One-Dimensional Approximation of Measures in Wasserstein Distances: A Variational Approach with Length Regularization
This paper proposes a novel variational method to approximate probability measures using measures uniformly distributed over one-dimensional connected sets, leveraging Wasserstein distances and length regularization to address the challenge of finding optimal approximations.
예상 슬라이스 전송 계획 (Expected Sliced Transport Plans) - 확률 측정 간의 효율적인 전송 계획 구성 및 새로운 메트릭 제안
이 논문에서는 슬라이스 최적 전송 (Sliced Optimal Transport, SOT) 프레임워크를 사용하여 두 확률 측정 간의 전송 계획을 효율적으로 구성하는 방법을 제안하고, 이를 통해 계산 효율성을 유지하면서 명시적인 질량 결합을 가능하게 하는 새로운 메트릭인 EST(Expected Sliced Transport) 거리를 소개합니다.
Expected Sliced Transport Plans: A Novel Approach to Efficiently Compute Transportation Plans and Metrics for Discrete Probability Measures
This research paper introduces Expected Sliced Transport (EST), a computationally efficient method for constructing transportation plans and defining a metric between discrete probability measures, leveraging the sliced optimal transport framework.
Congestion and Penalization in Discrete Optimal Transport: Exploring Two Novel Models
This paper introduces and analyzes two novel models inspired by the discrete optimal transport problem, incorporating congestion costs and penalized constraints to provide a more realistic approach to resource allocation problems.
Orthogonal Coupling Dynamics: A Novel Approach to Optimal Transportation
This research paper introduces Orthogonal Coupling Dynamics (OCD), a novel algorithm for solving the Monge-Kantorovich problem, which forms the basis for calculating Wasserstein distances and finding optimal transport maps between probability distributions.
Optimal Transport with Wasserstein Cost: Existence and Uniqueness of Optimal Maps on Wasserstein Spaces
This research paper proves the existence and uniqueness of optimal transport maps on Wasserstein spaces, extending classical results to the case where the cost function is itself the squared Wasserstein distance.
외부 최적 운송 문제
이 논문에서는 특정 Wasserstein 거리를 기반으로 분산을 선호하는 함수와 관련된 최적화 문제, 특히 주어진 부피 제약 조건에서 이러한 함수를 최대화하는 문제를 연구합니다.
Simulation-Free Entropic Unbalanced Optimal Transport for Scalable Generative Modeling and Image-to-Image Translation
This paper introduces SF-EUOT, a scalable and simulation-free algorithm for solving the Entropic Unbalanced Optimal Transport (EUOT) problem, which demonstrates significant improvements in generative modeling and image-to-image translation tasks compared to previous Schr¨odinger Bridge methods.
Optimal Transport for Measures with Noisy Tree Metric: Robust Approach for Uncertain Tree Structures
Robuste OT für Maße mit rauschigem Baummetrik
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