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...
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. ...
Transport map A vector-to-vector function T that associates to each point x in the support of a source distribution another point T(x) that is in the support of a target distribution, while satisfying a pushforward constraint T♯μ = ν. Transport plan A coupling (either in matrix ...
Optimal transport and von Neumann entropy in a Heisenberg XXZ chain out of equilibrium 来自 国家科技图书文献中心 喜欢 0 阅读量: 41 作者:Mario Salerno,Vladislav Popkov 摘要: DOI: http://dx.doi.org/10.1103/PhysRevE.87.022108 关键词: Transport processes Decoherence open systems quantum statistical ...
We would intuitively like theoptimal transportproblem to also solve for the best latent transformation together with the optimal coupling. 也就是说, 希望能找到一种适应于全局的 optimal transport formulation. 1.5 Methods 提供了一种 离散最佳运输问题的一般化的解决方案, 可以让 transformation 具有全局不变性...
It is important to note that we utilized the entropy regularization version of optimal transport, resulting in a probabilistic mapping between cells and spots. This probabilistic coupling, represented by the left-stochastic matrix [Math Processing Error]γ, indicates the likelihood of a specific cell ...
expensivewhend⌧nsincetheprimaryoptimizationvariableisalargetransportcoupling(i.e., Rn⇥n),whileinrealitythealignmentmappingismerelyRd7!Rd.Moreover,itassumesthatthe sourceandtargetdistributionsarecloseintermsoftheirsquaredEuclideandistance(i.e.,anidentity ...
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 ...
For a probability measure Q on Wiener space, Talagrand's transport inequality takes the form W ( Q , P )2 ≤2 H ( Q | P ), where theWasserstein distance W is defined in terms of the Cameron-Martin norm, and where H ( Q | P ) denotes the relative entropy with respect to Wiener...
(e.g., cell types) or induced cell clusters to improve mapping, and an entropy of transport to speed up OT computations. The optimal transport optimization tries to find an efficient mappingπ∗between cells ofYandY^that is used to transport cells inYto the same space as cells inY^. ...