Fisher information geometry, Poisson kernel and asymptotical harmonicity
نویسندگان
چکیده
منابع مشابه
Minimality and Harmonicity in Differential Geometry
The theory of minimal surfaces and more generally of minimal immersions is one of the most fashionable branches in Diierential Geometry. Since the very early stage of the theory it was clear that there was a strong link between minimality and harmonicity. From a relation of E. Beltrami 4] follows that a surface in R 3 is minimal if and only if the components of the position vector are harmonic ...
متن کاملFisher Kernel
Jaakkola and Haussler (1999a) introduced the Fisher kernel (named in honour of Sir Ronald Fisher), thus creating a generic mechanism for incorporating generative probability models into discriminative classifiers such as SVMs. Jaakkola and Haussler (1999b) introduced a generic class of probabilistic regression models and a parameter estimation technique that can make use of arbitrary kernel fun...
متن کاملRelations between Renyi Distance and Fisher Information
In this paper, we first show that Renyi distance between any member of a parametric family and its perturbations, is proportional to its Fisher information. We, then, prove some relations between the Renyi distance of two distributions and the Fisher information of their exponentially twisted family of densities. Finally, we show that the partial ordering of families induced by Renyi dis...
متن کاملGeometry of Fisher Information Metric and the Barycenter Map
Geometry of Fisher metric and geodesics on a space of probability measures defined on a compact manifold is discussed and is applied to geometry of a barycenter map associated with Busemann function on an Hadamard manifold X . We obtain an explicit formula of geodesic and then several theorems on geodesics, one of which asserts that any two probability measures can be joined by a unique geodesi...
متن کاملParsimonious Kernel Fisher Discrimination
By applying recent results in optimization transfer, a new algorithm for kernel Fisher Discriminant Analysis is provided that makes use of a non-smooth penalty on the coefficients to provide a parsimonious solution. The algorithm is simple, easily programmed and is shown to perform as well as or better than a number of leading machine learning algorithms on a substantial benchmark. It is then a...
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: Differential Geometry and its Applications
سال: 2011
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2011.04.015