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)|
|Number of pages||11|
|State||Published - 2020|
|Event||37th International Conference on Machine Learning, ICML 2020 - Virtual, Online|
Duration: Jul 13 2020 → Jul 18 2020
|Name||37th International Conference on Machine Learning, ICML 2020|
|Conference||37th International Conference on Machine Learning, ICML 2020|
|Period||7/13/20 → 7/18/20|
Bibliographical noteFunding 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.
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