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• W2405944767 abstract "A function is exponentially concave if its exponential is concave. We consider exponentially concave functions on the unit simplex. In a previous paper we showed that gradient maps of exponentially concave functions provide solutions to a Monge-Kantorovich optimal transport problem and give a better gradient approximation than those of ordinary concave functions. The approximation error, called L-divergence, is different from the usual Bregman divergence. Using tools of information geometry and optimal transport, we show that L-divergence induces a new information geometry on the simplex consisting of a Riemannian metric and a pair of dually coupled affine connections which defines two kinds of geodesics. We show that the induced geometry is dually projectively flat but not flat. Nevertheless, we prove an analogue of the celebrated generalized Pythagorean theorem from classical information geometry. On the other hand, we consider displacement interpolation under a Lagrangian integral action that is consistent with the optimal transport problem and show that the action minimizing curves are dual geodesics. The Pythagorean theorem is also shown to have an interesting application of determining the optimal trading frequency in stochastic portfolio theory." @default.
• W2405944767 created "2016-06-24" @default.
• W2405944767 creator A5053260623 @default.
• W2405944767 creator A5061400083 @default.
• W2405944767 date "2016-05-19" @default.
• W2405944767 modified "2023-09-27" @default.
• W2405944767 title "Exponentially concave functions and a new information geometry" @default.
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• W2405944767 hasPublicationYear "2016" @default.
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