Congruent families and invariant tensors
Statistics Theory
2017-06-01 v1 Statistics Theory
Abstract
Classical results of Chentsov and Campbell state that -- up to constant multiples -- the only -tensor field of a statistical model which is invariant under congruent Markov morphisms is the Fisher metric and the only invariant -tensor field is the Amari-Chentsov tensor. We generalize this result for arbitrary degree , showing that any family of -tensors which is invariant under congruent Markov morphisms is algebraically generated by the canonical tensor fields defined in an earlier paper.
Keywords
Cite
@article{arxiv.1705.11014,
title = {Congruent families and invariant tensors},
author = {Lorenz Schwachhöfer and Nihat Ay and Jürgen Jost and Hông Vân Lê},
journal= {arXiv preprint arXiv:1705.11014},
year = {2017}
}