8 February 2024: Mona Azadkia (LSE)

Title: A Simple Measure of Conditional Dependence
Abstract: We propose 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. 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. In this talk, we explore the recent advancement on this measure.
Note: no sound until minute 5.