相关论文: Embedding Empirical Distributions for Computing Op…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…
We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., $\ell^1$ or $\ell^2$, such functionals provide more flexibility and allow…
Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…
Optimal transport (OT) theory has attracted much attention in machine learning and signal processing applications. OT defines a notion of distance between probability distributions of source and target data points. A crucial factor that…
Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming…
We compare several approaches to learn an Optimal Map, represented as a neural network, between probability distributions. The approaches fall into two categories: ``Heuristics'' and approaches with a more sound mathematical justification,…
Given samples from two joint distributions, we consider the problem of Optimal Transportation (OT) between them when conditioned on a common variable. We focus on the general setting where the conditioned variable may be continuous, and the…
Optimal Transport (OT) is a mathematical framework that first emerged in the eighteenth century and has led to a plethora of methods for answering many theoretical and applied questions. The last decade has been a witness to the remarkable…
We investigate the problem of efficiently computing optimal transport (OT) distances, which is equivalent to the node-capacitated minimum cost maximum flow problem in a bipartite graph. We compare runtimes in computing OT distances on data…
Optimal transport (OT) theory focuses, among all maps $T:\mathbb{R}^d\rightarrow \mathbb{R}^d$ that can morph a probability measure onto another, on those that are the ``thriftiest'', i.e. such that the averaged cost $c(x, T(x))$ between…
Optimal transport (OT) is a framework that can be used to guide the optimal allocation of a limited amount of resources. The classical OT paradigm does not consider malicious attacks in its formulation and thus the designed transport plan…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
We present a novel hierarchical framework for optimal transport (OT) using string diagrams, namely string diagrams of optimal transports. This framework reduces complex hierarchical OT problems to standard OT problems, allowing efficient…
With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks. In these tasks, OT cost is typically used as the loss for training GANs. In contrast to this approach, we…
In this paper, we aim to forecast a future trajectory distribution of a moving agent in the real world, given the social scene images and historical trajectories. Yet, it is a challenging task because the ground-truth distribution is…
Network topology has significant impacts on operational performance of power systems. While extensive research efforts have been devoted to optimization of network topology for improving various system performances, the problem of how to…
We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…
When deploying a trained machine learning model in the real world, it is inevitable to receive inputs from out-of-distribution (OOD) sources. For instance, in continual learning settings, it is common to encounter OOD samples due to the…
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…