Date: July 21, 2004

Venue: Room 4-508, Department of Mathematics, Hokkaido University

Organizer: MATSUZOE Hiroshi (Saga Univ.), FURUHATA Hitoshi (Hokkaido Univ.)

http://www.math.sci.hokudai.ac.jp/

http://coe.math.sci.hokudai.ac.jp/

Program:

10:00- Khadiga ARWINI (UMIST, Manchester UK)

Neighbourhoods of randomness, independence, uniformity and associated geometry

Abstract: We provide explicit information geometric representations of neighbourhoods for: randomness,independence and uniformity. We present tubular neighbourhoods containing: all processes sufficiently close to a Poisson process, all processes sufficiently close to a uniform process, all bivariate processes sufficiently close to the independent bivariate exponential process with identical marginals, and all bivariate processes sufficiently close to the independent bivariate Gaussian process with identical marginals. These neighbourhoods are constructed via affine immersions of the 3-manifold of gamma distributions, the Freund 4-manifold of bivariate exponentials and the 5-manifold of bivariate Gaussians. The results are significant theoretically because very general, and practically because topological and hence stable under perturbations.

References:
Khadiga Arwini and C.T.J. Dodson, Information geometric neighbourhoods of randomness and geometry of the McKay bivariate gamma 3-manifold, Sankhya: Indian Journal of Statistics 66, 2 (2004) 211-231.
http://www.ma.umist.ac.uk/kd/PREPRINTS/gamran.pdf
Khadiga Arwini and C.T.J. Dodson, Neighbourhoods of independence and associated geometry.
http://www.ma.umist.ac.uk/kd/PREPRINTS/nhdindep.pdf

14:30- KUROSU Sanae (Tokyo Univ. of Science)

On the alpha-conformally equivalence of a statistical manifold

Abstract: For a statistical manifold, some conformal classes, $\alpha$-conformally equivalence and conformally-projectively equivalence, are defined and studied. A $1$-conformally flat statistical manifold and a conformally-projectively flat statistical manifold are characterized by certain tensor and affine immersions. In this talk, I will review about the $\alpha$-conformally equivalence of statistical manifolds and derive some fundamental properties for such a statistical manifold.

16:00- MATSUZOE Hiroshi (Saga Univ.)

Information geometry for neural networks

Abstract: Differential geometry is an useful tool for the study of neural networks. In this talk, we would like to review the information geometry for neural networks.

Seminar:

July 20 15:00-

July 20 16:30- KON Mayuko (Hokkaido Univ.), Affine immersions of Hermitian manifolds

July 20 18:30- Party

[poster]

[photo]

[MATSUZOE] [FURUHATA]