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Activity Number: 63 - Inference and Interpretability in a Model-Free Setting
Type: Invited
Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
Sponsor: IMS
Abstract #316773
Title: A Simple Measure of Conditional Dependence
Author(s): Mona Azadkia* and Sourav Chatterjee
Companies: ETH and Stanford University
Keywords: Conditional dependence; non-parametric measures of association; variable selection
Abstract:

We propose a coefficient of conditional dependence between two random variables $Y$ and $Z$ given a set of other variables $X_1,\ldots,X_p$, 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 $X_1,\ldots,X_p$, and is $1$ if and only if $Y$ is equal to a measurable function of $Z$ given $X_1,\ldots,X_p$. 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.


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