# A Note On Nonlinear Regression Under L2 Loss

arXiv: https://arxiv.org/abs/2303.17745 · HTML: https://mlsanity.com/paper/2303.17745/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 30 Mar 2023.

## Builds on (most cited first, 7 of 7)

- [Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statistics](https://mlsanity.com/paper/2108.12627/) (2021)
- [Nonparametric Extrema Analysis in Time Series for Envelope Extraction, Peak Detection and Clustering](https://mlsanity.com/paper/2109.02082/) (2021)
- [Low Regret Binary Sampling Method for Efficient Global Optimization of Univariate Functions](https://mlsanity.com/paper/2201.07164/) (2022)
- [Optimal and Efficient Algorithms for General Mixable Losses against Switching Oracles](https://mlsanity.com/paper/2108.06411/) (2021)
- [Nonconvex Extension of Generalized Huber Loss for Robust Learning and Pseudo-Mode Statistics](https://mlsanity.com/paper/2202.11141/) (2022)
- [Efficient, Anytime Algorithms for Calibration with Isotonic Regression under Strictly Convex Losses](https://mlsanity.com/paper/2111.00468/) (2021)
- [Efficient Minimax Optimal Global Optimization of Lipschitz Continuous Multivariate Functions](https://mlsanity.com/paper/2206.02383/) (2022)

## Abstract (arXiv)

We investigate the nonlinear regression problem under L2 loss (square loss) functions. Traditional nonlinear regression models often result in non-convex optimization problems with respect to the parameter set. We show that a convex nonlinear regression model exists for the traditional least squares problem, which can be a promising towards designing more complex systems with easier to train models.