Related papers: Empirical Regularized Optimal Transport: Statistic…
We consider regularised quadratic optimal transport with subquadratic polynomial or entropic regularisation. In both cases, we prove interior Lipschitz-estimates on a transport-like map and interior gradient Lipschitz-estimates on the…
Optimal transport (OT) provides effective tools for comparing and mapping probability measures. We propose to leverage the flexibility of neural networks to learn an approximate optimal transport map. More precisely, we present a new and…
In this paper, we address the problem of sampling-based motion planning under motion and measurement uncertainty with probabilistic guarantees. We generalize traditional sampling-based tree-based motion planning algorithms for deterministic…
This survey has been written in occasion of the School and Workshop about Optimal Transport on Quantum Structures at Erd\"os Center in September 2022. We discuss some recent results on noncommutative entropic optimal transport problems and…
Trajectory optimization and model predictive control are essential techniques underpinning advanced robotic applications, ranging from autonomous driving to full-body humanoid control. State-of-the-art algorithms have focused on data-driven…
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
Many causal parameters depend on a moment of the joint distribution of potential outcomes. Such parameters are especially relevant in policy evaluation settings, where noncompliance is common and accommodated through the model of Imbens &…
We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…
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…
Computational implementation of optimal transport barycenters for a set of target probability measures requires a form of approximation, a widespread solution being empirical approximation of measures. We provide an $O(\sqrt{N/n})$…
Sinkhorn algorithm is the de-facto standard approximation algorithm for optimal transport, which has been applied to a variety of applications, including image processing and natural language processing. In theory, the proof of its…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
The optimal transport map between the standard Gaussian measure and an $\alpha$-strongly log-concave probability measure is $\alpha^{-1/2}$-Lipschitz, as first observed in a celebrated theorem of Caffarelli. In this paper, we apply two…
Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak…
Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization and the Sinkhorn algorithm, which utilizes only matrix…
We consider the problem of optimal transportation with general cost between a empirical measure and a general target probability on R d , with d $\ge$ 1. We extend results in [19] and prove asymptotic stability of both optimal transport…
Optimal Transport is a theory that allows to define geometrical notions of distance between probability distributions and to find correspondences, relationships, between sets of points. Many machine learning applications are derived from…
In the field of optimal transport, two prominent subfields face each other: (i) unregularized optimal transport, "\`a-la-Kantorovich", which leads to extremely sparse plans but with algorithms that scale poorly, and (ii)…
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.…
A general theory is provided delivering convergence of maximal cyclically monotone mappings containing the supports of coupling measures of sequences of pairs of possibly random probability measures on Euclidean space. The theory is based…