Consistent Nonparametric Different-Feature Selection via the Sparsest $k$-Subgraph Problem

TL;DR

This paper introduces a nonparametric, computationally efficient method for two-sample feature selection by formulating it as a sparsest $k$-subgraph problem, ensuring consistency without restrictive assumptions.

Contribution

It proposes a novel nonparametric approach to feature selection that is computationally efficient and guarantees consistency under mild conditions, overcoming limitations of existing methods.

Findings

Outperforms existing methods in accuracy

Reduces computation time significantly

Provides consistent feature estimation

Abstract

Two-sample feature selection is the problem of finding features that describe a difference between two probability distributions, which is a ubiquitous problem in both scientific and engineering studies. However, existing methods have limited applicability because of their restrictive assumptions on data distributoins or computational difficulty. In this paper, we resolve these difficulties by formulating the problem as a sparsest $k$-subgraph problem. The proposed method is nonparametric and does not assume any specific parametric models on the data distributions. We show that the proposed method is computationally efficient and does not require any extra computation for model selection. Moreover, we prove that the proposed method provides a consistent estimator of features under mild conditions. Our experimental results show that the proposed method outperforms the current method with regard to both accuracy and computation time.