|
Title
|
|
|
|
Rho-tau embedding and gauge freedom in information geometry
| |
|
Author
|
|
|
|
| |
|
Abstract
|
|
|
|
| The standard model of information geometry, expressed as FisherRao metric and Amari-Chensov tensor, reflects an embedding of probability density by log log -transform. The present paper studies parametrized statistical models and the induced geometry using arbitrary embedding functions, comparing single-function approaches (Eguchis U-embedding and Naudts deformed-log or phi-embedding) and a two-function embedding approach (Zhangs conjugate rho-tau embedding). In terms of geometry, the rho-tau embedding of a parametric statistical model defines both a Riemannian metric, called rho-tau metric, and an alpha-family of rho-tau connections, with the former controlled by a single function and the latter by both embedding functions ρ ρ and τ τ in general. We identify conditions under which the rho-tau metric becomes Hessian and hence the ±1 ±1 rho-tau connections are dually flat. For any choice of rho and tau there exist models belonging to the phi-deformed exponential family for which the rho-tau metric is Hessian. In other cases the rhotau metric may be only conformally equivalent with a Hessian metric. Finally, we show a formulation of the maximum entropy framework which yields the phi-exponential family as the solution. |
| |
|
Language
|
|
|
|
English
| |
|
Source (journal)
|
|
|
|
Information geometry. - Singapore, 2018, currens
| |
|
Publication
|
|
|
|
Singapore
:
Springer
,
2018
| |
|
ISSN
|
|
|
|
2511-249X
[online]
2511-2481
[print]
| |
|
DOI
|
|
|
|
10.1007/S41884-018-0004-6
| |
|
Volume/pages
|
|
|
|
(2018)
, p. 1-37
| |
|
Full text (Publisher's DOI)
|
|
|
|
| |
|
Full text (open access)
|
|
|
|
| |
|