Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem

نویسندگان
چکیده

برای دانلود باید عضویت طلایی داشته باشید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Information Geometry Connecting Wasserstein Distance and Kullback-Leibler Divergence via the Entropy-Relaxed Transportation Problem

Two geometrical structures have been extensively studied for a manifold of probability distributions. One is based on the Fisher information metric, which is invariant under reversible transformations of random variables, while the other is based on the Wasserstein distance of optimal transportation, which reflects the structure of the distance between random variables. Here, we propose a new i...

متن کامل

Divergence Function, Information Monotonicity and Information Geometry

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 fdivergence...

متن کامل

The discretizable distance geometry problem

We introduce the Discretizable Distance Geometry Problem in R (DDGP3), which consists in a subclass of instances of the Distance Geometry Problem for which an embedding in R can be found by means of a discrete search. We show that the DDGP3 is a generalization of the Discretizable Molecular Distance Geometry Problem (DMDGP), and we discuss the main differences between the two problems. We prove...

متن کامل

The unassigned distance geometry problem

Studies of distance geometry problems (DGP) have focused on cases where the vertices at the ends of all ormost of the given distances are known or assigned, whichwe call assigned distance geometry problems (aDGPs). In this contribution we consider the unassigned distance geometry problem (uDGP) where the vertices associatedwith a given distance are unknown, so the graph structure has to be disc...

متن کامل

Connecting Information Geometry and Geometric Mechanics

The divergence function in information geometry, and the discrete Lagrangian in discrete geometric mechanics each induce a differential geometric structure on the product manifold Q×Q. We aim to investigate the relationship between these two objects, and the fundamental role that duality, in the form of Legendre transforms, plays in both fields. By establishing an analogy between these two appr...

متن کامل

ذخیره 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: Information Geometry

سال: 2018

ISSN: 2511-2481,2511-249X

DOI: 10.1007/s41884-018-0002-8