# Generalized Huber Loss for Robust Learning and its Efficient Minimization for a Robust Statistics

arXiv: https://arxiv.org/abs/2108.12627 · HTML: https://mlsanity.com/paper/2108.12627/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 28 Aug 2021.

## Builds on (most cited first, 5 of 5)

- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Dive into Deep Learning](https://mlsanity.com/paper/2106.11342/) (2021)
- [Sequential Outlier Detection based on Incremental Decision Trees](https://mlsanity.com/paper/1803.03674/) (2018)
- [Optimally Efficient Sequential Calibration of Binary Classifiers to Minimize Classification Error](https://mlsanity.com/paper/2108.08780/) (2021)
- [Cumulative Regret Analysis of the Piyavskii--Shubert Algorithm and Its Variants for Global Optimization](https://mlsanity.com/paper/2108.10859/) (2021)

## Built on by (most cited first, 30 of 32)

- [Nonparametric Extrema Analysis in Time Series for Envelope Extraction, Peak Detection and Clustering](https://mlsanity.com/paper/2109.02082/) (2021)
- [FinCast: A Foundation Model for Financial Time-Series Forecasting](https://mlsanity.com/paper/2508.19609/) (2025)
- [Nonconvex Extension of Generalized Huber Loss for Robust Learning and Pseudo-Mode Statistics](https://mlsanity.com/paper/2202.11141/) (2022)
- [DiffImpute: Tabular Data Imputation With Denoising Diffusion Probabilistic Model](https://mlsanity.com/paper/2403.13863/) (2024)
- [ATACompressor: Adaptive Task-Aware Compression for Efficient Long-Context Processing in LLMs](https://mlsanity.com/paper/2602.03226/) (2026)
- [Efficient Locally Optimal Number Set Partitioning for Scheduling, Allocation and Fair Selection](https://mlsanity.com/paper/2109.04809/) (2021)
- [Pretraining Large Brain Language Model for Active BCI: Silent Speech](https://mlsanity.com/paper/2504.21214/) (2025)
- [A Quadratic Time Locally Optimal Algorithm for NP-hard Equal Cardinality Partition Optimization](https://mlsanity.com/paper/2109.07882/) (2021)
- [Smoothing with the Best Rectangle Window is Optimal for All Tapered Rectangle Windows](https://mlsanity.com/paper/2203.02997/) (2022)
- [Video super-resolution for single-photon LIDAR](https://mlsanity.com/paper/2210.10474/) (2022)
- [A Linearithmic Time Locally Optimal Algorithm for the Multiway Number Partition Optimization](https://mlsanity.com/paper/2203.05618/) (2022)
- [A Robust Quantile Huber Loss With Interpretable Parameter Adjustment In Distributional Reinforcement Learning](https://mlsanity.com/paper/2401.02325/) (2024)
- [GlyRAG: Context-Aware Retrieval-Augmented Framework for Blood Glucose Forecasting](https://mlsanity.com/paper/2601.05353/) (2026)
- [Blind Source Separation for Mixture of Sinusoids with Near-Linear Computational Complexity](https://mlsanity.com/paper/2203.14324/) (2022)
- [Attention Loss Adjusted Prioritized Experience Replay](https://mlsanity.com/paper/2309.06684/) (2023)
- [One Step Closer to Ground Truth: A Multi-Scale Residual-Aware Representation Learning Pipeline for Predicting Time Series Data](https://mlsanity.com/paper/2606.10678/) (2026)
- [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)
- [1D to nD: A Meta Algorithm for Multivariate Global Optimization via Univariate Optimizers](https://mlsanity.com/paper/2209.03246/) (2022)
- [Fast Disparity Estimation from a Single Compressed Light Field Measurement](https://mlsanity.com/paper/2209.11342/) (2022)
- [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)
- [Scope Loss for Imbalanced Classification and RL Exploration](https://mlsanity.com/paper/2308.04024/) (2023)
- [LEARN: An Invex Loss for Outlier Oblivious Robust Online Optimization](https://mlsanity.com/paper/2408.06297/) (2024)
- [Residual-based Adaptive Huber Loss (RAHL) -- Design of an improved Huber loss for CQI prediction in 5G networks](https://mlsanity.com/paper/2408.14718/) (2024)
- [FOCUS on Contamination: Hydrology-Informed Noise-Aware Learning for Geospatial PFAS Mapping](https://mlsanity.com/paper/2502.14894/) (2025)
- [LVADNet3D: A Deep Autoencoder for Reconstructing 3D Intraventricular Flow from Sparse Hemodynamic Data](https://mlsanity.com/paper/2509.16860/) (2025)
- [CRACQ: A Multi-Dimensional Approach To Automated Document Assessment](https://mlsanity.com/paper/2510.02337/) (2025)
- [Evaluating the Clinical Impact of Generative Inpainting on Bone Age Estimation](https://mlsanity.com/paper/2511.23066/) (2025)

## Abstract (arXiv)

We propose a generalized formulation of the Huber loss. We show that with a suitable function of choice, specifically the log-exp transform; we can achieve a loss function which combines the desirable properties of both the absolute and the quadratic loss. We provide an algorithm to find the minimizer of such loss functions and show that finding a centralizing metric is not that much harder than the traditional mean and median.