# Nonconvex Extension of Generalized Huber Loss for Robust Learning and Pseudo-Mode Statistics

arXiv: https://arxiv.org/abs/2202.11141 · HTML: https://mlsanity.com/paper/2202.11141/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 31 references that are in the map.
- First posted on arXiv 22 Feb 2022.

## Builds on (most cited first, 4 of 4)

- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statistics](https://mlsanity.com/paper/2108.12627/) (2021)
- [Sequential Outlier Detection based on Incremental Decision Trees](https://mlsanity.com/paper/1803.03674/) (2018)
- [Low Regret Binary Sampling Method for Efficient Global Optimization of Univariate Functions](https://mlsanity.com/paper/2201.07164/) (2022)

## Built on by (most cited first, 8 of 8)

- [Smoothing with the Best Rectangle Window is Optimal for All Tapered Rectangle Windows](https://mlsanity.com/paper/2203.02997/) (2022)
- [Blind Source Separation for Mixture of Sinusoids with Near-Linear Computational Complexity](https://mlsanity.com/paper/2203.14324/) (2022)
- [Merging Knockout and Round-Robin Tournaments: A Flexible Linear Elimination Tournament Design](https://mlsanity.com/paper/2203.12011/) (2022)
- [Robust, Nonparametric, Efficient Decomposition of Spectral Peaks under Distortion and Interference](https://mlsanity.com/paper/2204.08411/) (2022)
- [An Auto-Regressive Formulation for Smoothing and Moving Mean with Exponentially Tapered Windows](https://mlsanity.com/paper/2206.14749/) (2022)
- [A 2-opt Algorithm for Locally Optimal Set Partition Optimization](https://mlsanity.com/paper/2303.08219/) (2023)
- [Formulation of Weighted Average Smoothing as a Projection of the Origin onto a Convex Polytope](https://mlsanity.com/paper/2303.11958/) (2023)
- [A Note On Nonlinear Regression Under L2 Loss](https://mlsanity.com/paper/2303.17745/) (2023)

## Abstract (arXiv)

We propose an extended generalization of the pseudo Huber loss formulation. We show that using the log-exp transform together with the logistic function, we can create a loss which combines the desirable properties of the strictly convex losses with robust loss functions. With this formulation, we show that a linear convergence algorithm can be utilized to find a minimizer. We further discuss the creation of a quasi-convex composite loss and provide a derivative-free exponential convergence rate algorithm.