INFORMATION GEOMETRY OF BAYESIAN UPDATING AND REPLICATION

Speaker(s)

ŁUKASZ KACZMARCZYK

Affiliation

Uniwersytet Warszawski, Poland

Language of the talk

English

Date

March 26, 2025, 5:15 p.m.

Information about the event

IMPAN 405 & ZOOM

Title in Polish

INFORMATION GEOMETRY OF BAYESIAN UPDATING AND REPLICATION

Seminar

North Atlantic Noncommutative Geometry Seminar

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In this talk, I will show that the Kullback-Leibler divergence can be promoted to a functor from probabilistic spaces to convex polyhedra with a distinguished convex function. Both domain and codomain of this functor enjoy a canonical group action rendering the functor equivariant. Better still, this functor extends to a functor from probability spaces to stratified Riemannian manifolds equipped with group actions. This extension emphasises the role of the Jaynes principle in the canonical information dynamics and allows for future noncommutative generalizations. Based on joint work with T. Maszczyk.

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