Title: Rate-optimal Meta Learning of Classification Error,
Abstract: Meta learning of optimal classifier error rates allows an experimenter to
empirically estimate the intrinsic ability of any estimator to discriminate
between two populations, circumventing the difficult problem of estimating the
optimal Bayes classifier. To this end we propose a weighted nearest neighbor
(WNN) graph estimator for a tight bound on the Bayes classification error; the
Henze-Penrose (HP) divergence. Similar to recently proposed HP estimators
[berisha2016], the proposed estimator is non-parametric and does not require
density estimation. However, unlike previous approaches the proposed estimator
is rate-optimal, i.e., its mean squared estimation error (MSEE) decays to zero
at the fastest possible rate of $O(1/M+1/N)$ where $M,N$ are the sample sizes
of the respective populations. We illustrate the proposed WNN meta estimator
for several simulated and real data sets.