Path Thresholding: Asymptotically Tuning-Free High-Dimensional Sparse Regression

TL;DR

This paper introduces Path Thresholding (PaTh), a method that makes high-dimensional sparse regression tuning-free asymptotically, reducing computational complexity and maintaining accuracy as problem size grows.

Contribution

The paper presents PaTh, a simple, efficient approach that transforms existing sparse regression algorithms into tuning-free methods with proven asymptotic accuracy.

Findings

PaTh performs accurate sparse regression without tuning parameters in large problems.

PaTh reduces computational burden by narrowing the tuning parameter search space.

The method is effective under certain theoretical conditions.

Abstract

In this paper, we address the challenging problem of selecting tuning parameters for high-dimensional sparse regression. We propose a simple and computationally efficient method, called path thresholding (PaTh), that transforms any tuning parameter-dependent sparse regression algorithm into an asymptotically tuning-free sparse regression algorithm. More specifically, we prove that, as the problem size becomes large (in the number of variables and in the number of observations), PaTh performs accurate sparse regression, under appropriate conditions, without specifying a tuning parameter. In finite-dimensional settings, we demonstrate that PaTh can alleviate the computational burden of model selection algorithms by significantly reducing the search space of tuning parameters.