Learning High Dimensional Wasserstein Geodesics

• URL: http://arxiv.org/abs/2102.02992v2
• Date: Mon, 8 Feb 2021 01:33:56 GMT
• Title: Learning High Dimensional Wasserstein Geodesics
• Authors: Shu Liu, Shaojun Ma, Yongxin Chen, Hongyuan Zha, Haomin Zhou
• Abstract summary: We propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagrange multipliers to the dynamic formulation of the optimal transport (OT) problem, we derive a minimax problem whose saddle point is the Wasserstein geodesic. We then parametrize the functions by deep neural networks and design a sample based bidirectional learning algorithm for training.
• Score: 55.086626708837635
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagrange multipliers to the dynamic formulation of the optimal transport (OT) problem, we derive a minimax problem whose saddle point is the Wasserstein geodesic. We then parametrize the functions by deep neural networks and design a sample based bidirectional learning algorithm for training. The trained networks enable sampling from the Wasserstein geodesic. As by-products, the algorithm also computes the Wasserstein distance and OT map between the marginal distributions. We demonstrate the performance of our algorithms through a series of experiments with both synthetic and realistic data.

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