The Minimax Rate of HSIC Estimation for Translation-Invariant Kernels

Such embeddings induce the so-called maximum mean discrepancy (MMD; [Smola et al., 2007, Gretton et al., 2012]), which quantifies the discrepancy Many estimators for HSIC exist. The classical ones rely on U-statistics or V -statistics [Gretton et al., 2005, Quadrianto et al., 2009, Pfister et al., 2018] and are known to converge at a rate of Lower bounds for the related MMD are known [Tolstikhin et al., 2016], but the existing analysis considers radial kernels and relies on independent Gaussian distributions.