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.

It has always been a research hotspot to use geographic information to assist the navigation of unmanned aerial vehicles. In this paper, a road-network-based localization method is proposed. We match roads in the measurement images to the reference road vector map, and realize successful localization on areas as large as a whole city. The road network matching problem is treated as a point cloud registration problem under two-dimensional projective transformation, and solved under a hypothesise-and-test framework. To deal with the projective point cloud registration problem, a global projective invariant feature is proposed, which consists of two road intersections augmented with the information of their tangents. We call it two road intersections tuple. We deduce the closed-form solution for determining the alignment transformation from a pair of matching two road intersections tuples. In addition, we propose the necessary conditions for the tuples to match. This can reduce the candidate matching tuples, thus accelerating the search to a great extent. We test all the candidate matching tuples under a hypothesise-and-test framework to search for the best match. The experiments show that our method can localize the target area over an area of 400 within 1 second on a single cpu.

Cooperation information sharing is important to theories of human learning and has potential implications for machine learning. Prior work derived conditions for achieving optimal Cooperative Inference given strong, relatively restrictive assumptions. We relax these assumptions by demonstrating convergence for any discrete joint distribution, robustness through equivalence classes and stability under perturbation, and effectiveness by deriving bounds from structural properties of the original joint distribution. We provide geometric interpretations, connections to and implications for optimal transport, and connections to importance sampling, and conclude by outlining open questions and challenges to realizing the promise of Cooperative Inference.