Non-parametric Binary regression in metric spaces with KL loss
Abstract
We propose a non-parametric variant of binary regression, where the hypothesis is regularized to be a Lipschitz function taking a metric space to [0,1] and the loss is logarithmic. This setting presents novel computational and statistical challenges. On the computational front, we derive a novel efficient optimization algorithm based on interior point methods; an attractive feature is that it is parameter-free (i.e., does not require tuning an update step size). On the statistical front, the unbounded loss function presents a problem for classic generalization bounds, based on covering-number and Rademacher techniques. We get around this challenge via an adaptive truncation approach, and also present a lower bound indicating that the truncation is, in some sense, necessary.
Cite
@article{arxiv.2010.09886,
title = {Non-parametric Binary regression in metric spaces with KL loss},
author = {Ariel Avital and Klim Efremenko and Aryeh Kontorovich and David Toplin and Bo Waggoner},
journal= {arXiv preprint arXiv:2010.09886},
year = {2020}
}