Statistical Test for Feature Selection Pipelines by Selective Inference

TL;DR

This paper introduces a new statistical test based on selective inference to evaluate the significance of feature selection pipelines, ensuring valid false positive control in data analysis workflows.

Contribution

It develops a general framework for statistically testing feature selection pipelines, applicable to various components, with theoretical guarantees and practical implementation.

Findings

The test controls false positive rates at any desired level.

Experimental validation on synthetic and real data confirms effectiveness.

Framework enables testing of diverse pipeline configurations without extra costs.

Abstract

A data analysis pipeline is a structured sequence of steps that transforms raw data into meaningful insights by integrating various analysis algorithms. In this paper, we propose a novel statistical test to assess the significance of data analysis pipelines in feature selection problems. Our approach enables the systematic development of valid statistical tests applicable to any feature selection pipeline composed of predefined components. We develop this framework based on selective inference, a statistical technique that has recently gained attention for data-driven hypotheses. As a proof of concept, we consider feature selection pipelines for linear models, composed of three missing value imputation algorithms, three outlier detection algorithms, and three feature selection algorithms. We theoretically prove that our statistical test can control the probability of false positive feature selection at any desired level, and demonstrate its validity and effectiveness through experiments on synthetic and real data. Additionally, we present an implementation framework that facilitates testing across any configuration of these feature selection pipelines without extra implementation costs.