Learning with a Wasserstein loss
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1506.05439.pdf
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Author(s)
Araya-Polo, Mauricio
Frogner, Charles Albert
Zhang, Chiyuan
Mobahi, Hossein
Poggio, Tomaso A
Date Issued
December 2015
Journal
Proceedings of the 28th International Conference on Neural Information Processing Systems (NIPS 2015)
Publisher
MIT Press
Citation
Frogner, Charlie et al. "Learning with a Wasserstein loss." Proceedings of the 28th International Conference on Neural Information Processing Systems (NIPS 2015), December 7-12 2015, Montreal, Canada, MIT Press, December 2015 © 2015 MIT Press Cambridge, MA, USA
Version
Author's final manuscript
Abstract
Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions.In this paper we develop a loss function for multi-label learning, based on the Wasserstein distance. The Wasserstein distance provides a natural notion of dissimilarity for probability measures. Although optimizing with respect to the exact Wasserstein distance is costly, recent work has described a regularized approximation that is efficiently computed. We describe an efficient learning algorithm based on this regularization, as well as a novel extension of the Wasserstein distance from probability measures to unnormalized measures. We also describe a statistical learning bound for the loss. The Wasserstein loss can encourage smoothness of the predictions with respect to a chosen metric on the output space. We demonstrate this property on a real-data tag prediction problem, using the Yahoo Flickr Creative Commons dataset, outperforming a baseline that doesn't use the metric.
MIT Department
Center for Brains, Minds, and Machines
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://dl.acm.org/citation.cfm?id=2969469
