Related papers: Spherical Harmonic Optimal Transport: Application …
We consider inference (filtering) problems over probabilistic graphical models with aggregate data generated by a large population of individuals. We propose a new efficient belief propagation type algorithm over tree-structured graphs with…
A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…
Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the…
Entropic regularization provides a generalization of the original optimal transport problem. It introduces a penalty term defined by the Kullback-Leibler divergence, making the problem more tractable via the celebrated Sinkhorn algorithm.…
Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…
We consider the optimal transportation problem on a globally hyperbolic spacetime for some cost function $c_2$, which corresponds to the optimal transportation problem on a complete Riemannian manifold where the cost function is the…
We study Benamou's domain decomposition algorithm for optimal transport in the entropy regularized setting. The key observation is that the regularized variant converges to the globally optimal solution under very mild assumptions. We prove…
This paper describes an angular adaptivity algorithm for Boltzmann transport applications which for the first time shows evidence of $\mathcal{O}(n)$ scaling in both runtime and memory usage, where $n$ is the number of adapted angles. This…
We propose a new metric between probability measures on a compact metric space that mirrors the Riemannian manifold-like structure of quadratic optimal transport but includes entropic regularization. Its metric tensor is given by the…
Optimal transport (OT) plays an essential role in various areas like machine learning and deep learning. However, computing discrete optimal transport plan for large scale problems with adequate accuracy and efficiency is still highly…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
We derive new equations using the mixed-frame approach for one- and two-dimensional (axisymmetric) time-dependent radiation transport and the associated couplings with matter. Our formulation is multi-group and multi-angle and includes…
We give sufficient conditions on initial and target measures supported on the sphere $\S^n$ to ensure the solution to the optimal transport problem with the cost $|x-y|^2/2$ is a diffeomorphism.
We study the multi-marginal partial optimal transport (POT) problem between $m$ discrete (unbalanced) measures with at most $n$ supports. We first prove that we can obtain two equivalence forms of the multimarginal POT problem in terms of…
Transportation cost is an attractive similarity measure between probability distributions due to its many useful theoretical properties. However, solving optimal transport exactly can be prohibitively expensive. Therefore, there has been…
The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in…
The specific heat and susceptibilities for the two- and one-dimensional spin--orbital models are calculated in the framework of a spherically symmetric self-consistent approach at different temperatures and relations between the parameters…
Improved results using a method similar to the Munn-Silbey approach have been obtained on the temperature dependence of transport properties of an extended Holstein model incorporating simultaneous diagonal and off-diagonal exciton-phonon…
Discrete optimal transport solvers do not scale well on dense large problems since they do not explicitly exploit the geometric structure of the cost function. In analogy to continuous optimal transport we provide a framework to verify…
We discuss methods of Optimal Transportation Theory and its relations to problems in quantum mechanics. This essentially means that the cost function is some Hamiltonian $H(q,p)$ on a phase space (symplectic manifold), and the marginal…