Related papers: The Lasso Problem and Uniqueness
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
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…
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…
We introduce c-lasso, a Python package that enables sparse and robust linear regression and classification with linear equality constraints. The underlying statistical forward model is assumed to be of the following form: \[ y = X \beta +…
We analyze the performance of the least absolute shrinkage and selection operator (Lasso) for the linear model when the number of regressors $N$ grows larger keeping the true support size $d$ finite, i.e., the ultra-sparse case. The result…
Sparse linear regression methods such as Lasso require a tuning parameter that depends on the noise variance, which is typically unknown and difficult to estimate in practice. In the presence of heavy-tailed noise or adversarial outliers,…
We consider ``one-at-a-time'' coordinate-wise descent algorithms for a class of convex optimization problems. An algorithm of this kind has been proposed for the $L_1$-penalized regression (lasso) in the literature, but it seems to have…
We study the limitations of the well known LASSO regression as a variable selector when there exists dependence structures among covariates. We analyze both the classic situation with $n\geq p$ and the high dimensional framework with $p>n$.…
The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical…
In statistics, the least absolute shrinkage and selection operator (Lasso) is a regression method that performs both variable selection and regularization. There is a lot of literature available, discussing the statistical properties of the…
We apply the network Lasso to solve binary classification and clustering problems for network-structured data. To this end, we generalize ordinary logistic regression to non-Euclidean data with an intrinsic network structure. The resulting…
Regularization is widely used in statistics and machine learning to prevent overfitting and gear solution towards prior information. In general, a regularized estimation problem minimizes the sum of a loss function and a penalty term. The…
The sparse linear regression problem is difficult to handle with usual sparse optimization models when both predictors and measurements are either quantized or represented in low-precision, due to non-convexity. In this paper, we provide a…
Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings. In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated…
The general setting of this work is the constraint-based synthesis of termination arguments. We consider a restricted class of programs called lasso programs. The termination argument for a lasso program is a pair of a ranking function and…
We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…
In exciting new work, Bertsimas et al. (2016) showed that the classical best subset selection problem in regression modeling can be formulated as a mixed integer optimization (MIO) problem. Using recent advances in MIO algorithms, they…
We propose a generalization of the lasso that allows the model coefficients to vary as a function of a general set of modifying variables. These modifiers might be variables such as gender, age or time. The paradigm is quite general, with…