Related papers: LASSO-Patternsearch algorithm with application to …
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…
A reciprocal LASSO (rLASSO) regularization employs a decreasing penalty function as opposed to conventional penalization approaches that use increasing penalties on the coefficients, leading to stronger parsimony and superior model…
There has been much recent work on inference after model selection when the noise level is known, however, $\sigma$ is rarely known in practice and its estimation is difficult in high-dimensional settings. In this work we propose using the…
In linear models it is common to have situations where several regression coefficients are zero. In these situations a common tool to perform regression is a variable selection operator. One of the most common such operators is the LASSO…
The Graphical Lasso (GLasso) algorithm is fast and widely used for estimating sparse precision matrices (Friedman et al., 2008). Its central role in the literature of high-dimensional covariance estimation rivals that of Lasso regression…
The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…
The Lasso is a computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a…
Granger causality is among the widely used data-driven approaches for causal analysis of time series data with applications in various areas including economics, molecular biology, and neuroscience. Two of the main challenges of this…
We propose a rescaled LASSO, by premultipying the LASSO with a matrix term, namely linear unified LASSO (LLASSO) for multicollinear situations. Our numerical study has shown that the LLASSO is comparable with other sparse modeling…
One main obstacle for the wide use of deep learning in medical and engineering sciences is its interpretability. While neural network models are strong tools for making predictions, they often provide little information about which features…
We establish statistical properties of random-weighting methods in LASSO regression under different regularization parameters $\lambda_n$ and suitable regularity conditions. The random-weighting methods in view concern repeated optimization…
Causal variable selection in time-varying treatment settings is challenging due to evolving confounding effects. Existing methods mainly focus on time-fixed exposures and are not directly applicable to time-varying scenarios. We propose a…
The Lasso is one of the most important approaches for parameter estimation and variable selection in high dimensional linear regression. At the heart of its success is the attractive rate of convergence result even when $p$, the dimension…
The problem of consistently estimating the sparsity pattern of a vector $\betastar \in \real^\mdim$ based on observations contaminated by noise arises in various contexts, including subset selection in regression, structure estimation in…
The Least Absolute Shrinkage and Selection Operator (LASSO) has gained attention in a wide class of continuous parametric estimation problems with promising results. It has been a subject of research for more than a decade. Due to the…
The lasso has been studied extensively as a tool for estimating the coefficient vector in the high-dimensional linear model; however, considerably less is known about estimating the error variance in this context. In this paper, we propose…
This article presents a novel methodology for detecting multiple biomarkers in high-dimensional mediation models by utilizing a modified Least Absolute Shrinkage and Selection Operator (LASSO) alongside Pathway LASSO. This approach…
Lasso is a popular and efficient approach to simultaneous estimation and variable selection in high-dimensional regression models. In this paper, a robust LAD-lasso method for multiple outcomes is presented that addresses the challenges of…
Recent computational strategies based on screening tests have been proposed to accelerate algorithms addressing penalized sparse regression problems such as the Lasso. Such approaches build upon the idea that it is worth dedicating some…
In a polynomial regression model, the divisibility conditions implicit in polynomial hierarchy give way to a natural construction of constraints for the model parameters. We use this principle to derive versions of strong and weak hierarchy…