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- W3046115174 abstract "Here we examine some connections between the notions of generalized arithmetic means, geodesics, Lagrange-Hamilton dynamics and Bregman divergences. In a previous paper we developed a predictive interpretation of generalized arithmetic means. That work was more probabilistically oriented. Here we take a geometric turn, and see that generalized arithmetic means actually minimize a geodesic distance on $mathbb{R}^n.$ Such metrics might result from pull-backs of the Euclidean metric in $mathbb{R}^n.$ We shall furthermore see that in some cases these pull-backs might coincide with the Hessian of a convex function. This occurs when the Hessian of a convex function has a square root that is the Jacobian of a diffeomorphism in $mathbb{R}^n.$ In this case we obtain a comparison between the Bregman divergence defined by the convex function and the geodesic distance in the metric defined by its Hessian." @default.
- W3046115174 created "2020-08-03" @default.
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- W3046115174 date "2020-07-29" @default.
- W3046115174 modified "2023-09-25" @default.
- W3046115174 title "From generalized arithmetic means to geodesics to Hamilton dynamics to Bregman divergences" @default.
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