# A Unified Representation of Density-Power-Based Divergences Reducible to M-Estimation

arXiv: https://arxiv.org/abs/2501.16287 · HTML: https://mlsanity.com/paper/2501.16287/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 23 references that are in the map.
- First posted on arXiv 27 Jan 2025.

## Builds on (most cited first, 3 of 3)

- [Statistical Inference based on Bridge Divergences](https://mlsanity.com/paper/1706.05745/) (2017)
- [The B-Exponential Divergence and its Generalizations with Applications to Parametric Estimation](https://mlsanity.com/paper/1810.11721/) (2018)
- [Robust Inference Using the Exponential-Polynomial Divergence](https://mlsanity.com/paper/2012.11735/) (2020)

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

- [Relationship between H"older Divergence and Functional Density Power Divergence: Intersection and Generalization](https://mlsanity.com/paper/2504.17008/) (2025)

## Abstract (arXiv)

Density-power-based divergences are known to provide robust inference procedures against outliers, and their extensions have been widely studied. A characteristic of successful divergences is that the estimation problem can be reduced to M-estimation. In this paper, we define a norm-based Bregman density power divergence (NB-DPD) -- density-power-based divergence with functional flexibility within the framework of Bregman divergences that can be reduced to M-estimation. We show that, by specifying the function φγ, NB-DPD reduces to well-known divergences, such as the density power divergence and the γ-divergence. Furthermore, by examining the combinations of functions φγ corresponding to existing divergences, we show that a new divergence connecting these existing divergences can be derived. Finally, we show that the redescending property, one of the key indicators of robustness, holds only for the γ-divergence.