2021/12/17 by W. Henry Chiu, Pei Wang, Chiu, Wei-Ting +3 · 1 citation
Computer Science · Mathematics · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Markov Chains and Monte Carlo Methods
paper · pdf · doi:10.48550/arxiv.2112.09754
openalex publication_date 2021/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Optimal transport (OT) formalizes the problem of finding an optimal coupling between probability measures given a cost matrix. The inverse problem of inferring the cost given a coupling is Inverse Optimal Transport (IOT). IOT is less well understood than OT. We formalize and systematically analyze the properties of IOT using tools from the study of entropy-regularized OT. Theoretical contributions include characterization of the manifold of cross-ratio equivalent costs, the implications of model priors, and derivation of an MCMC sampler. Empirical contributions include visualizations of cross-ratio equivalent effect on basic examples and simulations validating theoretical results.