Related papers: Metrics and barycenters for point pattern data
General circulation models (GCMs) are essential tools for climate studies. Such climate models may have varying accuracy across the input domain, but no model is uniformly best. One can improve climate model prediction performance by…
We develop a statistical inference method for an optimal transport map between distributions on real numbers with uniform confidence bands. The concept of optimal transport (OT) is used to measure distances between distributions, and OT…
Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport. In this paper, we present a scalable algorithm to compute Wasserstein-2 barycenters given sample access to the…
The concept of fixed point plays a crucial role in various fields of applied mathematics. The aim of this paper is to establish the existence of a unique fixed point of some type of functions which satisfy a new contraction principle,…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
We prove several fundamental statistical bounds for entropic OT with the squared Euclidean cost between subgaussian probability measures in arbitrary dimension. First, through a new sample complexity result we establish the rate of…
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…
We propose a method to infer the presence and location of change-points in the distribution of a sequence of independent data taking values in a general metric space, where change-points are viewed as locations at which the distribution of…
We introduce and study a variant of the Wasserstein distance on the space of probability measures, specially designed to deal with measures whose support has a dendritic, or treelike structure with a particular direction of orientation. Our…
Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals, and as such have a wide range of applications ranging from economics to statistics and computer science. When the marginal probability…
This paper extends algorithms that remove the fixed point bias of decentralized gradient descent to solve the more general problem of distributed optimization over subspace constraints. Leveraging the integral quadratic constraint…
In a communication network, point-to-point traffic volumes over time are critical for designing protocols that route information efficiently and for maintaining security, whether at the scale of an internet service provider or within a…
This paper leverages macroscopic models and multi-source spatiotemporal data collected from automatic traffic counters and probe vehicles to accurately estimate traffic flow and travel time in links where these measurements are unavailable.…
We use the transport methods developped in [3] to obtain universality results for local statistics of eigenvalues in the bulk and at the edge for $\beta$-matrix models in the multi-cut regime. We construct an approximate transport map…
Wasserstein Barycenter is a principled approach to represent the weighted mean of a given set of probability distributions, utilizing the geometry induced by optimal transport. In this work, we present a novel scalable algorithm to…
Ubiquitous mobile devices are generating vast amounts of location-based service data that reveal how individuals navigate and utilize urban spaces in detail. In this study, we utilize these extensive, unlabeled sequences of user…
This paper addresses the problem of short-term traffic prediction for signalized traffic operations management. Specifically, we focus on predicting sensor states in high-resolution (second-by-second). This contrasts with traditional…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
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…
Self-exciting point processes are widely used to model the contagious effects of crime events living within continuous geographic space, using their occurrence time and locations. However, in urban environments, most events are naturally…