Nonparametric Independence Testing for Small Sample Sizes

Understand

This paper deals with the problem of nonparametric independence testing, a fundamental decision-theoretic problem that asks if two arbitrary (possibly multivariate) random variables $X,Y$ are independent or not, a question that comes up in many fields like causality and neuroscience.

• While quantities like correlation of $X,Y$ only test for (univariate) linear independence, natural alternatives like mutual information of $X,Y$ are hard to estimate due to a serious curse of dimensionality.
• A recent approach, avoiding both issues, estimates norms of an \textit{operator} in Reproducing Kernel Hilbert Spaces (RKHSs).
• Our main contribution is strong empirical evidence that by employing \textit{shrunk} operators when the sample size is small, one can attain an improvement in power at low false positive rates.