The Bregman chord divergence
This work addresses the problem of distance selection for practitioners in ML and signal processing, offering a more tunable and computationally efficient alternative, though it appears incremental as an extension of existing Bregman divergences.
The authors tackled the challenge of selecting appropriate distances for machine learning and signal processing by introducing Bregman chord divergences, which extend Bregman divergences to avoid gradient calculations and use easily tunable scalar parameters while generalizing asymptotically to Bregman divergences.
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.