Robust Reproducible Network Exploration

TL;DR

This paper introduces a statistically rigorous method for discovering and visualizing relationships in high-dimensional binary time series data as networks, ensuring reproducibility and control over false discoveries.

Contribution

It develops a new multiple testing approach using specially constructed p-variables and the BH procedure to reliably uncover network edges with controlled FDR in high-dimensional settings.

Findings

FDR control is valid under arbitrary dependence and any sample size.

Method achieves asymptotic power one under mild conditions.

Validated by simulations and real data analysis.

Abstract

We propose a novel methodology for discovering the presence of relationships realized as binary time series between variables in high dimension. To make it visually intuitive, we regard the existence of a relationship as an edge connection, and call a collection of such edges a network. Our objective is thus rephrased as uncovering the network by selecting relevant edges, referred to as the network exploration. Our methodology is based on multiple testing for the presence or absence of each edge, designed to ensure statistical reproducibility via controlling the false discovery rate (FDR). In particular, we carefully construct $p$-variables, and apply the Benjamini-Hochberg (BH) procedure. We show that the BH with our $p$-variables controls the FDR under arbitrary dependence structure with any sample size and dimension, and has asymptotic power one under mild conditions. The validity is also confirmed by simulations and a real data example.