# Smooth Strongly Convex Regression

arXiv: https://arxiv.org/abs/2003.00771 · HTML: https://mlsanity.com/paper/2003.00771/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2020.

## Built on by (most cited first, 2 of 2)

- [Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization](https://mlsanity.com/paper/2501.14635/) (2025)
- [OpReg-Boost: Learning to Accelerate Online Algorithms with Operator Regression](https://mlsanity.com/paper/2105.13271/) (2021)

## Abstract (arXiv)

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(n2) for n observations. Numerical results support our findings.