Dually flat structure with escort probability and its application to alpha-Voronoi diagrams

2010/10/24 by Atsumi Ohara, Ohara, Atsumi, Hiroshi Matsuzoe +3
Computer Science · Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #Bayesian Modeling and Causal Inference #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Information Theory (cs.IT) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1010.4965

openalex publication_date 2010/10/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

This paper studies geometrical structure of the manifold of escort probability distributions and shows its new applicability to information science. In order to realize escort probabilities we use a conformal transformation that flattens so-called alpha-geometry of the space of discrete probability distributions, which well characterizes nonadditive statistics on the space. As a result escort probabilities are proved to be flat coordinates of the usual probabilities for the derived dually flat structure. Finally, we demonstrate that escort probabilities with the new structure admits a simple algorithm to compute Voronoi diagrams and centroids with respect to alpha-divergences.

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