Séance Séminaire

Séminaire Gaston Darboux

(Para-)Complexifying Statistical Manifold

A statistical manifold is one prescribed with a Riemannian metric g and a pair of torsion-free g-conjugate connections; the connection and metric is Codazzi-coupled. Statistical manifolds arise out of Information Geometry, i.e., geometric characterization of statistical (probability) models, machine learning algorithms, and other topics of information science. Assuming that a statistical manifold (of even dimension) further admits an almost complex or almost para-complex structure. We consider conjugate connections that admit torsion in the (para-)Hermitian setting, and demonstrate a quadruple of torsion-and curvature-carrying connections that are compatible with (para-)Kahler and (para-)Hermitian structures. (Collaborative work with Teng Fei @Columbia University and with Sergey Gregorian @University of Texas Grande Rio Valley)