  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.
