相关论文: Embedding Empirical Distributions for Computing Op…

We propose a neural embedding algorithm called Network Vector, which learns distributed representations of nodes and the entire networks simultaneously. By embedding networks in a low-dimensional space, the algorithm allows us to compare…

We introduce \emph{in-context operator learning on probability measure spaces} for optimal transport (OT). The goal is to learn a single solution operator that maps a pair of distributions to the OT map, using only few-shot samples from…

Nowadays, the Internet of Things (IoT) has become one of the most important technologies which enables a variety of connected and intelligent applications in smart cities. The smart decision making process of IoT devices not only relies on…

Recently, deep learning has achieved promising results in the calculation of Estimated Time of Arrival (ETA), which is considered as predicting the travel time from the start point to a certain place along a given path. ETA plays an…

Optimal Transport (OT) problems are a cornerstone of many applications, but solving them is computationally expensive. To address this problem, we propose UNOT (Universal Neural Optimal Transport), a novel framework capable of accurately…

The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dimensional space) is a crucial problem arising in the…

This paper studies the convergence rates of optimal transport (OT) map estimators, a topic of growing interest in statistics, machine learning, and various scientific fields. Despite recent advancements, existing results rely on regularity…

A class of neural networks that gained particular interest in the last years are neural ordinary differential equations (neural ODEs). We study input-output relations of neural ODEs using dynamical systems theory and prove several results…

Optimal transport has been one of the most exciting subjects in mathematics, starting from the 18th century. As a powerful tool to transport between two probability measures, optimal transport methods have been reinvigorated nowadays in a…

Quantile-Quantile (Q-Q) plots are widely used for assessing the distributional similarity between two datasets. Traditionally, Q-Q plots are constructed for univariate distributions, making them less effective in capturing complex…

We introduce a novel gene regulatory network (GRN) inference method that integrates optimal transport (OT) with a deep-learning structural inference model. Advances in next-generation sequencing enable detailed yet destructive gene…

We study statistical inference for the optimal transport (OT) map (also known as the Brenier map) from a known absolutely continuous reference distribution onto an unknown finitely discrete target distribution. We derive limit distributions…

Traffic prediction is pivotal for rational transportation supply scheduling and allocation. Existing researches into short-term traffic prediction, however, face challenges in adequately addressing exceptional circumstances and integrating…

The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between…

Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…

The optimal transport problem for measures supported on non-Euclidean spaces has recently gained ample interest in diverse applications involving representation learning. In this paper, we focus on circular probability measures, i.e.,…

We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…

Integration against, and hence sampling from, high-dimensional probability distributions is of essential importance in many application areas and has been an active research area for decades. One approach that has drawn increasing attention…

Learning generic representations with deep networks requires massive training samples and significant computer resources. To learn a new specific task, an important issue is to transfer the generic teacher's representation to a student…

Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…