Distributed Feature Screening via Componentwise Debiasing

TL;DR

This paper introduces a distributed feature screening method for high-dimensional data that leverages componentwise debiasing and U-statistics, enabling efficient, accurate, and scalable feature selection in big data contexts.

Contribution

It proposes a novel distributed screening framework that uses componentwise debiasing and U-statistics, achieving high accuracy and computational efficiency in large-scale data analysis.

Findings

Achieves screening accuracy comparable to centralized methods.

Enables scalable parallel computation for large datasets.

Demonstrates effectiveness through extensive numerical experiments.

Abstract

Feature screening is a powerful tool in the analysis of high dimensional data. When the sample size $N$ and the number of features $p$ are both large, the implementation of classic screening methods can be numerically challenging. In this paper, we propose a distributed screening framework for big data setup. In the spirit of "divide-and-conquer", the proposed framework expresses a correlation measure as a function of several component parameters, each of which can be distributively estimated using a natural U-statistic from data segments. With the component estimates aggregated, we obtain a final correlation estimate that can be readily used for screening features. This framework enables distributed storage and parallel computing and thus is computationally attractive. Due to the unbiased distributive estimation of the component parameters, the final aggregated estimate achieves a high accuracy that is insensitive to the number of data segments $m$ specified by the problem itself or to be chosen by users. Under mild conditions, we show that the aggregated correlation estimator is as efficient as the classic centralized estimator in terms of the probability convergence bound; the corresponding screening procedure enjoys sure screening property for a wide range of correlation measures. The promising performances of the new method are supported by extensive numerical examples.