Near-optimal max-affine estimators for convex regression. Balázs, G., György, A., & Szepesvári, C. In *AISTATS*, pages 56–64, 2015.

Paper abstract bibtex 3 downloads

Paper abstract bibtex 3 downloads

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.

@inproceedings{BaGySz15, 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. }, acceptrate = {127 out of 442=29\%}, author = {Bal{\'a}zs, G. and Gy{\"o}rgy, A. and Szepesv{\'a}ri, Cs.}, booktitle = {AISTATS}, keywords = {regression, nonparametrics, convex regression}, pages = {56--64}, title = {Near-optimal max-affine estimators for convex regression}, url_paper = {AISTAT15-cvxreg.pdf}, year = {2015}}

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G.","György, A.","Szepesvári, C."],"bibdata":{"bibtype":"inproceedings","type":"inproceedings","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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