A simple measure of conditional dependence

Azadkia, Mona ORCID: 0000-0001-5480-8791 and Chatterjee, Sourav (2021) A simple measure of conditional dependence. Annals of Statistics. ISSN 0090-5364

Text (1910.12327v6) - Accepted Version Download (323kB)

Abstract

We propose a coefficient of conditional dependence between two random variables Y and Z given a set of other variables X1, . . . , Xp, based on an i.i.d. sample. The coefficient has a long list of desirable properties, the most important of which is that under absolutely no distributional assumptions, it converges to a limit in [0, 1], where the limit is 0 if and only if Y and Z are conditionally independent given X1, . . . , Xp, and is 1 if and only if Y is equal to a measurable function of Z given X1, . . . , Xp. Moreover, it has a natural interpretation as a nonlinear generalization of the familiar partial R2 statistic for measuring conditional dependence by regression. Using this statistic, we devise a new variable selection algorithm, called Feature Ordering by Conditional Independence (FOCI), which is model-free, has no tuning parameters, and is provably consistent under sparsity assumptions. A number of applications to synthetic and real datasets are worked out.

Item Type:	Article
Additional Information:	© 2021 Institute of Mathematical Statistics
Divisions:	LSE
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	13 Feb 2025 09:33
Last Modified:	23 Feb 2025 19:04
URI:	http://eprints.lse.ac.uk/id/eprint/125584

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