A Permutation-Free Kernel Independence Test

In nonparametric independence testing, we observe i.i.d.\ data $\{(X_i,Y_i)\}_{i=1}^n$, where $X \in \mathcal{X}, Y \in \mathcal{Y}$ lie in any general spaces, and we wish to test the null that $X$ is independent of $Y$. Modern test statistics such as the kernel Hilbert--Schmidt Independence Criterion (HSIC) and Distance Covariance (dCov) have intractable null distributions due to the degeneracy of the underlying U-statistics. Hence, in practice, one often resorts to using permutation testing, which provides a nonasymptotic guarantee at the expense of …

covariance criterion data free general independent kernel modern null observe schmidt spaces statistics test testing