Mechanics of geodesics in Information geometry

12/14/2022

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by   Sumanto Chanda, et al.

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In this article we attempt to formulate Riemannian and Randers-Finsler metrics in information geometry and study their mechanical properties. Starting from the gradient flow equations, we show how to formulate Riemannian metrics, and demonstrate their duality under canonical transformation. Then we show how to formulate a Randers-Finsler metric from deformed gradient equations. The theories described are finally applied to the Gaussian model and tested to verify consistency.