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PTLp : Partial Transport Lp Distances
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Liu, Xinran, Bai, Yikun, Tran, Huy, Zhu, Zhanqi, Thorpe, Matthew and Kolouri, Soheil (2023) PTLp : Partial Transport Lp Distances. In: Optimal Transport and Machine Learning Workshop at NeurIPS 2023, New Orleans, USA, 10-16 Dec 2023 (Unpublished)
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WRAP-PTL-Partial-Transport-distances-23.pdf - Accepted Version - Requires a PDF viewer. Download (2716Kb) | Preview |
Official URL: https://openreview.net/forum?id=RXYURNZzfs
Abstract
Optimal transport and its related problems, including optimal partial transport, have proven to be valuable tools in machine learning for computing meaningful distances between probability or positive measures. This success has led to a growing interest in defining transport-based distances that allow for comparing signed measures and, more generally, multi-channeled signals. Transport
distances are notable extensions of the optimal transport framework to signed and possibly multi-channeled signals. In this paper, we introduce partial transport
distances as a new family of metrics for comparing generic signals, benefiting from the robustness of partial transport distances. We provide theoretical background such as the existence of optimal plans and the behavior of the distance in various limits. Furthermore, we introduce the sliced variation of these distances, which allows for faster comparison of generic signals. Finally, we demonstrate the application of the proposed distances in signal class separability and nearest neighbor classification.
Item Type: | Conference Item (UNSPECIFIED) | ||||||
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Subjects: | Q Science > QA Mathematics > QA76 Electronic computers. Computer science. Computer software | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Library of Congress Subject Headings (LCSH): | Transportation problems (Programming), Mathematical optimization -- Computer programs, Machine learning | ||||||
Official Date: | 2023 | ||||||
Dates: |
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Status: | Peer Reviewed | ||||||
Publication Status: | Unpublished | ||||||
Access rights to Published version: | Free Access (unspecified licence, 'bronze OA') | ||||||
Date of first compliant deposit: | 7 May 2024 | ||||||
Date of first compliant Open Access: | 7 May 2024 | ||||||
Title of Event: | Optimal Transport and Machine Learning Workshop at NeurIPS 2023 | ||||||
Type of Event: | Workshop | ||||||
Location of Event: | New Orleans, USA | ||||||
Date(s) of Event: | 10-16 Dec 2023 | ||||||
Related URLs: | |||||||
Open Access Version: |
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