Journal article 365 views 4 downloads
Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance
Journal of Functional Analysis, Volume: 285, Issue: 5, Start page: 109997
Swansea University Author: Feng-yu Wang
-
PDF | Accepted Manuscript
Distributed under the terms of a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).
Download (234.66KB)
DOI (Published version): 10.1016/j.jfa.2023.109997
Abstract
For a complete connected Riemannian manifold M let V ∈ C2(M) be such that μ(dx) =e−V(x) vol(dx) is a probability measure on M. Taking μ as reference measure, we derive in-equalities for probability measures on M linking relative entropy, Fisher information, Steindiscrepancy and Wasserstein distance....
Published in: | Journal of Functional Analysis |
---|---|
ISSN: | 0022-1236 |
Published: |
Elsevier BV
2023
|
Online Access: |
Check full text
|
URI: | https://cronfa.swan.ac.uk/Record/cronfa63390 |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
first_indexed |
2023-05-10T10:06:52Z |
---|---|
last_indexed |
2023-05-10T10:06:52Z |
id |
cronfa63390 |
recordtype |
SURis |
fullrecord |
<?xml version="1.0" encoding="utf-8"?><rfc1807 xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:xsd="http://www.w3.org/2001/XMLSchema"><bib-version>v2</bib-version><id>63390</id><entry>2023-05-10</entry><title>Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance</title><swanseaauthors><author><sid>6734caa6d9a388bd3bd8eb0a1131d0de</sid><firstname>Feng-yu</firstname><surname>Wang</surname><name>Feng-yu Wang</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2023-05-10</date><abstract>For a complete connected Riemannian manifold M let V ∈ C2(M) be such that μ(dx) =e−V(x) vol(dx) is a probability measure on M. Taking μ as reference measure, we derive in-equalities for probability measures on M linking relative entropy, Fisher information, Steindiscrepancy and Wasserstein distance. These inequalities strengthen in particular the fa-mous log-Sobolev and transportation-cost inequality and extend the so-called Entropy/Stein-discrepancy/Information (HSI) inequality established by Ledoux, Nourdin and Peccati (2015)for the standard Gaussian measure on Euclidean space to the setting of Riemannian manifolds.</abstract><type>Journal Article</type><journal>Journal of Functional Analysis</journal><volume>285</volume><journalNumber>5</journalNumber><paginationStart>109997</paginationStart><paginationEnd/><publisher>Elsevier BV</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0022-1236</issnPrint><issnElectronic/><keywords>Relative entropy, Fisher information, Stein discrepancy, Wasserstein distance</keywords><publishedDay>1</publishedDay><publishedMonth>9</publishedMonth><publishedYear>2023</publishedYear><publishedDate>2023-09-01</publishedDate><doi>10.1016/j.jfa.2023.109997</doi><url/><notes/><college>COLLEGE NANME</college><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><apcterm/><funders/><projectreference/><lastEdited>2024-07-29T14:21:39.1405030</lastEdited><Created>2023-05-10T11:03:48.3778305</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Mathematics and Computer Science - Mathematics</level></path><authors><author><firstname>Li-Juan</firstname><surname>Cheng</surname><orcid>0000-0001-6778-2770</orcid><order>1</order></author><author><firstname>Anton</firstname><surname>Thalmaier</surname><orcid>0000-0002-0567-2469</orcid><order>2</order></author><author><firstname>Feng-yu</firstname><surname>Wang</surname><order>3</order></author></authors><documents><document><filename>63390__27441__0d20141fb0aa49059fc3654d95584443.pdf</filename><originalFilename>63390.pdf</originalFilename><uploaded>2023-05-11T13:37:47.8824742</uploaded><type>Output</type><contentLength>240292</contentLength><contentType>application/pdf</contentType><version>Accepted Manuscript</version><cronfaStatus>true</cronfaStatus><embargoDate>2024-05-03T00:00:00.0000000</embargoDate><documentNotes>Distributed under the terms of a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0).</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>https://creativecommons.org/licenses/by-nc-nd/4.0/</licence></document></documents><OutputDurs/></rfc1807> |
spelling |
v2 63390 2023-05-10 Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance 6734caa6d9a388bd3bd8eb0a1131d0de Feng-yu Wang Feng-yu Wang true false 2023-05-10 For a complete connected Riemannian manifold M let V ∈ C2(M) be such that μ(dx) =e−V(x) vol(dx) is a probability measure on M. Taking μ as reference measure, we derive in-equalities for probability measures on M linking relative entropy, Fisher information, Steindiscrepancy and Wasserstein distance. These inequalities strengthen in particular the fa-mous log-Sobolev and transportation-cost inequality and extend the so-called Entropy/Stein-discrepancy/Information (HSI) inequality established by Ledoux, Nourdin and Peccati (2015)for the standard Gaussian measure on Euclidean space to the setting of Riemannian manifolds. Journal Article Journal of Functional Analysis 285 5 109997 Elsevier BV 0022-1236 Relative entropy, Fisher information, Stein discrepancy, Wasserstein distance 1 9 2023 2023-09-01 10.1016/j.jfa.2023.109997 COLLEGE NANME COLLEGE CODE Swansea University 2024-07-29T14:21:39.1405030 2023-05-10T11:03:48.3778305 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Li-Juan Cheng 0000-0001-6778-2770 1 Anton Thalmaier 0000-0002-0567-2469 2 Feng-yu Wang 3 63390__27441__0d20141fb0aa49059fc3654d95584443.pdf 63390.pdf 2023-05-11T13:37:47.8824742 Output 240292 application/pdf Accepted Manuscript true 2024-05-03T00:00:00.0000000 Distributed under the terms of a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). true eng https://creativecommons.org/licenses/by-nc-nd/4.0/ |
title |
Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance |
spellingShingle |
Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance Feng-yu Wang |
title_short |
Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance |
title_full |
Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance |
title_fullStr |
Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance |
title_full_unstemmed |
Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance |
title_sort |
Some inequalities on Riemannian manifolds linking Entropy, Fisher information, Stein discrepancy and Wasserstein distance |
author_id_str_mv |
6734caa6d9a388bd3bd8eb0a1131d0de |
author_id_fullname_str_mv |
6734caa6d9a388bd3bd8eb0a1131d0de_***_Feng-yu Wang |
author |
Feng-yu Wang |
author2 |
Li-Juan Cheng Anton Thalmaier Feng-yu Wang |
format |
Journal article |
container_title |
Journal of Functional Analysis |
container_volume |
285 |
container_issue |
5 |
container_start_page |
109997 |
publishDate |
2023 |
institution |
Swansea University |
issn |
0022-1236 |
doi_str_mv |
10.1016/j.jfa.2023.109997 |
publisher |
Elsevier BV |
college_str |
Faculty of Science and Engineering |
hierarchytype |
|
hierarchy_top_id |
facultyofscienceandengineering |
hierarchy_top_title |
Faculty of Science and Engineering |
hierarchy_parent_id |
facultyofscienceandengineering |
hierarchy_parent_title |
Faculty of Science and Engineering |
department_str |
School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics |
document_store_str |
1 |
active_str |
0 |
description |
For a complete connected Riemannian manifold M let V ∈ C2(M) be such that μ(dx) =e−V(x) vol(dx) is a probability measure on M. Taking μ as reference measure, we derive in-equalities for probability measures on M linking relative entropy, Fisher information, Steindiscrepancy and Wasserstein distance. These inequalities strengthen in particular the fa-mous log-Sobolev and transportation-cost inequality and extend the so-called Entropy/Stein-discrepancy/Information (HSI) inequality established by Ledoux, Nourdin and Peccati (2015)for the standard Gaussian measure on Euclidean space to the setting of Riemannian manifolds. |
published_date |
2023-09-01T14:21:38Z |
_version_ |
1805919765692153856 |
score |
11.021648 |