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We introduce and analyze a statistical estimator for Monge transport maps: solutions to the quadratic optimal transport problem in Euclidean space. For absolutely continuous source measures, this map is uniquely defined as the gradient of a…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
Motivated by global warming issues, we consider a time se- ries that consists of a nondecreasing trend observed with station- ary fluctuations, nonparametric estimation of the trend under monotonicity assumption is considered. The rescaled…
We consider the Monge problem of optimal transport between a compactly supported source measure and a target probability measure with unbounded support. We consider the convergence of optimal maps and potential functions when the target…
We consider the optimal mass transportation problem in $\RR^d$ with measurably parameterized marginals, for general cost functions and under conditions ensuring the existence of a unique optimal transport map. We prove a joint measurability…
Safe autonomous driving critically depends on how well the ego-vehicle can predict the trajectories of neighboring vehicles. To this end, several trajectory prediction algorithms have been presented in the existing literature. Many of these…
In this paper, we present a semantic mapping approach with multiple hypothesis tracking for data association. As semantic information has the potential to overcome ambiguity in measurements and place recognition, it forms an eminent…
We consider the following problem : we have a high-resolution street network of a given city, and low-resolution measurements of traffic within this city. We want to associate to each measurement the set of streets corresponding to the…
In this paper, we are motivated by two important applications: entropy-regularized optimal transport problem and road or IP traffic demand matrix estimation by entropy model. Both of them include solving a special type of optimization…
We propose a quantitative approach for calibrating and validating key features of traffic instabilities based on speed time series obtained from aggregated data of a series of neighboring stationary detectors. We apply the proposed criteria…
Transportation companies and organizations routinely collect huge volumes of passenger transportation data. By aggregating these data (e.g., counting the number of passengers going from a place to another in every 30 minute interval), it…
Urban rail services are the principal means of public transportation in many cities. To understand the crowding patterns and develop efficient operation strategies in the system, obtaining path choices is important. This paper proposed an…
We prove smoothing estimates for velocity averages of the kinetic transport equation in hyperbolic Sobolev spaces at the critical regularity, leading to a complete characterisation of the allowable regularity exponents. Such estimates will…
The Gromov--Wasserstein problem is a non-convex optimization problem over the polytope of transportation plans between two probability measures supported on two spaces, each equipped with a cost function evaluating similarities between…
We introduce a new framework for efficient sampling from complex probability distributions, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core idea is to use continuous transportation to transform…
In crowded scenes, detection and localization of abnormal behaviors is challenging in that high-density people make object segmentation and tracking extremely difficult. We associate the optical flows of multiple frames to capture…
This paper proposes a new stochastic model of traffic dynamics in Lagrangian coordinates. The source of uncertainty is heterogeneity in driving behavior, captured using driver-specific speed-spacing relations, i.e., parametric uncertainty.…
Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…
Data-target association is an important step in multi-target localization for the intelligent operation of un- manned systems in numerous applications such as search and rescue, traffic management and surveillance. The objective of this…
Multi-object tracking (MOT) is the task of estimating the state trajectories of an unknown and time-varying number of objects over a certain time window. Several algorithms have been proposed to tackle the multi-object smoothing task, where…