Semi-analytic approximate stability selection for correlated data in generalized linear models

TL;DR

This paper introduces a fast, approximate stability selection algorithm for generalized linear models that avoids repeated fitting by leveraging statistical mechanics and message passing, demonstrating high accuracy and efficiency.

Contribution

The authors develop a novel approximate inference algorithm for stability selection in GLMs, reducing computational cost while maintaining accuracy, based on the replica method and message passing techniques.

Findings

The algorithm converges quickly and accurately on synthetic data.

It performs well on real-world datasets, matching traditional methods.

State evolution equations describe the algorithm's dynamics.

Abstract

We consider the variable selection problem of generalized linear models (GLMs). Stability selection (SS) is a promising method proposed for solving this problem. Although SS provides practical variable selection criteria, it is computationally demanding because it needs to fit GLMs to many re-sampled datasets. We propose a novel approximate inference algorithm that can conduct SS without the repeated fitting. The algorithm is based on the replica method of statistical mechanics and vector approximate message passing of information theory. For datasets characterized by rotation-invariant matrix ensembles, we derive state evolution equations that macroscopically describe the dynamics of the proposed algorithm. We also show that their fixed points are consistent with the replica symmetric solution obtained by the replica method. Numerical experiments indicate that the algorithm exhibits fast convergence and high approximation accuracy for both synthetic and real-world data.