Optimal Transport with Tempered Exponential Measures
DOI:
https://doi.org/10.1609/aaai.v38i10.28957Keywords:
ML: Applications, ML: Other Foundations of Machine LearningAbstract
In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, ``a-la-Kantorovich'', which leads to extremely sparse plans but with algorithms that scale poorly, and (ii) entropic-regularized optimal transport, ``a-la-Sinkhorn-Cuturi'', which gets near-linear approximation algorithms but leads to maximally un-sparse plans. In this paper, we show that an extension of the latter to tempered exponential measures, a generalization of exponential families with indirect measure normalization, gets to a very convenient middle ground, with both very fast approximation algorithms and sparsity, which is under control up to sparsity patterns. In addition, our formulation fits naturally in the unbalanced optimal transport problem setting.Downloads
Published
2024-03-24
How to Cite
Amid, E., Nielsen, F., Nock, R., & Warmuth, M. K. (2024). Optimal Transport with Tempered Exponential Measures. Proceedings of the AAAI Conference on Artificial Intelligence, 38(10), 10838-10846. https://doi.org/10.1609/aaai.v38i10.28957
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Section
AAAI Technical Track on Machine Learning I