Title: Large sample analysis of the median heuristic,
Abstract: In kernel methods, the median heuristic has been widely used as a way of
setting the bandwidth of RBF kernels. While its empirical performances make it
a safe choice under many circumstances, there is little theoretical
understanding of why this is the case. Our aim in this paper is to advance our
understanding of the median heuristic by focusing on the setting of kernel
two-sample test. We collect new findings that may be of interest for both
theoreticians and practitioners. In theory, we provide a convergence analysis
that shows the asymptotic normality of the bandwidth chosen by the median
heuristic in the setting of kernel two-sample test. Systematic empirical
investigations are also conducted in simple settings, comparing the
performances based on the bandwidths chosen by the median heuristic and those
by the maximization of test power.