感觉Optimal Transport Theory逐步成为近年热门的机器学习theoretical tool。其在ML中的应用也是很广泛,如一大类生成模型。其众多成功案例中,背后有OT来做支撑的如Wasserstein GAN。从理论分析出发,实现很小的改变就解决了原始GAN训练稳定性,collapse mode等问题。近来涉及到要使用相关理论,故将该
We propose optimal transportation theory as a unified view for modeling species interaction networks with different intensities of interactions. We pose the coupling of two distributions as a constrained optimization problem, maximizing both the system's average utility and its global entropy, that is,...
Engineering multilayer networks that efficiently connect sets of points in space is a crucial task in all practical applications that concern the transport of people or the delivery of goods. Unfortunately, our current theoretical understanding of the sh
In this paper, we give an overview of (nonlinear) pricing-hedging duality and of its connection with the theory of entropy martingale optimal transport (EM
The optimal transport (OT) problem is a classical optimization problem having the form of linear programming. Machine learning applications put forward new computational challenges in their solution. In particular, the OT problem defines a distance betwe
Optimal transportation theory gives us an application to map the measure associated with the variable in database A to the measure associated with the same variable in database B. To do so, a cost function has to be introduced and an allocation rule has to be defined. Such a function and...
we propose to adaptively retrieve a more efficient optimal transport plan to boost the recurrent flow learning. Both FLOT27and GotFlow3D seek guidance from optimal transport theory, but implement that in different ways. The former directly employs optimal transport to compute a coarse flow, whereas...
[13] Mémoli, Facundo (2011).Gromov–Wasserstein distances and the metric approach to object matching. Foundations of computational mathematics 11.4 : 417-487. [14] Knott, M. and Smith, C. S. (1984).On the optimal mapping of distributions, Journal of Optimization Theory and Applications Vol ...
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[13] Mémoli, Facundo (2011).Gromov–Wasserstein distances and the metric approach to object matching. Foundations of computational mathematics 11.4 : 417-487. [14] Knott, M. and Smith, C. S. (1984).On the optimal mapping of distributions, Journal of Optimization Theory and Applications Vol ...