Linear optimal partial transport embedding

Yikun Bai, Ivan Vladimir Medri, Rocio Diaz Martin, Rana Shahroz, Soheil Kolouri
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:1492-1520, 2023.

Abstract

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed. In this paper, we propose the Linear optimal partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem. The proposed embedding allows for faster computation of OPT distance between pairs of positive measures. Besides our theoretical contributions, we demonstrate the LOPT embedding technique in point-cloud interpolation and PCA analysis. Our code is available at https://github.com/Baio0/LinearOPT.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-bai23c, title = {Linear optimal partial transport embedding}, author = {Bai, Yikun and Medri, Ivan Vladimir and Diaz Martin, Rocio and Shahroz, Rana and Kolouri, Soheil}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {1492--1520}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/bai23c/bai23c.pdf}, url = {https://proceedings.mlr.press/v202/bai23c.html}, abstract = {Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed. In this paper, we propose the Linear optimal partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem. The proposed embedding allows for faster computation of OPT distance between pairs of positive measures. Besides our theoretical contributions, we demonstrate the LOPT embedding technique in point-cloud interpolation and PCA analysis. Our code is available at https://github.com/Baio0/LinearOPT.} }
Endnote
%0 Conference Paper %T Linear optimal partial transport embedding %A Yikun Bai %A Ivan Vladimir Medri %A Rocio Diaz Martin %A Rana Shahroz %A Soheil Kolouri %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-bai23c %I PMLR %P 1492--1520 %U https://proceedings.mlr.press/v202/bai23c.html %V 202 %X Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed. In this paper, we propose the Linear optimal partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem. The proposed embedding allows for faster computation of OPT distance between pairs of positive measures. Besides our theoretical contributions, we demonstrate the LOPT embedding technique in point-cloud interpolation and PCA analysis. Our code is available at https://github.com/Baio0/LinearOPT.
APA
Bai, Y., Medri, I.V., Diaz Martin, R., Shahroz, R. & Kolouri, S.. (2023). Linear optimal partial transport embedding. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:1492-1520 Available from https://proceedings.mlr.press/v202/bai23c.html.

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