The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning
Martin de Tours School of Management and Economics, Assumption University, MSME Building, 4th Floor, 88 Moo 8 Bang Na-Trad Km. 26 Bangsaothong, 10540 Samuthprakarn, Thailand
Entropy 2014, 16(12), 6338-6381; https://doi.org/10.3390/e16126338
Received: 19 October 2014 / Revised: 24 November 2014 / Accepted: 25 November 2014 / Published: 1 December 2014
(This article belongs to the Special Issue Maximum Entropy Applied to Inductive Logic and Reasoning)
The aim of this paper is to develop a comprehensive study of the geometry involved in combining Bregman divergences with pooling operators over closed convex sets in a discrete probabilistic space. A particular connection we develop leads to an iterative procedure, which is similar to the alternating projection procedure by Csiszár and Tusnády. Although such iterative procedures are well studied over much more general spaces than the one we consider, only a few authors have investigated combining projections with pooling operators. We aspire to achieve here a comprehensive study of such a combination. Besides, pooling operators combining the opinions of several rational experts allows us to discuss possible applications in multi-expert reasoning.
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Keywords:
Bregman divergence; information geometry; pooling operator; discrete probability function; probabilistic merging; multi-expert reasoning
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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
MDPI and ACS Style
Adamčík, M. The Information Geometry of Bregman Divergences and Some Applications in Multi-Expert Reasoning. Entropy 2014, 16, 6338-6381.
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