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Your search keyword '"Stromme, Austin J."' showing total 7 results
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7 results on '"Stromme, Austin J."'

1. Minimum intrinsic dimension scaling for entropic optimal transport

Author

Stromme, Austin J.

Subjects
Mathematics - Statistics Theory, Computer Science - Machine Learning, Mathematics - Probability
Abstract

Motivated by the manifold hypothesis, which states that data with a high extrinsic dimension may yet have a low intrinsic dimension, we develop refined statistical bounds for entropic optimal transport that are sensitive to the intrinsic dimension of the data. Our bounds involve a robust notion of intrinsic dimension, measured at only a single distance scale depending on the regularization parameter, and show that it is only the minimum of these single-scale intrinsic dimensions which governs the rate of convergence. We call this the Minimum Intrinsic Dimension scaling (MID scaling) phenomenon, and establish MID scaling with no assumptions on the data distributions so long as the cost is bounded and Lipschitz, and for various entropic optimal transport quantities beyond just values, with stronger analogs when one distribution is supported on a manifold. Our results significantly advance the theoretical state of the art by showing that MID scaling is a generic phenomenon, and provide the first rigorous interpretation of the statistical effect of entropic regularization as a distance scale., Comment: 53 pages

Published
2023

2. Minimum Intrinsic Dimension Scaling for Entropic Optimal Transport

Author

Stromme, Austin J., Kacprzyk, Janusz, Series Editor, Pal, Nikhil R., Advisory Editor, Bello Perez, Rafael, Advisory Editor, Corchado, Emilio S., Advisory Editor, Hagras, Hani, Advisory Editor, Kóczy, László T., Advisory Editor, Kreinovich, Vladik, Advisory Editor, Lin, Chin-Teng, Advisory Editor, Lu, Jie, Advisory Editor, Melin, Patricia, Advisory Editor, Nedjah, Nadia, Advisory Editor, Nguyen, Ngoc Thanh, Advisory Editor, Wang, Jun, Advisory Editor, Ansari, Jonathan, editor, Fuchs, Sebastian, editor, Trutschnig, Wolfgang, editor, Lubiano, María Asunción, editor, Gil, María Ángeles, editor, Grzegorzewski, Przemyslaw, editor, and Hryniewicz, Olgierd, editor

Published
2024
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3. On the sample complexity of entropic optimal transport

Author

Rigollet, Philippe and Stromme, Austin J.

Subjects
Mathematics - Statistics Theory
Abstract

We study the sample complexity of entropic optimal transport in high dimensions using computationally efficient plug-in estimators. We significantly advance the state of the art by establishing dimension-free, parametric rates for estimating various quantities of interest, including the entropic regression function which is a natural analog to the optimal transport map. As an application, we propose a practical model for transfer learning based on entropic optimal transport and establish parametric rates of convergence for nonparametric regression and classification., Comment: 28 pages

Published
2022

4. Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space

Author

Gouic, Thibaut Le, Paris, Quentin, Rigollet, Philippe, and Stromme, Austin J.

Subjects
Mathematics - Metric Geometry, Applied Mathematics, General Mathematics, FOS: Mathematics, Mathematics::Metric Geometry, Mathematics - Statistics Theory, Metric Geometry (math.MG), Mathematics::Differential Geometry, Statistics Theory (math.ST)
Abstract

This work establishes fast rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically, we show that parametric rates of convergence are achievable under natural conditions that characterize the bi-extendibility of geodesics emanating from a barycenter. These results largely advance the state-of-the-art on the subject both in terms of rates of convergence and the variety of spaces covered. In particular, our results apply to infinite-dimensional spaces such as the 2-Wasserstein space, where bi-extendibility of geodesics translates into regularity of Kantorovich potentials.

Published
2022

5. Fast convergence of empirical barycenters in Alexandrov spaces and the Wasserstein space.

Author

Le Gouic, Thibaut, Paris, Quentin, Rigollet, Philippe, and Stromme, Austin J.

Subjects
STOCHASTIC convergence, KANTOROVICH method, GEODESIC spaces, MATHEMATICAL models, CURVATURE
Abstract

This work establishes fast rates of convergence for empirical barycenters over a large class of geodesic spaces with curvature bounds in the sense of Alexandrov. More specifically, we show that parametric rates of convergence are achievable under natural conditions that characterize the bi-extendibility of geodesics emanating from a barycenter. These results largely advance the state-of-the-art on the subject both in terms of rates of convergence and the variety of spaces covered. In particular, our results apply to infinite-dimensional spaces such as the 2-Wasserstein space, where bi-extendibility of geodesics translates into regularity of Kantorovich potentials. [ABSTRACT FROM AUTHOR]

Published
2023
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