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Entropy 2017, 19(7), 309; doi:10.3390/e19070309

Conjugate Representations and Characterizing Escort Expectations in Information Geometry

1
Department of Electrical and Electronic Engineering, Ibaraki University, Nakanarusawa-cho, Hitachi, Ibaraki 316-8511, Japan
2
Department of Computer Science and Engineering, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
*
Author to whom correspondence should be addressed.
Received: 29 May 2017 / Revised: 22 June 2017 / Accepted: 27 June 2017 / Published: 28 June 2017
(This article belongs to the Special Issue Information Geometry II)
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Abstract

Based on the maximum entropy (MaxEnt) principle for a generalized entropy functional and the conjugate representations introduced by Zhang, we have reformulated the method of information geometry. For a set of conjugate representations, the associated escort expectation is naturally introduced and characterized by the generalized score function which has zero-escort expectation. Furthermore, we show that the escort expectation induces a conformal divergence. View Full-Text
Keywords: conjugate representations; information geometry; escort expectations; deformed exponential functions; conformal divergences conjugate representations; information geometry; escort expectations; deformed exponential functions; conformal divergences
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Wada, T.; Matsuzoe, H. Conjugate Representations and Characterizing Escort Expectations in Information Geometry. Entropy 2017, 19, 309.

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