Related papers: Large-scale optimal transport map estimation using…
This paper proposes an efficient numerical optimization approach for solving dynamic optimal transport (DOT) problems on general smooth surfaces, computing both the quadratic Wasserstein distance and the associated transportation path.…
Trajectory prediction is critical for autonomous driving, enabling safe and efficient planning in dense, dynamic traffic. Most existing methods optimize prediction accuracy under fixed-length observations. However, real-world driving often…
The Wasserstein distance from optimal mass transport (OMT) is a powerful mathematical tool with numerous applications that provides a natural measure of the distance between two probability distributions. Several methods to incorporate OMT…
Path planning is a crucial algorithmic approach for designing robot behaviors. Sampling-based approaches, like rapidly exploring random trees (RRTs) or probabilistic roadmaps, are prominent algorithmic solutions for path planning problems.…
The Traveling Thief Problem (TTP) is a multi-component optimization problem that captures the interplay between routing and packing decisions by combining the classical Traveling Salesperson Problem (TSP) and the Knapsack Problem (KP). The…
Optimal transport (OT) theory underlies many emerging machine learning (ML) methods nowadays solving a wide range of tasks such as generative modeling, transfer learning and information retrieval. These latter works, however, usually build…
Sufficient dimension reduction is used pervasively as a supervised dimension reduction approach. Most existing sufficient dimension reduction methods are developed for data with a continuous response and may have an unsatisfactory…
In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by…
A probabilistic method for solving the Monge-Kantorovich mass transport problem on $R^d$ is introduced. A system of empirical measures of independent particles is built in such a way that it obeys a doubly indexed large deviation principle…
We consider a class of structured, nonconvex, nonsmooth optimization problems under orthogonality constraints, where the objectives combine a smooth function, a nonsmooth concave function, and a nonsmooth weakly convex function. This class…
Due to the rapid development of Internet of Things (IoT) technologies, many online web apps (e.g., Google Map and Uber) estimate the travel time of trajectory data collected by mobile devices. However, in reality, complex factors, such as…
Orthogonal Matching pursuit (OMP) is a popular algorithm to estimate an unknown sparse vector from multiple linear measurements of it. Assuming exact sparsity and that the measurements are corrupted by additive Gaussian noise, the success…
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…
We present a novel approach called Optimized Directed Roadmap Graph (ODRM). It is a method to build a directed roadmap graph that allows for collision avoidance in multi-robot navigation. This is a highly relevant problem, for example for…
Flow Matching (FM) method in generative modeling maps arbitrary probability distributions by constructing an interpolation between them and then learning the vector field that defines ODE for this interpolation. Recently, it was shown that…
Online optimization has emerged as powerful tool in large scale optimization. In this paper, we introduce efficient online algorithms based on the alternating directions method (ADM). We introduce a new proof technique for ADM in the batch…
In the modern transportation industry, accurate prediction of travelers' next destinations brings multiple benefits to companies, such as customer satisfaction and targeted marketing. This study focuses on developing a precise model that…
In this paper, we present a new ensemble-based filter method by reconstructing the analysis step of the particle filter through a transport map, which directly transports prior particles to posterior particles. The transport map is…
The estimation of origin-destination (OD) matrices is a crucial aspect of Intelligent Transport Systems (ITS). It involves adjusting an initial OD matrix by regressing the current observations like traffic counts of road sections (e.g.,…
In this paper, we propose first a mmWave channel tracking algorithm based on multidimensional orthogonal matching pursuit algorithm (MOMP) using reduced sparsifying dictionaries, which exploits information from channel estimates in previous…