19 citations · 33 across the 6 of their papers we have counts for
6 papers
Doubly autoparallel structure on the probability simplex
Atsumi Ohara, Hideyuki Ishi
On the probability simplex, we can consider the standard information geometric structure with the e- and m-affine connections mutually dual with respect to the Fisher metric. The g…
Dually flat structure with escort probability and its application to alpha-Voronoi diagrams
Atsumi Ohara, Hiroshi Matsuzoe, Shun-ichi Amari
This paper studies geometrical structure of the manifold of escort probability distributions and shows its new applicability to information science. In order to realize escort prob…
A Bregman Extension of quasi-Newton updates I: An Information Geometrical framework
Takafumi Kanamori, Atsumi Ohara
We study quasi-Newton methods from the viewpoint of information geometry induced associated with Bregman divergences. Fletcher has studied a variational problem which derives the a…
A Bregman Extension of quasi-Newton updates II: Convergence and Robustness Properties
Takafumi Kanamori, Atsumi Ohara
We propose an extension of quasi-Newton methods, and investigate the convergence and the robustness properties of the proposed update formulae for the approximate Hessian matrix. F…
Geometric study for the Legendre duality of generalized entropies and its application to the porous medium equation
Atsumi Ohara
We geometrically study the Legendre duality relation that plays an important role in statistical physics with the standard or generalized entropies. For this purpose, we introduce…
Information Geometry of q-Gaussian Densities and Behaviors of Solutions to Related Diffusion Equations
Atsumi Ohara, Tatsuaki Wada
This paper presents new geometric aspects of the behaviors of solutions to the porous medium equation (PME) and its associated equation. First we discuss the Legendre structure wit…