Abstract

AbstractWe introduce the dual of the mixture connection with respect to the Otto metric which represents a new kind of exponential connection. This provides a dual structure consisting of the mixture connection, the Otto metric as a Riemannian metric, and the new exponential connection. We derive the geodesic equation of this exponential connection, which coincides with the Kolmogorov forward equation of a gradient flow. We then derive the canonical contrast function of the introduced dual structure.

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