# pyBregMan: A Python library for Bregman Manifolds

arXiv: https://arxiv.org/abs/2408.04175 · HTML: https://mlsanity.com/paper/2408.04175/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 42 references that are in the map.
- First posted on arXiv 8 Aug 2024.

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

- [Learning with Fenchel-Young Losses](https://mlsanity.com/paper/1901.02324/) (2019)
- [On geodesic triangles with right angles in a dually flat space](https://mlsanity.com/paper/1910.03935/) (2019)
- [Parametric information geometry with the package Geomstats](https://mlsanity.com/paper/2211.11643/) (2022)
- [Divergences induced by dual subtractive and divisive normalizations of exponential families and their convex deformations](https://mlsanity.com/paper/2312.12849/) (2023)
- [Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical models](https://mlsanity.com/paper/2403.10089/) (2024)

## Built on by (most cited first, 2 of 2)

- [Fast proxy centers for Jeffreys centroids: The Jeffreys-Fisher-Rao and the inductive Gauss-Bregman centers](https://mlsanity.com/paper/2410.14326/) (2024)
- [Supervised Quadratic Feature Analysis: Information Geometry Approach for Dimensionality Reduction](https://mlsanity.com/paper/2502.00168/) (2025)

## Abstract (arXiv)

A Bregman manifold is a synonym for a dually flat space in information geometry which admits as a canonical divergence a Bregman divergence. Bregman manifolds are induced by smooth strictly convex functions like the cumulant or partition functions of regular exponential families, the negative entropy of mixture families, or the characteristic functions of regular cones just to list a few such convex Bregman generators. We describe the design of pyBregMan, a library which implements generic operations on Bregman manifolds and instantiate several common Bregman manifolds used in information sciences. At the core of the library is the notion of Legendre-Fenchel duality inducing a canonical pair of dual potential functions and dual Bregman divergences. The library also implements the Fisher-Rao manifolds of categorical/multinomial distributions and multivariate normal distributions. To demonstrate the use of the pyBregMan kernel manipulating those Bregman and Fisher-Rao manifolds, the library also provides several core algorithms for various applications in statistics, machine learning, information fusion, and so on.