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arXiv · 1506.05439

Learning with a Wasserstein Loss

Charlie Frogner·Chiyuan Zhang·Hossein Mobahi·Mauricio Araya-Polo·Tomaso Poggio
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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.

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Charlie Frogner, Chiyuan Zhang, Hossein Mobahi, Mauricio Araya-Polo, Tomaso Poggio. 2015-06-17. Learning with a Wasserstein Loss. https://arxiv.org/abs/1506.05439

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