Support Recovery with Stochastic Gates: Theory and Application for Linear Models

TL;DR

This paper introduces a new projection-based algorithm for support recovery in linear models using stochastic gates, providing theoretical guarantees and demonstrating superior performance over existing methods.

Contribution

It proposes a novel projection-based algorithm for STG regularization, with proven convergence and support recovery guarantees, advancing support estimation techniques in noisy linear models.

Findings

Outperforms existing STG algorithms in support recovery tasks

Provides convergence and support recovery guarantees for the proposed method

Demonstrates effectiveness on real and synthetic datasets

Abstract

Consider the problem of simultaneous estimation and support recovery of the coefficient vector in a linear data model with additive Gaussian noise. We study the problem of estimating the model coefficients based on a recently proposed non-convex regularizer, namely the stochastic gates (STG) [Yamada et al. 2020]. We suggest a new projection-based algorithm for solving the STG regularized minimization problem, and prove convergence and support recovery guarantees of the STG-estimator for a range of random and non-random design matrix setups. Our new algorithm has been shown to outperform the existing STG algorithm and other classical estimators for support recovery in various real and synthetic data analyses.