A Dependence Measure: Integrated R^2 and its kernelized extension

Recently, Chatterjee introduced a dependence measure that is as simple to compute as classical coefficients such as Pearson’s or Spearman’s, while consistently estimating an interpretable quantity: it equals 0 if and only if the variables are independent and 1 if and only if one variable is a measurable function of the other. Although the coefficient enjoys many desirable properties, it has been shown to exhibit low power against certain local dependency structures. To address this limitation, we propose a simple modification that increases its sensitivity in such settings. We show that the modified dependence measure preserves all theoretical guarantees of the original while remaining computationally efficient. Furthermore, we demonstrate that it is more powerful for detecting functional dependence in multivariate settings compared to competing methods and outperforms them in variable selection. Finally, we discuss an ongoing extension that leverages the flexibility of kernel methods.