New connections on the fiber-bundle
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Abstract
In this paper we construct a family of α-connections on a fiber-bundle of a generalized statistical manifold. We prove that the exponential and mixture connections are curvature-free and we investigate the associated parallel transport.
Description
Information geometry investigates the differential-geometric structure of statistical models and has many applications in statistical inference or machine learning for example (see [4]). Since the seminal work of Rao[14] where Fisher information is viewed as a Riemannian metric on a probability distributions space, statistical manifolds have been widely studied.
Citation
A. Gbaguidi Amoussou, F. Djibril Moussa, C. Ogouyandjou, M. A. Diop. (2019). New connections on the fiber-bundle of generalized statistical manifolds. Pg 24-32.