B1185
Title: A simple measure conditional dependence and its application in causal inference
Authors: Mona Azadkia - London School of Economics (United Kingdom) [presenting]
Peter Buehlmann - ETH Zurich (Switzerland)
Armeen Taeb - ETH Zurich (Switzerland)
Sourav chatterjee - Stanford University (United States)
Abstract: A coefficient of conditional dependence between two random variables $Y$ and $Z$ given a set of other variables $X_1$, ..., $X_p$, based on an i.i.d. sample is proposed. 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 $X_1$, ..., $X_p$, and is 1 if and only if Y is equal to a measurable function of Z given $X_1$, ..., $X_p$. 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. We focus on an application of this method in casual structure discovery.
