arXiv research

PLS-Lasso integrates dimension reduction into regression for financial index tracking.

Paper examines LASSO for high-dimensional predictive regression, improving its performance in forecasting unemployment.

A fast method for Lasso and Logistic Lasso problems.

We analyze coresets for regularized regression problems and propose a modified lasso that yields smaller coresets.

Heavy Lasso improves robustness in high-dimensional linear regression with heavy-tailed errors.

In this paper, we investigate a multivariate multi-response (MVMR) linear regression problem, which contains multiple linear regression models with differently distributed design matrices, and different regression and output vectors. The goal is to recover the support union of all regression vectors using $l_1/l_2$-reg…

The paper examines the consistency of Lasso regression applied to signature analysis of time series data.

The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that takes the hierarchical model formulation of the Bayesian Lasso. The main differenc…

We apply network Lasso to semi-supervised regression problems involving network structured data. This approach lends quite naturally to highly scalable learning algorithms in the form of message passing over an empirical graph which represents the network structure of the data. By using a simple non-parametric regressi…

Improves robustness of high-dimensional regression with rank objective and group lasso regularization.

Nested model averaging improves high-dimensional linear regression performance.

A new estimator corrects bias in high-dimensional predictive regressions.

The fused lasso is analyzed for high-dimensional piecewise-constant regression coefficients.

New robust estimator for high-dimensional data with outliers and leverage points.

The group lasso is a penalized regression method, used in regression problems where the covariates are partitioned into groups to promote sparsity at the group level. Existing methods for finding the group lasso estimator either use gradient projection methods to update the entire coefficient vector simultaneously at e…

New GLS estimator handles high-dimensional data with autocorrelated errors.

A new screening rule improves lasso solving speed.

New weighted Lasso estimates improve logistic regression performance with measurement error.

c-lasso is a Python tool for robust and sparse regression with linear constraints.

High-dimensional feature selection arises in many areas of modern science. For example, in genomic research we want to find the genes that can be used to separate tissues of different classes (e.g. cancer and normal) from tens of thousands of genes that are active (expressed) in certain tissue cells. To this end, we wi…

This review summarizes five Lasso optimization algorithms.

We study the complexity of the entire regularization path for least squares regression with 1-norm penalty, known as the Lasso. Every regression parameter in the Lasso changes linearly as a function of the regularization value. The number of changes is regarded as the Lasso's complexity. Experimental results using exac…

Efficient algorithms for clustered Lasso and OSCAR reduce computational costs.

When the design matrix has orthonormal columns, "soft thresholding" the ordinary least squares (OLS) solution produces the Lasso solution [Tibshirani, 1996]. If one uses the Puffer preconditioned Lasso [Jia and Rohe, 2012], then this result generalizes from orthonormal designs to full rank designs (Theorem 1). Theorem …

Ridge regression is revisited with debiasing and thresholding, offering advantages over Lasso.

Autotune optimizes Lasso tuning parameters efficiently and accurately.

The fused lasso penalizes a loss function by the $L_1$ norm for both the regression coefficients and their successive differences to encourage sparsity of both. In this paper, we propose a Bayesian generalized fused lasso modeling based on a normal-exponential-gamma (NEG) prior distribution. The NEG prior is assumed in…

The Lasso is suboptimal in sparse linear regression due to design matrix constraints.

In high dimension, it is customary to consider Lasso-type estimators to enforce sparsity. For standard Lasso theory to hold, the regularization parameter should be proportional to the noise level, yet the latter is generally unknown in practice. A possible remedy is to consider estimators, such as the Concomitant/Scale…

Exclusive Lasso improves survival prediction in cancer datasets.

Study improves statistical inference for CATEs using Lasso and DML.

In the high-dimensional regression model a response variable is linearly related to $p$ covariates, but the sample size $n$ is smaller than $p$. We assume that only a small subset of covariates is `active' (i.e., the corresponding coefficients are non-zero), and consider the model-selection problem of identifying the a…

PROD method improves high-dimensional regression by handling strong correlations.

New method improves regression estimates, reducing bias.

Proposes a new Lasso method with performance constraints.

Javanmard and Montanari propose a debiased estimator for high-dimensional regression.

Lecture notes on advanced linear regression methods.

We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the subproblems separately, obtaining a coefficient vector for each one. Then, it uses n…

In this paper, we propose an adaptive group lasso procedure to efficiently estimate structural breaks in cointegrating regressions. It is well-known that the group lasso estimator is not simultaneously estimation consistent and model selection consistent in structural break settings. Hence, we use a first step group la…

Lasso performs poorly with correlated covariates, but a rescaled approach fixes this.

In high dimensional settings, sparse structures are crucial for efficiency, both in term of memory, computation and performance. It is customary to consider $\ell_1$ penalty to enforce sparsity in such scenarios. Sparsity enforcing methods, the Lasso being a canonical example, are popular candidates to address high dim…

LLM-Lasso uses LLMs to improve feature selection in Lasso regression.

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 high-dimensional statistical problems. In this article, we consider a class of weigh…

In this paper we combine two important extensions of ordinary least squares regression: regularization and optimal scaling. Optimal scaling (sometimes also called optimal scoring) has originally been developed for categorical data, and the process finds quantifications for the categories that are optimal for the regres…

We consider the finite sample properties of the regularized high-dimensional Cox regression via lasso. Existing literature focuses on linear models or generalized linear models with Lipschitz loss functions, where the empirical risk functions are the summations of independent and identically distributed (iid) losses. T…

Paper proposes a new method combining random forests and Lasso selection.

We consider the least-square linear regression problem with regularization by the l1-norm, a problem usually referred to as the Lasso. In this paper, we present a detailed asymptotic analysis of model consistency of the Lasso. For various decays of the regularization parameter, we compute asymptotic equivalents of the …

Proposes a lasso variant of MARS for nonparametric regression.