Nonparametric independence testing via mutual information

Author:

Berrett T B1,Samworth R J1

Affiliation:

1. Statistical Laboratory, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, UK

Abstract

Summary We propose a test of independence of two multivariate random vectors, given a sample from the underlying population. Our approach is based on the estimation of mutual information, whose decomposition into joint and marginal entropies facilitates the use of recently developed efficient entropy estimators derived from nearest neighbour distances. The proposed critical values may be obtained by simulation in the case where an approximation to one marginal is available or by permuting the data otherwise. This facilitates size guarantees, and we provide local power analyses, uniformly over classes of densities whose mutual information satisfies a lower bound. Our ideas may be extended to provide new goodness-of-fit tests for normal linear models based on assessing the independence of our vector of covariates and an appropriately defined notion of an error vector. The theory is supported by numerical studies on both simulated and real data.

Funder

Engineering and Physical Sciences Research Council

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Statistics, Probability and Uncertainty,General Agricultural and Biological Sciences,Agricultural and Biological Sciences (miscellaneous),General Mathematics,Statistics and Probability

Reference59 articles.

1. Bootstrap and permutation tests of independence for point processes;Albert,;Ann. Statist.,2015

2. Kernel independent component analysis;Bach,;J. Mach. Learn. Res.,2002

3. Efficient multivariate entropy estimation via $k$-nearest neighbour distances;Berrett,;Ann. Statist.,2019

4. The conditional permutation test;Berrett,,2019

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