Wasserstein barycenters : statistics and optimization
Name
1192495680-MIT.pdf
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935.38 KB
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Adobe PDF
Checksum (MD5)
e0974fa793d744b5e6eff9c472505f16
Author(s)
Stromme, Austin J.(Austin James)
Advisor(s)
Philippe Rigollet.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
We study a geometric notion of average, the barycenter, over 2-Wasserstein space. We significantly advance the state of the art by introducing extendible geodesics, a simple synthetic geometric condition which implies non-asymptotic convergence of the empirical barycenter in non-negatively curved spaces such as Wasserstein space. We further establish convergence of first-order methods in the Gaussian case, overcoming the nonconvexity of the barycenter functional. These results are accomplished by various novel geometrically inspired estimates for the barycenter functional including a variance inequality, new so-called quantitative stability estimates, and a Polyak-Łojasiewicz (PL) inequality. These inequalities may be of independent interest.
Description
Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 67-71).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.
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