Publication
EUSIPCO 2020
Conference paper

Smooth strongly convex regression

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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 Opn2q for n observations. Numerical results support our findings.

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Publication

EUSIPCO 2020

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