A method to construct exponential families by representation theory
Statistics Theory
2022-10-14 v4 Machine Learning
Probability
Statistics Theory
Abstract
In this paper, we give a method to construct "good" exponential families systematically by representation theory. More precisely, we consider a homogeneous space as a sample space and construct an exponential family invariant under the transformation group by using a representation of . The method generates widely used exponential families such as normal, gamma, Bernoulli, categorical, Wishart, von Mises, Fisher-Bingham and hyperboloid distributions.
Cite
@article{arxiv.1811.01394,
title = {A method to construct exponential families by representation theory},
author = {Koichi Tojo and Taro Yoshino},
journal= {arXiv preprint arXiv:1811.01394},
year = {2022}
}