Learning with a Wasserstein Loss

TitleLearning with a Wasserstein Loss
Publication TypeConference Paper
Year of Publication2015
AuthorsFrogner, C, Zhang, C, Mobahi, H, Araya-Polo, M, Poggio, T
Conference NameAdvances in Neural Information Processing Systems (NIPS 2015) 28
Other NumbersarXiv:1506.05439v2

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 prob- ability measures to unnormalized measures. We also describe a statistical learning bound for the loss. The Wasserstein loss can encourage smoothness of the predic- tions 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.


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