  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.
