Related papers: Discrete Probabilistic Inverse Optimal Transport
The purpose of this paper is to introduce a new numerical method to solve multi-marginal optimal transport problems with pairwise interaction costs. The complexity of multi-marginal optimal transport generally scales exponentially in the…
Empirical optimal transport (OT) plans and distances provide effective tools to compare and statistically match probability measures defined on a given ground space. Fundamental to this are distributional limit laws and we derive a central…
This work establishes a framework for solving inverse boundary problems with the geodesic based quadratic Wasserstein distance ($W_{2}$). A general form of the Fr\'echet gradient is systematically derived by optimal transportation (OT)…
Classic optimal transport theory is formulated through minimizing the expected transport cost between two given distributions. We propose the framework of distorted optimal transport by minimizing a distorted expected cost, which is the…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
This paper studies the equitable and optimal transport (EOT) problem, which has many applications such as fair division problems and optimal transport with multiple agents etc. In the discrete distributions case, the EOT problem can be…
Inverse Optimal Control (IOC) aims to infer the underlying cost functional of an agent from observations of its expert behavior. This paper focuses on the IOC problem within the continuous-time linear quadratic regulator framework,…
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…
Ensuring fairness in matching algorithms is a key challenge in allocating scarce resources and positions. Focusing on Optimal Transport (OT), we introduce a novel notion of group fairness requiring that the probability of matching two…
We introduce optimal transport (OT) as a physics-based intermediate event representation for weakly supervised anomaly detection. With only $0.5\%$ injection of resonant signals in the LHC Olympics benchmark datasets, the OT-augmented…
Optimal transport (OT) has profoundly impacted machine learning by providing theoretical and computational tools to realign datasets. In this context, given two large point clouds of sizes $n$ and $m$ in $\mathbb{R}^d$, entropic OT (EOT)…
We investigate the optimal transport problem between probability measures when the underlying cost function is understood to satisfy a least action principle, also known as a Lagrangian cost. These generalizations are useful when connecting…
Matching a source to a target probability measure is often solved by instantiating a linear optimal transport (OT) problem, parameterized by a ground cost function that quantifies discrepancy between points. When these measures live in the…
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…
This paper develops a computational framework for Multi-Period Martingale Optimal Transport (MMOT), addressing convergence rates, algorithmic efficiency, and financial calibration. Our contributions include: (1) Theoretical analysis: We…
In this article we explore an algorithm for diffeomorphic random sampling of nonuniform probability distributions on Riemannian manifolds. The algorithm is based on optimal information transport (OIT)---an analogue of optimal mass transport…
In this article we revisit the weak optimal transport (WOT) problem, introduced by Gozlan, Roberto, Samson and Tetali (2017). We work on the real line, with barycentric cost functions, and as our first result give the following…
The theory of weak optimal transport (WOT), introduced by [Gozlan et al., 2017], generalizes the classic Monge-Kantorovich framework by allowing the transport cost between one point and the points it is matched with to be nonlinear. In the…
Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is…
Reinforcement learning can acquire complex behaviors from high-level specifications. However, defining a cost function that can be optimized effectively and encodes the correct task is challenging in practice. We explore how inverse optimal…