Asymptotic Distribution-Free Independence Test for High Dimension Data

TL;DR

This paper introduces a universal, distribution-free independence test for high-dimensional data that leverages modern classifiers and permutation techniques, demonstrating superior performance in complex, sparse datasets.

Contribution

The paper proposes a novel independence testing framework using classifiers and permutation, applicable to high-dimensional, complex data without distributional assumptions.

Findings

Test statistic follows a fixed Gaussian null distribution.

Outperforms existing methods in simulations.

Successfully applied to single-cell sequencing data.

Abstract

Test of independence is of fundamental importance in modern data analysis, with broad applications in variable selection, graphical models, and causal inference. When the data is high dimensional and the potential dependence signal is sparse, independence testing becomes very challenging without distributional or structural assumptions. In this paper, we propose a general framework for independence testing by first fitting a classifier that distinguishes the joint and product distributions, and then testing the significance of the fitted classifier. This framework allows us to borrow the strength of the most advanced classification algorithms developed from the modern machine learning community, making it applicable to high dimensional, complex data. By combining a sample split and a fixed permutation, our test statistic has a universal, fixed Gaussian null distribution that is independent of the underlying data distribution. Extensive simulations demonstrate the advantages of the newly proposed test compared with existing methods. We further apply the new test to a single-cell data set to test the independence between two types of single-cell sequencing measurements, whose high dimensionality and sparsity make existing methods hard to apply.