Nonparametric Information Geometry: From Divergence Function to Referential-Representational Biduality on Statistical Manifolds

Entropy

关键词: Fisher information;    alpha-connection;    infinite-dimensional manifold;    convex function;   

DOI  :  10.3390/e15125384

来源: mdpi

【 摘 要 】

Divergence functions are the non-symmetric “distance” on the manifold, , generalizing the results of Amari’s α-embedding. The present analysis illuminates two different types of duality in information geometry, one concerning the referential status of a point (measurable function) expressed in the divergence function (“referential duality”) and the other concerning its representation under an arbitrary monotone scaling (“representational duality”).

【 授权许可】

CC BY   
© 2013 by the author; licensee MDPI, Basel, Switzerland.