Title




Rhotau embedding and gauge freedom in information geometry
 
Author




 
Abstract




The standard model of information geometry, expressed as FisherRao metric and AmariChensov 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 singlefunction approaches (Eguchis Uembedding and Naudts deformedlog or phiembedding) and a twofunction embedding approach (Zhangs conjugate rhotau embedding). In terms of geometry, the rhotau embedding of a parametric statistical model defines both a Riemannian metric, called rhotau metric, and an alphafamily of rhotau 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 rhotau metric becomes Hessian and hence the ±1 ±1 rhotau connections are dually flat. For any choice of rho and tau there exist models belonging to the phideformed exponential family for which the rhotau 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 phiexponential family as the solution. 
 
Language




English
 
Source (journal)




Information geometry
 
Publication




2018
 
Volume/pages




(2018)
, p. 137
 
Full text (Publisher's DOI)




 
Full text (open access)




 
