- Tytuł:
- Information geometry of divergence functions
- Autorzy:
-
Amari, S.
Cichocki, A. - Powiązania:
- https://bibliotekanauki.pl/articles/199901.pdf
- Data publikacji:
- 2010
- Wydawca:
- Polska Akademia Nauk. Czytelnia Czasopism PAN
- Tematy:
-
information geometry
divergence functions - Opis:
- Measures of divergence between two points play a key role in many engineering problems. One such measure is a distance function, but there are many important measures which do not satisfy the properties of the distance. The Bregman divergence, Kullback-Leibler divergence and f-divergence are such measures. In the present article, we study the differential-geometrical structure of a manifold induced by a divergence function. It consists of a Riemannian metric, and a pair of dually coupled affine connections, which are studied in information geometry. The class of Bregman divergences are characterized by a dually flat structure, which is originated from the Legendre duality. A dually flat space admits a generalized Pythagorean theorem. The class of f-divergences, defined on a manifold of probability distributions, is characterized by information monotonicity, and the Kullback-Leibler divergence belongs to the intersection of both classes. The f-divergence always gives the -geometry, which consists of the Fisher information metric and a dual pair of š-connections. The -divergence is a special class of f-divergences. This is unique, sitting at the intersection of the f-divergence and Bregman divergence classes in a manifold of positive measures. The geometry derived from the Tsallis q-entropy and related divergences are also addressed.
- Źródło:
-
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2010, 58, 1; 183-195
0239-7528 - Pojawia się w:
- Bulletin of the Polish Academy of Sciences. Technical Sciences
- Dostawca treści:
- Biblioteka Nauki
Artykuł