我们希望能够找到一种能够找到 optimal coupling(最佳耦合) 的 latent transformation 形式的. 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 Me...
Entropy regularized optimal transportOptimal transport (OT) is a powerful tool for measuring the distance between two probability distributions. In this paper, we introduce a new manifold named as the coupling matrix manifold (CMM), where each point on this novel manifold can be regarded as a ...
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 ...
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 γ, indicates the likelihood of a specific cell being associated with a...
expensivewhend⌧nsincetheprimaryoptimizationvariableisalargetransportcoupling(i.e., Rn⇥n),whileinrealitythealignmentmappingismerelyRd7!Rd.Moreover,itassumesthatthe sourceandtargetdistributionsarecloseintermsoftheirsquaredEuclideandistance(i.e.,anidentity ...
M. Bollt, "Identifying coupling structure in complex systems through the optimal causation entropy principle," Entropy, vol. 16, p. 3416, 2014.Sun, J.; Cafaro, C.; Bollt, E.M. Identifying coupling structure in complex systems through the optimal causation entropy principle. Entropy 2014, ...
The rank constraint on the transport matrix can help recover the corrupted subspace structures and eliminate the noise to some extent when dealing with corrupted source data. The solution to this relaxed and regularized optimal transport framework is a convex optimization problem that can be solved ...
First, we align the clean barycenters to the all rest samples via optimal transport. Based on the result of op- timal transport, we can infer the labels of the all rest sam- ples. We consider the route with the max mass transport that forms a coupling a...
(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 mapping{\pi }^{*}between cells ofYand\widehat{Y}that is used to transport cells inYto the same space ...
(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 ...