# The Bregman chord divergence

arXiv: https://arxiv.org/abs/1810.09113 · HTML: https://mlsanity.com/paper/1810.09113/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Oct 2018.

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

- [How to Boost Any Loss Function](https://mlsanity.com/paper/2407.02279/) (2024)

## Abstract (arXiv)

Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of testing one by one the entries of an ever-expanding dictionary of em ad hoc distances, one rather prefers to consider parametric classes of distances that are exhaustively characterized by axioms derived from first principles. Bregman divergences are such a class. However fine-tuning a Bregman divergence is delicate since it requires to smoothly adjust a functional generator. In this work, we propose an extension of Bregman divergences called the Bregman chord divergences. This new class of distances does not require gradient calculations, uses two scalar parameters that can be easily tailored in applications, and generalizes asymptotically Bregman divergences.