Related papers: Entropic Regularisation of Robust Optimal Transpor…
In optimal transport, quadratic regularization is an alternative to entropic regularization when sparse couplings or small regularization parameters are desired. Quadratic regularization penalizes transport couplings by the squared $L^2$…
Capacity constrained optimal transport is a variant of optimal transport, which adds extra constraints on the set of feasible couplings in the original optimal transport problem to limit the mass transported between each pair of source and…
Optimal transport (OT) aims to find a map $T$ that transports mass from one probability measure to another while minimizing a cost function. Recently, neural OT solvers have gained popularity in high dimensional biological applications such…
We study the entropic regularization of the optimal transport problem in dimension 1 when the cost function is the distance c(x, y) = |y -- x|. The selected plan at the limit is, among those which are optimal for the non-penalized problem,…
We propose a regularization framework inspired by thermodynamic work for guiding pre-trained probability flow generative models (e.g., continuous normalizing flows or diffusion models) by minimizing excess work, a concept rooted in…
In recent works - both experimental and theoretical - it has been shown how to use computational geometry to efficently construct approximations to the optimal transport map between two given probability measures on Euclidean space, by…
We study the regularity properties of the minimisers of entropic optimal transport providing a natural analogue of the $\varepsilon$-regularity theory of quadratic optimal transport in the entropic setting. More precisely, we show that if…
Entropic optimal transport (EOT) in continuous spaces with quadratic cost is a classical tool for solving the domain translation problem. In practice, recent approaches optimize a weak dual EOT objective depending on a single potential, but…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures is…
Autoencoders are important generative models that, among others, have the ability to interpolate image sequences. However, interpolated images are usually not semantically meaningful.In this paper, motivated by dynamic optimal transport, we…
Optimal transport (OT) and Gromov-Wasserstein (GW) alignment are powerful frameworks for geometrically driven matching of probability distributions, yet their large-scale usage is hampered by high statistical and computational costs.…
Developing a contemporary optimal transport (OT) solver requires navigating trade-offs among several critical requirements: GPU parallelization, scalability to high-dimensional problems, theoretical convergence guarantees, empirical…
We commonly encounter the problem of identifying an optimally weight adjusted version of the empirical distribution of observed data, adhering to predefined constraints on the weights. Such constraints often manifest as restrictions on the…
Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…
We consider the conjecture proposed in Matsumoto, Zhang and Schiebinger (2022) suggesting that optimal transport with quadratic regularisation can be used to construct a graph whose discrete Laplace operator converges to the…
We present a 2-step optimal transport approach that performs a mapping from a source distribution to a target distribution. Here, the target has the particularity to present new classes not present in the source domain. The first step of…
In many unpaired image domain translation problems, e.g., style transfer or super-resolution, it is important to keep the translated image similar to its respective input image. We propose the extremal transport (ET) which is a mathematical…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
Optimal transport (OT) is a central framework for modeling distribution shifts. Because OT compares distributions directly in input space, a well-designed ground metric between observations is essential to ensure that the optimizer does not…
Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph…