A Wasserstein Minimum Velocity Approach to Learning Unnormalized Models


Ziyu Wang, Shuyu Cheng, Li Yueru, Jun Zhu, Bo Zhang ;
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:3728-3738, 2020.


Score matching provides an effective approach to learning flexible unnormalized models, but its scalability is limited by the need to evaluate a second-order derivative. In this paper, we present a scalable approximation to a general family of learning objectives including score matching, by observing a new connection between these objectives and Wasserstein gradient flows. We present applications with promise in learning neural density estimators on manifolds, and training implicit variational and Wasserstein auto-encoders with a manifold-valued prior.

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