Diffeological Statistical Models, the Fisher Metric and Probabilistic Mappings
نویسندگان
چکیده
منابع مشابه
Completeness in Probabilistic Metric Spaces
The idea of probabilistic metric space was introduced by Menger and he showed that probabilistic metric spaces are generalizations of metric spaces. Thus, in this paper, we prove some of the important features and theorems and conclusions that are found in metric spaces. At the beginning of this paper, the distance distribution functions are proposed. These functions are essential in defining p...
متن کاملThe Wasserstein-Fisher-Rao metric
This note gives a summary of the presentation that I gave at the workshop on shape analysis. Based on [CSPV15, CPSV15], we present a generalization of optimal transport to measures that have different total masses. This generalization enjoys most of the properties of standard optimal transport but we will focus on the geometric formulation of the model. We expect this new metric to have interes...
متن کاملProbabilistic Fisher discriminant analysis
Fisher Discriminant Analysis (FDA) is a powerful and popular method for dimensionality reduction and classification which has unfortunately poor performances in the cases of label noise and sparse labeled data. To overcome these limitations, we propose a probabilistic framework for FDA and extend it to the semi-supervised case. Experiments on realworld datasets show that the proposed approach w...
متن کاملDynamics of the Fisher information metric.
We present a method to generate probability distributions that correspond to metrics obeying partial differential equations generated by extremizing a functional J [g(mu nu) (theta(i)) ] , where g(mu nu) (theta(i)) is the Fisher metric. We postulate that this functional of the dynamical variable g(mu nu) (theta(i)) is stationary with respect to small variations of these variables. Our approach ...
متن کاملFisher Information and Statistical Mechanics
Fisher information is an important concept in statistical estimation theory and information theory, but it has received relatively little consideration in statistical physics. In order to rectify this oversight, in this brief note I will review the correspondence between Fisher information and uctuations at thermodynamic equilibrium, and discuss various applications of Fisher information to equ...
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: Mathematics
سال: 2020
ISSN: 2227-7390
DOI: 10.3390/math8020167