, but it faces challenges when the variables are moderately or strongly correlated. This motivates alternative approaches such as using a non-convex penalty, adding a ridge…

We consider a $l_1$-penalization procedure in the non-parametric Gaussian regression model. In many concrete examples, the dimension $d$ of the input variable $X$ is very large (sometimes depending on the number of observations). Estimation…

Learning under distribution shifts is a challenging task. One principled approach is to exploit the invariance principle via the structural causal models. However, the invariance principle is violated when the response is intervened, making…

Basis Pursuit (BP), Basis Pursuit DeNoising (BPDN), and LASSO are popular methods for identifying important predictors in the high-dimensional linear regression model, i.e. when the number of rows of the design matrix X is smaller than the…

So-called sparse estimators arise in the context of model fitting, when one a priori assumes that only a few (unknown) model parameters deviate from zero. Sparsity constraints can be useful when the estimation problem is under-determined,…

Standard likelihood penalties to learn Gaussian graphical models are based on regularising the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the…

L1 -penalized regression methods such as the Lasso (Tibshirani 1996) that achieve both variable selection and shrinkage have been very popular. An extension of this method is the Fused Lasso (Tibshirani and Wang 2007), which allows for the…

Sparse linear regression -- finding an unknown vector from linear measurements -- is now known to be possible with fewer samples than variables, via methods like the LASSO. We consider the multiple sparse linear regression problem, where…