Statistical exponential families: A digest with flash cards
Frank Nielsen, Vincent Garcia

TL;DR
This paper provides a concise overview of exponential family distributions, their properties, dualities, and geometric structures, serving as a comprehensive reference for statisticians and researchers.
Contribution
It offers a summarized, organized digest of exponential family distributions, including definitions, properties, decompositions, and geometric perspectives, with plans for ongoing updates.
Findings
Summarizes key properties of exponential families
Details decompositions and formulas of common distributions
Explores geometric structures like Fisher-Rao and dual affine connections
Abstract
This document describes concisely the ubiquitous class of exponential family distributions met in statistics. The first part recalls definitions and summarizes main properties and duality with Bregman divergences (all proofs are skipped). The second part lists decompositions and related formula of common exponential family distributions. We recall the Fisher-Rao-Riemannian geometries and the dual affine connection information geometries of statistical manifolds. It is intended to maintain and update this document and catalog by adding new distribution items.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Statistical Methods and Models · Statistical Mechanics and Entropy · Bayesian Methods and Mixture Models
