Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916270311473152 |
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| author | Calder, Jeff Drenska, Nadejda |
| author_facet | Calder, Jeff Drenska, Nadejda |
| contents | In this paper we give a broad overview of the intersection of partial differential equations (PDEs) and graph-based semi-supervised learning. The overview is focused on a large body of recent work on PDE continuum limits of graph-based learning, which have been used to prove well-posedness of semi-supervised learning algorithms in the large data limit. We highlight some interesting research directions revolving around consistency of graph-based semi-supervised learning, and present some new results on the consistency of $p$-Laplacian semi-supervised learning using the stochastic tug-of-war game interpretation of the $p$-Laplacian. We also present the results of some numerical experiments that illustrate our results and suggest directions for future work. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07463 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian Calder, Jeff Drenska, Nadejda Statistics Theory Machine Learning Numerical Analysis Analysis of PDEs Probability 91A05, 68T05, 68Q32, 35D40, 35J60, 65N06 In this paper we give a broad overview of the intersection of partial differential equations (PDEs) and graph-based semi-supervised learning. The overview is focused on a large body of recent work on PDE continuum limits of graph-based learning, which have been used to prove well-posedness of semi-supervised learning algorithms in the large data limit. We highlight some interesting research directions revolving around consistency of graph-based semi-supervised learning, and present some new results on the consistency of $p$-Laplacian semi-supervised learning using the stochastic tug-of-war game interpretation of the $p$-Laplacian. We also present the results of some numerical experiments that illustrate our results and suggest directions for future work. |
| title | Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian |
| topic | Statistics Theory Machine Learning Numerical Analysis Analysis of PDEs Probability 91A05, 68T05, 68Q32, 35D40, 35J60, 65N06 |
| url | https://arxiv.org/abs/2401.07463 |