Search
Workshop

Information Geometry: finite vs infinite sample space

  • Giovanni Pistone (Collegio Carlo Alberto, Torino, Italy)
E1 05 (Leibniz-Saal)

Abstract

The scope of IG has been clearly defined ​in S. Amari and H. ​Nagaoka ​monograph ​by emphasizing the crucial importance of the dua​l ​affine structure of regular parametric statistical models. Amari’s research program is today still in progress e.g., the papers presented in this conference.​ ​One direction of research​ ​is​ ​the​ ​extension​ ​of the dual affine structure​ ​to non-parametric models. While the parametric assumption can ​fit​ ​most of the needs of Statististics and Machine Learning, this assumption​ ​is​ ​too restrictive​ ​in such fields as Statistical Phisics, Stochastics,​ ​or Evolution Equations. It is an easy but useful exercise to retell the geometry of finite dimensional models—-such as the probability simplex or the Gaussian distribution—-in a non-parametric language. In the first part of the talk, we give a non-parametric ​presentation of the IG of the finite probability simplex based on the idea of statistical bundle. ​After that, we discuss some of the available proposals for generalizing the same set-up to technically more complex situation.

Antje Vandenberg

Max Planck Institute for Mathematics in the Sciences (Leipzig), Germany Contact via Mail

Nihat Ay

Max Planck Institute for Mathematics in the Sciences (Leipzig), Germany

Mikhail Prokopenko

University of Sydney, Australia