Near-Optimal Max-Affine Estimators for Convex Regression

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.

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Text

Balázs et al. "Near-Optimal Max-Affine Estimators for Convex Regression." International Conference on Artificial Intelligence and Statistics, 2015.

Markdown

[Balázs et al. "Near-Optimal Max-Affine Estimators for Convex Regression." International Conference on Artificial Intelligence and Statistics, 2015.](https://mlanthology.org/aistats/2015/balazs2015aistats-near/)

BibTeX

@inproceedings{balazs2015aistats-near,
  title     = {{Near-Optimal Max-Affine Estimators for Convex Regression}},
  author    = {Balázs, Gábor and György, András and Szepesvári, Csaba},
  booktitle = {International Conference on Artificial Intelligence and Statistics},
  year      = {2015},
  url       = {https://mlanthology.org/aistats/2015/balazs2015aistats-near/}
}