# Overfitting Reduction in Convex Regression

arXiv: https://arxiv.org/abs/2404.09528 · HTML: https://mlsanity.com/paper/2404.09528/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2024.

## Built on by (most cited first, 1 of 1)

- [Convex Regression with a Penalty](https://mlsanity.com/paper/2509.19788/) (2025)

## Abstract (arXiv)

Convex regression is a method for estimating the convex function from a data set. This method has played an important role in operations research, economics, machine learning, and many other areas. However, it has been empirically observed that convex regression produces inconsistent estimates of convex functions and extremely large subgradients near the boundary as the sample size increases. In this paper, we provide theoretical evidence of this overfitting behavior. To eliminate this behavior, we propose two new estimators by placing a bound on the subgradients of the convex function. We further show that our proposed estimators can reduce overfitting by proving that they converge to the underlying true convex function and that their subgradients converge to the gradient of the underlying function, both uniformly over the domain with probability one as the sample size is increasing to infinity. An application to Finnish electricity distribution firms confirms the superior performance of the proposed methods in predictive power over the existing methods.