Legendre duality: from thermodynamics to information geometry

被引：0
|
作者：
Naudts, Jan [1 ]
Zhang, Jun [2 ,3 ]
机构：
[1] Univ Antwerp, Dept Phys, Univ Pl 1, B-2610 Antwerp, Belgium
[2] Univ Michigan, Dept Psychol, 530 Church St, Ann Arbor, MI 48109 USA
[3] Univ Michigan, Dept Stat, 530 Church St, Ann Arbor, MI 48109 USA
来源：
INFORMATION GEOMETRY | 2024年 / 7卷 / SUPPL1期
关键词：
Convex duality; Dually-flat geometry; Deformed exponential and logarithmic functions; Rho-tau connections; STATISTICAL MANIFOLD; DIVERGENCE FUNCTION;
D O I：
10.1007/s41884-023-00121-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper reviews the role of convex duality in Information Geometry. It clarifies the notion of bi-orthogonal coordinates associated with Legendre duality by treating its two underlying aspects separately: as a dual coordinate system and as a bi-orthogonal frame. It addresses the deformation of exponential families in a way that stills preserves the dually-flat geometry of 1- and (-1)-connections. The deformation involves a metric which generalizes the Fisher-Rao metric controlled by one degree of freedom and a pair of connections controlled by an additional degree of freedom.
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页码：623 / 649
页数：27
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