Seminario Q-Math
Information geometry and statistical potentials: Classical and Quantum
Ponente: Marco Pacelli (Scuola Superiore Meridionale di Napoli)Fecha: martes 10 de diciembre de 2024 - 13:00Lugar: Room 2.2.D08, Universidad Carlos III de Madrid
Online: https://eu.bbcollab.com/guest/22f7877a774148a3aee3e398a4a86380 (active on request)
Resumen:
Statistical manifolds provide the abstract realisation of parametric models in statistics and information theory. They consist of a Riemannian manifold equipped with a pair of conjugate torsion-free affine connections. These geometric objects can be encoded into a 2-point function, termed contrast function. More general statistical structures have recently been considered where the torsion-free assumptions are relaxed or wholly removed. Even in this case, one can capture the geometrical structures through a single object, termed bi-form. In this talk, we review bi-form formalism and explain how it can be exploited to generate general statistical structures. Paradigmatic examples from classical and quantum information theory are discussed.
