The Minimax Rate of HSIC Estimation for Translation-Invariant Kernels

arXiv:2403.07735v1 Announce Type: cross
Abstract: Kernel techniques are among the most influential approaches in data science and statistics. Under mild conditions, the reproducing kernel Hilbert space associated to a kernel is capable of encoding the independence of $M\ge 2$ random variables. Probably the most widespread independence measure relying on kernels is the so-called Hilbert-Schmidt independence criterion (HSIC; also referred to as distance covariance in the statistics literature). Despite various existing HSIC estimators designed since its introduction close to two decades …

abstract arxiv cs.it cs.lg data data science encoding kernel math.it math.st minimax random rate science space statistics stat.ml stat.th translation type variables