Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates

Jeff Calder, Brendan Cook, Matthew Thorpe, Dejan Slepcev
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:1306-1316, 2020.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-calder20a, title = {Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates}, author = {Calder, Jeff and Cook, Brendan and Thorpe, Matthew and Slepcev, Dejan}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {1306--1316}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/calder20a/calder20a.pdf}, url = {https://proceedings.mlr.press/v119/calder20a.html}, 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.} }
Endnote
%0 Conference Paper %T Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates %A Jeff Calder %A Brendan Cook %A Matthew Thorpe %A Dejan Slepcev %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-calder20a %I PMLR %P 1306--1316 %U https://proceedings.mlr.press/v119/calder20a.html %V 119 %X 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.
APA
Calder, J., Cook, B., Thorpe, M. & Slepcev, D.. (2020). Poisson Learning: Graph Based Semi-Supervised Learning At Very Low Label Rates. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:1306-1316 Available from https://proceedings.mlr.press/v119/calder20a.html.

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