Dual connections in nonparametric classical information geometry
نویسندگان
چکیده
منابع مشابه
Dual Connections in Nonparametric Classical Information Geometry
We show how to obtain the mixture connection in an infinite dimensional information manifold and prove that it is dual to the exponential connection with respect to the Fisher information. We also define the α-connections and prove that they are convex mixtures of the extremal (±1)-connections.
متن کاملDual Connections in Nonparametrci Classical Information Geometry
We show how to obtain the mixture connection in an infinite dimensional information manifold and prove that it is dual to the exponential connection with respect to the Fisher information. We also define the α-connections and prove that they are convex mixtures of the extremal (±1)-connections.
متن کاملSpecial connections in almost paracontact metric geometry
Two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections: Levi-Civita, canonical (Zamkovoy), Golab and generalized dual. Their relationship is also analyzed with a special view towards their curvature. The particular case of an almost paracosymplectic manifold giv...
متن کاملspecial connections in almost paracontact metric geometry
two types of properties for linear connections (natural and almost paracontact metric) are discussed in almost paracontact metric geometry with respect to four linear connections: levi-civita, canonical (zamkovoy), golab and generalized dual. their relationship is also analyzed with a special view towards their curvature. the particular case of an almost paracosymplectic manifold giv...
متن کاملConnections in sub-Riemannian geometry
We introduce the notion of a connection over a bundle map and apply it to a sub-Riemannian geometry. It is shown that the concepts of normal and abnormal extremals of a sub-Riemannian structure can be characterized as parallel transported sections with respect to these generalized connections. Using this formalism we are able to give necessary and sufficient conditions for the existence of a sp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annals of the Institute of Statistical Mathematics
سال: 2008
ISSN: 0020-3157,1572-9052
DOI: 10.1007/s10463-008-0191-3