Smooth Strongly Convex Regression

Andrea Simonetto

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arXiv · 2003.00771

Smooth Strongly Convex Regression

Andrea Simonetto

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Abstract

Convex regression (CR) is the problem of fitting a convex function to a finite number of noisy observations of an underlying convex function. CR is important in many domains and one of its workhorses is the non-parametric least square estimator (LSE). Currently, LSE delivers only non-smooth non-strongly convex function estimates. In this paper, leveraging recent results in convex interpolation, we generalize LSE to smooth strongly convex regression problems. The resulting algorithm relies on a convex quadratically constrained quadratic program. We also propose a parallel implementation, which leverages ADMM, that lessens the overall computational complexity to a tight $O(n^2)$ for $n$ observations. Numerical results support our findings.

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Andrea Simonetto. 2020-03-02. Smooth Strongly Convex Regression. https://arxiv.org/abs/2003.00771

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