Near-optimal max-affine estimators for convex regression

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

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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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