TY - UNPB
T1 - Non-parametric Binary regression in metric spaces with KL loss.
AU - Avital, Ariel
AU - Efremenko, Klim
AU - Kontorovich, Aryeh
AU - Toplin, David
AU - Waggoner, Bo
N1 - DBLP License: DBLP's bibliographic metadata records provided through http://dblp.org/ are distributed under a Creative Commons CC0 1.0 Universal Public Domain Dedication. Although the bibliographic metadata records are provided consistent with CC0 1.0 Dedication, the content described by the metadata records is not. Content may be subject to copyright, rights of privacy, rights of publicity and other restrictions.
PY - 2020/10/19
Y1 - 2020/10/19
N2 - 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.
AB - 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.
M3 - Preprint
BT - Non-parametric Binary regression in metric spaces with KL loss.
ER -