[11.24]Information geometry on the space of all probability measures having positive density function
- 수학전공
- 조회수2196
- 2016-12-08
Information geometry on the space of all probability measures having positive density function
▣ 연 사 : Hiroyasu Satoh (Nippon Institute of Technology)
▣ 일 시 : 2016년 11월 24일(목) 4:30 - 5:30
▣ 장 소 : 31316호(수학과 전공강의실)
▣ 대 상 : 수학과 학부생 및 대학원생
▣ 다 과 : 4시 20분부터
Abstract
Information geometry is, roughly speaking, investigating geometric structures on a family of probability distributions or measures by means of modern differential geometry. It defines a Riemannian metric, called the Fisher metric, together with dually coupled affine connection. Information geometry has provided statistics with a new analytic tool. In this talk, we present how geometric structures are derived from the underlying natures of probability distributions and consider the space of all probability measures on a measure space, which is regarded as an infinite dimensional manifold. Moreover, we define the notion of normalized means of two probability measures and describe its geometric properties in terms of geodesics.