Mona Azadkia (London School of Economics) – A New Measure of Dependence

Abstract: In this talk I will present Integrated R², a novel statistic for quantifying the dependence of a scalar random variable Y on a vector of predictors X. Integrated R² has the desirable property that it vanishes if and only if Y and X are independent, and attains the maximum value of one precisely when Y is a measurable function of X. Unlike many dependence measures that require strong parametric assumptions or complex tuning, its estimator is as simple to compute and interpret as classical correlation coefficients such as Pearson’s, Spearman’s, or Chatterjee’s.
Building on this measure, I will introduce the algorithm FORD (Feature Ordering by Dependence), which orders candidate features by their incremental contribution to dependence. I will discuss theoretical guarantees, including asymptotic normality results, and demonstrate through experiments (on synthetic and real datasets) how Integrated R² and FORD often outperform existing methods.