Related papers: Improving Mini-batch Optimal Transport via Partial…
Optimal mass transport is described by an approximation of transport cost via semi-discrete costs. The notions of optimal partition and optimal strong partition are given as well. We also suggest an algorithm for computation of Optimal…
Estimating optimal transport (OT) maps (a.k.a. Monge maps) between two measures $P$ and $Q$ is a problem fraught with computational and statistical challenges. A promising approach lies in using the dual potential functions obtained when…
Optimal transport (OT) has become a widely used tool in the machine learning field to measure the discrepancy between probability distributions. For instance, OT is a popular loss function that quantifies the discrepancy between an…
In this paper, we propose our information-theoretic equivalence of entropic multi-marginal optimal transport (MOT). This equivalence can be easily reduced to the case of entropic optimal transport (OT). Because OT is widely used to compare…
Diffusion Models (DMs) have achieved remarkable progress in generative modeling. However, the mismatch between the forward terminal distribution and reverse initial distribution introduces prior error, leading to deviations of sampling…
Motivated by robust dynamic resource allocation in operations research, we study the \textit{Online Learning to Transport} (OLT) problem where the decision variable is a probability measure, an infinite-dimensional object. We draw…
We propose novel fast algorithms for optimal transport (OT) utilizing a cyclic symmetry structure of input data. Such OT with cyclic symmetry appears universally in various real-world examples: image processing, urban planning, and graph…
Global pooling is one of the most significant operations in many machine learning models and tasks, which works for information fusion and structured data (like sets and graphs) representation. However, without solid mathematical…
Energy-based models (EBMs) are known in the Machine Learning community for decades. Since the seminal works devoted to EBMs dating back to the noughties, there have been a lot of efficient methods which solve the generative modelling…
Interpretable reinforcement learning policies are essential for high-stakes decision-making, yet optimizing decision tree policies in Markov Decision Processes (MDPs) remains challenging. We propose SPOT, a novel method for computing…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
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…
Optimal transport (OT) is a framework that can guide the design of efficient resource allocation strategies in a network of multiple sources and targets. This paper applies discrete OT to a swarm of UAVs in a novel way to achieve…
Optimal transport (OT) is a powerful geometric tool for comparing two distributions and has been employed in various machine learning applications. In this work, we propose a novel OT formulation that takes feature correlations into account…
Partial domain adaptation (PDA) problem requires aligning cross-domain samples while distinguishing the outlier classes for accurate knowledge transfer. The widely used weighting framework tries to address the outlier classes by introducing…
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…
Optimal transport (OT) theory can be informally described using the words of the French mathematician Gaspard Monge (1746-1818): A worker with a shovel in hand has to move a large pile of sand lying on a construction site. The goal of the…
Mismatch capacity characterizes the highest information rate for a channel under a prescribed decoding metric, and is thus a highly relevant fundamental performance metric when dealing with many practically important communication…
Optimal transport (OT) is a popular and powerful tool for comparing probability measures. However, OT suffers a few drawbacks: (i) input measures required to have the same mass, (ii) a high computational complexity, and (iii) indefiniteness…
Mapping is essential in robotics and autonomous systems because it provides the spatial foundation for path planning. Efficient mapping enables planning algorithms to generate reliable paths while ensuring safety and adapting in real time…