至此可以很自然引入接下来的Optimal Transport Theorem!核心思路就是找到一个可以处理non-overlapping情况的probability measures! OT theory involved Optimal Transport OT可以刻画分布之间很自然的变化过程,进而能给出衡量各种分布类型之间距离的度量(定义研究对象的distance,OT自动给出研究对象分布的distance)。比如离散-离散...
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,故将该工具分享给大家,若有谬误...
To achieve the density-aware multi-agent exploration, the optimal transport theory that quantifies a distance between two density distributions is employed as a tool, which also serves as a means of similarity measure. Energy constraints for a multi-agent system are then incorporated into the OT...
Trajectory inference methods based on the optimal transport theory have attracted attention in recent years to deal with this issue. The optimal transport (OT) is a mathematical theory that provides distances and optimal matchings between probability distributions [15,16,17]. It has recently been ...
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
This book concerns the theory of optimal transport (OT) and its applications to solving problems in geometric optics. It is a self-contained presentation including a detailed analysis of the Monge problem, the Monge-Kantorovich problem, the transshipment problem, and the network flow problem. A ch...
Optimal Transport (OT) theory boils down to finding the optimal way to transport or redistribute mass from one probability distribution to another with respect to some cost function. In this work, since the datasets\(X^a\)and\(X^b\)are discrete datasets, we use their empirical probability di...
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。
This paper harnesses the optimal transport (OT) theory to provide a fresh perspective on these challenges. By utilizing the Wasserstein distance from OT, we establish a geometric framework that allows for quantifying reward ambiguity and identifying a central representation or centroid of reward ...
Understanding and improving Generative Adversarial Networks (GAN) using notions from Optimal Transport (OT) theory has been a successful area of study, originally established by the introduction of the Wasserstein GAN (WGAN). An increasing number of GANs incorporate OT for improving their discriminator...