Sinkhorn Flow: A Continuous-Time Framework for Understanding and Generalizing the Sinkhorn Algorithm Article Swipe
Mohammad Reza Karimi
,
Ya‐Ping Hsieh
,
Andreas Krause
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2311.16706
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2311.16706
Many problems in machine learning can be formulated as solving entropy-regularized optimal transport on the space of probability measures. The canonical approach involves the Sinkhorn iterates, renowned for their rich mathematical properties. Recently, the Sinkhorn algorithm has been recast within the mirror descent framework, thus benefiting from classical optimization theory insights. Here, we build upon this result by introducing a continuous-time analogue of the Sinkhorn algorithm. This perspective allows us to derive novel variants of Sinkhorn schemes that are robust to noise and bias. Moreover, our continuous-time dynamics not only generalize but also offer a unified perspective on several recently discovered dynamics in machine learning and mathematics, such as the "Wasserstein mirror flow" of (Deb et al. 2023) or the "mean-field Schrödinger equation" of (Claisse et al. 2023).
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2311.16706
- https://arxiv.org/pdf/2311.16706
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4389156876
All OpenAlex metadata
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https://openalex.org/W4389156876Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2311.16706Digital Object Identifier
- Title
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Sinkhorn Flow: A Continuous-Time Framework for Understanding and Generalizing the Sinkhorn AlgorithmWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-11-28Full publication date if available
- Authors
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Mohammad Reza Karimi, Ya‐Ping Hsieh, Andreas KrauseList of authors in order
- Landing page
-
https://arxiv.org/abs/2311.16706Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2311.16706Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2311.16706Direct OA link when available
- Concepts
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Iterated function, Computer science, Perspective (graphical), Probability measure, Entropy (arrow of time), Algorithm, Mathematical optimization, Mathematical economics, Mathematics, Artificial intelligence, Discrete mathematics, Mathematical analysis, Quantum mechanics, PhysicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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