AISTATS 2015poster58 citations
Near-optimal max-affine estimators for convex regression
Gabor Balazs, András György, Csaba Szepesvari
Abstract
This paper considers least squares estimators for regression problems over convex, uniformly bounded, uniformly Lipschitz function classes minimizing the empirical risk over max-affine functions (the maximum of finitely many affine functions). Based on new results on nonlinear nonparametric regression and on the approximation accuracy of max-affine functions, these estimators are proved to achieve the optimal rate of convergence up to logarithmic factors. Preliminary experiments indicate that a simple randomized approximation to the optimal estimator is competitive with state-of-the-art alternatives.
BibTeX
@InProceedings{pmlr-v38-balazs15,
title = {{Near-optimal max-affine estimators for convex regression}},
author = {Balazs, Gabor and György, András and Szepesvari, Csaba},
booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics},
pages = {56--64},
year = {2015},
editor = {Lebanon, Guy and Vishwanathan, S. V. N.},
volume = {38},
series = {Proceedings of Machine Learning Research},
address = {San Diego, California, USA},
month = {09--12 May},
publisher = {PMLR},
pdf = {http://proceedings.mlr.press/v38/balazs15.pdf},
url = {https://proceedings.mlr.press/v38/balazs15.html},
abstract = {This paper considers least squares estimators for regression problems over convex, uniformly bounded, uniformly Lipschitz function classes minimizing the empirical risk over max-affine functions (the maximum of finitely many affine functions). Based on new results on nonlinear nonparametric regression and on the approximation accuracy of max-affine functions, these estimators are proved to achieve the optimal rate of convergence up to logarithmic factors. Preliminary experiments indicate that a simple randomized approximation to the optimal estimator is competitive with state-of-the-art alternatives.}
}