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Stein kernels, optimal transport and the CLT Fathi, Max

Description

Stein kernels are a way of measuring distance between probability measures, defined via integration by parts formulas. I will present a connection between these kernels and optimal transport. The main result is a way of deriving rates of convergence in the classical central limit theorem using regularity estimates for a variant of the Monge-Ampere PDE. As an application, we obtain new rates of convergence for the multi-dimensional CLT, with explicit dependence on the dimension.

Item Metadata

Title
Stein kernels, optimal transport and the CLT
Creator
Fathi, Max
Publisher
Banff International Research Station for Mathematical Innovation and Discovery
Date Issued
2018-04-12T16:44
Description
Stein kernels are a way of measuring distance between probability measures, defined via integration by parts formulas. I will present a connection between these kernels and optimal transport. The main result is a way of deriving rates of convergence in the classical central limit theorem using regularity estimates for a variant of the Monge-Ampere PDE. As an application, we obtain new rates of convergence for the multi-dimensional CLT, with explicit dependence on the dimension.
Extent
33 minutes
Subject
Mathematics; Partial differential equations; Statistical mechanics, structure of matter
Type
Moving Image
File Format
video/mp4
Language
eng
Notes
Author affiliation: CNRS and IMT
Series
BIRS Workshop Lecture Videos (Banff, Alta)
Date Available
2018-10-10
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0372485
URI
http://hdl.handle.net/2429/67472
Affiliation
Non UBC
Peer Review Status
Unreviewed
Scholarly Level
Faculty
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
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Attribution-NonCommercial-NoDerivatives 4.0 International