Learning with a Wasserstein Loss

TL;DR

This paper introduces a Wasserstein distance-based loss function for multi-label learning, leveraging a regularized approximation for efficiency, and demonstrates its effectiveness on real-world tag prediction tasks.

Contribution

The paper develops an efficient Wasserstein loss function for multi-label learning, including an extension to unnormalized measures and a statistical learning bound.

Findings

Outperforms baseline on Yahoo Flickr dataset

Encourages smoothness in predictions with respect to output metric

Provides a regularized approximation for computational efficiency

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.