Tsallis Regularized Optimal Transport and Ecological Inference

Understand

Optimal transport is a powerful framework for computing distances between probability distributions.

• We unify the two main approaches to optimal transport, namely Monge-Kantorovitch and Sinkhorn-Cuturi, into what we define as Tsallis regularized optimal transport (\trot).
• \trot~interpolates a rich family of distortions from Wasserstein to Kullback-Leibler, encompassing as well Pearson, Neyman and Hellinger divergences, to name a few.
• We show that metric properties known for Sinkhorn-Cuturi generalize to \trot, and provide efficient algorithms for finding the optimal transportation plan with formal convergence proofs.