Active Semi-Supervised Learning using Submodular Functions

Andrew Guillory, Jeff A. Bilmes
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:312-320, 2011.

Abstract

We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be used via symmetrization. Different choices of submodular functions give different versions of the error bound that are appropriate for different kinds of problems. Moreover, the bound is deterministic and holds for adversarially chosen labels. We show exactly minimizing this error bound is NP-complete. However, we also introduce for any submodular function an associated active semi-supervised learning method that approximately minimizes the corresponding error bound. We show that the error bound is tight in the sense that there is no other bound of the same form which is better. Our theoretical results are supported by experiments on real data.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-guillory11a, title = {Active Semi-Supervised Learning using Submodular Functions}, author = {Guillory, Andrew and Bilmes, Jeff A.}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {312--320}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/guillory11a/guillory11a.pdf}, url = {https://proceedings.mlr.press/r9/guillory11a.html}, abstract = {We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be used via symmetrization. Different choices of submodular functions give different versions of the error bound that are appropriate for different kinds of problems. Moreover, the bound is deterministic and holds for adversarially chosen labels. We show exactly minimizing this error bound is NP-complete. However, we also introduce for any submodular function an associated active semi-supervised learning method that approximately minimizes the corresponding error bound. We show that the error bound is tight in the sense that there is no other bound of the same form which is better. Our theoretical results are supported by experiments on real data.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Active Semi-Supervised Learning using Submodular Functions %A Andrew Guillory %A Jeff A. Bilmes %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-guillory11a %I PMLR %P 312--320 %U https://proceedings.mlr.press/r9/guillory11a.html %V R9 %X We consider active, semi-supervised learning in an offline transductive setting. We show that a previously proposed error bound for active learning on undirected weighted graphs can be generalized by replacing graph cut with an arbitrary symmetric submodular function. Arbitrary non-symmetric submodular functions can be used via symmetrization. Different choices of submodular functions give different versions of the error bound that are appropriate for different kinds of problems. Moreover, the bound is deterministic and holds for adversarially chosen labels. We show exactly minimizing this error bound is NP-complete. However, we also introduce for any submodular function an associated active semi-supervised learning method that approximately minimizes the corresponding error bound. We show that the error bound is tight in the sense that there is no other bound of the same form which is better. Our theoretical results are supported by experiments on real data. %Z Reissued by PMLR on 04 October 2026.
APA
Guillory, A. & Bilmes, J.A.. (2011). Active Semi-Supervised Learning using Submodular Functions. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:312-320 Available from https://proceedings.mlr.press/r9/guillory11a.html. Reissued by PMLR on 04 October 2026.

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