Poisson learning: Graph based semi-supervised learning at very low label rates

Jeff Calder; Brendan B Cook; Matthew Thorpe; Dejan Slepčev

Poisson learning: Graph based semi-supervised learning at very low label rates

Jeff Calder, Brendan B Cook, Matthew Thorpe, Dejan Slepčev

School of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

28 Scopus citations

Abstract

We propose a new framework, called Poisson learning, for graph based semi-supervised learning at very low label rates. Poisson learning is motivated by the need to address the degeneracy of Laplacian semi-supervised learning in this regime. The method replaces the assignment of label values at training points with the placement of sources and sinks, and solves the resulting Poisson equation on the graph. The outcomes are provably more stable and informative than those of Laplacian learning. Poisson learning is efficient and simple to implement, and we present numerical experiments showing the method is superior to other recent approaches to semi-supervised learning at low label rates on MNIST, FashionMNIST, and Cifar-10. We also propose a graph-cut enhancement of Poisson learning, called Poisson MBO, that gives higher accuracy and can incorporate prior knowledge of relative class sizes.

Original language	English (US)
Title of host publication	37th International Conference on Machine Learning, ICML 2020
Editors	Hal Daume, Aarti Singh
Publisher	International Machine Learning Society (IMLS)
Pages	1283-1293
Number of pages	11
ISBN (Electronic)	9781713821120
State	Published - 2020
Event	37th International Conference on Machine Learning, ICML 2020 - Virtual, Online Duration: Jul 13 2020 → Jul 18 2020

Publication series

Name	37th International Conference on Machine Learning, ICML 2020
Volume	PartF168147-2

Conference

Conference	37th International Conference on Machine Learning, ICML 2020
City	Virtual, Online
Period	7/13/20 → 7/18/20

Bibliographical note

Funding Information:
Calder was supported by NSF-DMS grants 1713691,1944925, Cook was supported by a University of Minnesota Grant In Aid award, Thorpe was supported by the European Research Council under the European Union’s Horizon 2020 research and innovation programme grant No 777826 (NoMADS) and 647812, and Slepcˇev was supported by NSF-DMS grant 1814991. The authors thank Matt Jacobs for providing code for volume constrained MBO. The authors also thank the Center for Nonlinear Analysis (CNA) at CMU for its support.

Publisher Copyright:
© 2020 37th International Conference on Machine Learning, ICML 2020. All rights reserved.

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Calder, J., Cook, B. B., Thorpe, M., & Slepčev, D. (2020). Poisson learning: Graph based semi-supervised learning at very low label rates. In H. Daume, & A. Singh (Eds.), 37th International Conference on Machine Learning, ICML 2020 (pp. 1283-1293). (37th International Conference on Machine Learning, ICML 2020; Vol. PartF168147-2). International Machine Learning Society (IMLS).

Poisson learning: Graph based semi-supervised learning at very low label rates. / Calder, Jeff; Cook, Brendan B; Thorpe, Matthew et al.
37th International Conference on Machine Learning, ICML 2020. ed. / Hal Daume; Aarti Singh. International Machine Learning Society (IMLS), 2020. p. 1283-1293 (37th International Conference on Machine Learning, ICML 2020; Vol. PartF168147-2).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Calder, J, Cook, BB, Thorpe, M & Slepčev, D 2020, Poisson learning: Graph based semi-supervised learning at very low label rates. in H Daume & A Singh (eds), 37th International Conference on Machine Learning, ICML 2020. 37th International Conference on Machine Learning, ICML 2020, vol. PartF168147-2, International Machine Learning Society (IMLS), pp. 1283-1293, 37th International Conference on Machine Learning, ICML 2020, Virtual, Online, 7/13/20.

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abstract = "We propose a new framework, called Poisson learning, for graph based semi-supervised learning at very low label rates. Poisson learning is motivated by the need to address the degeneracy of Laplacian semi-supervised learning in this regime. The method replaces the assignment of label values at training points with the placement of sources and sinks, and solves the resulting Poisson equation on the graph. The outcomes are provably more stable and informative than those of Laplacian learning. Poisson learning is efficient and simple to implement, and we present numerical experiments showing the method is superior to other recent approaches to semi-supervised learning at low label rates on MNIST, FashionMNIST, and Cifar-10. We also propose a graph-cut enhancement of Poisson learning, called Poisson MBO, that gives higher accuracy and can incorporate prior knowledge of relative class sizes.",

author = "Jeff Calder and Cook, {Brendan B} and Matthew Thorpe and Dejan Slep{\v c}ev",

note = "Funding Information: Calder was supported by NSF-DMS grants 1713691,1944925, Cook was supported by a University of Minnesota Grant In Aid award, Thorpe was supported by the European Research Council under the European Union{\textquoteright}s Horizon 2020 research and innovation programme grant No 777826 (NoMADS) and 647812, and Slepcˇev was supported by NSF-DMS grant 1814991. The authors thank Matt Jacobs for providing code for volume constrained MBO. The authors also thank the Center for Nonlinear Analysis (CNA) at CMU for its support. Publisher Copyright: {\textcopyright} 2020 37th International Conference on Machine Learning, ICML 2020. All rights reserved.; 37th International Conference on Machine Learning, ICML 2020 ; Conference date: 13-07-2020 Through 18-07-2020",

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Poisson learning: Graph based semi-supervised learning at very low label rates

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