Divergence Function, Information Monotonicity and Information Geometry
نویسنده
چکیده
A divergence function measures how different two points are in a base space. Well-known examples are the Kullback-Leibler divergence and f-divergence, which are defined in a manifold of probability distributions. The Bregman divergence is used in a more general situation. The present paper characterizes the geometrical structure which a divergence function gives, and proves that the fdivergences are unique in the sense of information-invariancy, giving the alpha-geometrical structure. Bregman divergences are characterized by dually flat geometrical structure. The paper also studies geometrical properties of hierarchical models which include singular structure.
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