A Data-Driven Line Search Rule for Support Recovery in High-dimensional Data Analysis

TL;DR

This paper introduces a novel data-driven line search method for support recovery in high-dimensional nonlinear regression with  penalty, improving step size selection and demonstrating superior empirical performance.

Contribution

It proposes an adaptive, data-driven line search rule for -penalized regression, reducing reliance on restrictive assumptions and enhancing algorithm stability and effectiveness.

Findings

Proves  error bounds for the proposed algorithm.

Demonstrates superior performance over state-of-the-art methods.

Shows stability and effectiveness in linear and logistic regression tasks.

Abstract

In this work, we consider the algorithm to the (nonlinear) regression problems with $\ell_0$ penalty. The existing algorithms for $\ell_0$ based optimization problem are often carried out with a fixed step size, and the selection of an appropriate step size depends on the restricted strong convexity and smoothness for the loss function, hence it is difficult to compute in practical calculation. In sprite of the ideas of support detection and root finding \cite{HJK2020}, we proposes a novel and efficient data-driven line search rule to adaptively determine the appropriate step size. We prove the $\ell_2$ error bound to the proposed algorithm without much restrictions for the cost functional. A large number of numerical comparisons with state-of-the-art algorithms in linear and logistic regression problems show the stability, effectiveness and superiority of the proposed algorithms.