"Introduction to Information Geometry"- kurs prof. Boyoma z Montpellier

Na początku marca w ramach wymiany ERASMUS przyjeżdża Michel Nguiffo Boyom, profesor Universite de Montpellier II i planuje wygłosić krótki cykl wykładów poświęcony wprowadzeniu do teorii "Geometrii informacji".

Opis kursu zamieszczam poniżej. Wszystkich zainteresowanych zachęcam do udziału.

"Introduction to Information Geometry"

Michel N. Boyom, I3M UMR CNRS 5149. University Montpellier2, France.

The aim of the lectures is a short introduction to the Information
Geometry in statistical models. Amount the relevant aspects of the
subject is its relationships to Differential Geometry in locally
flat manifolds. Here is the content of lectures.

1.Differentiable structures in topological spaces.

1.1 Atlas viewpoint
1.2 Parametrization viewpoint
1.3 Fonctionnal space viewpoint
1.4 Parametrized linear algebra viewpoint.


2. Introduction to KV topology.

2.1 Connections in vector bundles
2.2 Linear connections
2.3 Locally flat structures
2.4 Affine structures.
2.5 Hessian manifolds


3. Statistical models.

3.1 Measurable spaces.
3.2 Probabilized measurable spaces.
3.3 Models for measurable spaces.
3.4 Fisher information matrix
3.5 The main theorem.