Transition couplings are a constrained family of transport plans that capture the dynamics of Markov chains. Solutions of the optimal transition coupling (OTC) problem correspond to alignments of the two chains that minimize long-term average cost. We establish a connection between the OTC problem ...
公式一:Kantorovich Optimal Transport 在动作分割任务中,coupling \mathbf{T} \in \mathbb{R}^{N\times K} 可以被解释为视频帧与动作之间的匹配关系。 Gromov-Wasserstein Optimal Transport GW optimal transport 是Kantorovich OT的扩展,是用于比较定义在不同空间的分布(不能直接比较的两个空间)。具体地, 定义...
We thus posit that the evolution of probability distributions of single cells upon perturbation can be modeled via the mathematical theory of optimal transport. Following Makkuva et al.18, we thus learn the optimal transport map T (1) between ρc and ρk. Instead of computing a coupling γ ...
Our focus in this paper is on the optimal coupling mediating the transport 1.2 Questions1 - locally greedy 传统的 OT 问题 的一个缺陷, 其是对于两个sets的空间的假设太强: 问题中的两个sets都是存在于同一种空间之中的 或者, 其假设至少跨 space 之间的 pairwise distance 是可以计算的. 举个例子...
Winkler, L., Ojeda, C. & Opper, M. A score-based approach for training Schrödinger bridges for data modelling.Entropy25, 316 (2023). ArticleADSGoogle Scholar Tong, A. et al. Improving and generalizing flow-based generative models with minibatch optimal transport.Trans. Mach. Learn. Res....
In this paper, we propose a novel approach for unsupervised domain adaptation that relates notions of optimal transport, learning probability measures, and
Optima l Transporta tion—entropy I nequalities for S evera l Usual D istributions on R · (iii) let (X k)k>_l be .i.d.r.V.S of law ,then for nzf n ≥1,r > 0 p( ∑ ( > )+r) e-n~(r) k = 1 7 15 R emark 2.2. ...
† Gilles Mordant ‡AbstractThe quadratically regularized optimal transport problem has recently been considered invarious applications where the coupling needs to be sparse, i.e., the density of the coupling needsto be zero for a large subset of the product of the supports of the marginals....
optimal transport planγthus corresponds to the coupling between two probability distributions that minimizes the overall transportation cost. Given the OT couplingγ, the resulting distanceW(μ, ν) betweenμandνis known as the Wasserstein distance. Computing optimal transport distances in (2) ...
(L_t\)) domains can be any general class of loss functions that are twice differentiable. We opted for a traditional cross-entropy loss in both cases. Note that, as discussed in [35], the expected value over the minibtaches does not converge to the true OT coupling between every pair ...