Geometry of deformed exponential families: Invariant, dually-flat and conformal geometries

► Information geometries on a manifold of a deformed exponential family are studied. ► They define respective quantities such as deformed free energies and entropies. ► Geometry of the q-exponential family is characterized via invariance and flatness. ► Conformal structure of the flat geometry of the q-exponential family is studied.