Approximation and bounding techniques for the Fisher-Rao distances

arXiv:2403.10089v1 Announce Type: cross
Abstract: The Fisher-Rao distance between two probability distributions of a statistical model is defined as the Riemannian geodesic distance induced by the Fisher information metric. In order to calculate the Fisher-Rao distance in closed-form, we need (1) to elicit a formula for the Fisher-Rao geodesics, and (2) to integrate the Fisher length element along those geodesics. We consider several numerically robust approximation and bounding techniques for the Fisher-Rao distances: First, we report generic upper bounds on …

abstract approximation arxiv cs.cv cs.it cs.lg fisher form information math.it probability statistical type