Online Sinkhorn: Optimal Transport distances from sample streams
arXiv:2003.01415
Abstract
Optimal Transport (OT) distances are now routinely used as loss functions in ML tasks. Yet, computing OT distances between arbitrary (i.e. not necessarily discrete) probability distributions remains an open problem. This paper introduces a new online estimator of entropy-regularized OT distances between two such arbitrary distributions. It uses streams of samples from both distributions to iteratively enrich a non-parametric representation of the transportation plan. Compared to the classic Sinkhorn algorithm, our method leverages new samples at each iteration, which enables a consistent estimation of the true regularized OT distance. We provide a theoretical analysis of the convergence of the online Sinkhorn algorithm, showing a nearly-O(1/n) asymptotic sample complexity for the iterate sequence. We validate our method on synthetic 1D to 10D data and on real 3D shape data.
References in corpus (8)
- Learning with a Wasserstein Loss
- Sample Complexity of Sinkhorn divergences
- Interpolating between Optimal Transport and MMD using Sinkhorn Divergences
- Stochastic Majorization-Minimization Algorithms for Large-Scale Optimization
- Entropic Optimal Transport between Unbalanced Gaussian Measures has a Closed Form
- Finding Mixed Nash Equilibria of Generative Adversarial Networks
- Geometric Losses for Distributional Learning
- Sinkhorn Algorithm as a Special Case of Stochastic Mirror Descent