Statistical Inference for Feature Selection after Optimal Transport-based Domain Adaptation

TL;DR

This paper introduces SFS-DA, a statistical method for feature selection under domain adaptation that guarantees false positive control and improves true positive detection, validated through experiments.

Contribution

The paper develops a novel statistical testing framework for feature selection under domain adaptation using selective inference, ensuring FPR control and enhanced detection.

Findings

SFS-DA controls FPR below the specified level.

SFS-DA improves true positive detection rate.

Experimental results validate theoretical guarantees.

Abstract

Feature Selection (FS) under domain adaptation (DA) is a critical task in machine learning, especially when dealing with limited target data. However, existing methods lack the capability to guarantee the reliability of FS under DA. In this paper, we introduce a novel statistical method to statistically test FS reliability under DA, named SFS-DA (statistical FS-DA). The key strength of SFS-DA lies in its ability to control the false positive rate (FPR) below a pre-specified level $\alpha$ (e.g., 0.05) while maximizing the true positive rate. Compared to the literature on statistical FS, SFS-DA presents a unique challenge in addressing the effect of DA to ensure the validity of the inference on FS results. We overcome this challenge by leveraging the Selective Inference (SI) framework. Specifically, by carefully examining the FS process under DA whose operations can be characterized by linear and quadratic inequalities, we prove that achieving FPR control in SFS-DA is indeed possible. Furthermore, we enhance the true detection rate by introducing a more strategic approach. Experiments conducted on both synthetic and real-world datasets robustly support our theoretical results, showcasing the superior performance of the proposed SFS-DA method.