We introduce COT-GAN, an adversarial algorithm to train implicit generative models optimized for producing sequential data. The loss function of this algorithm is formulated using ideas from Causal Optimal Transport (COT), which combines classic optimal transport methods with an additional temporal causality constraint. Remarkably, we find that this causality condition provides a natural framework to parameterize the cost function that is learned by the discriminator as a robust (worst-case) distance, and an ideal mechanism for learning time dependent data distributions. Following Genevay et al.\ (2018), we also include an entropic penalization term which allows for the use of the Sinkhorn algorithm when computing the optimal transport cost. Our experiments show effectiveness and stability of COT-GAN when generating both low- and high-dimensional time series data. The success of the algorithm also relies on a new, improved version of the Sinkhorn divergence which demonstrates less bias in learning.

使用因果最优传输（COT）思想定义的COT-GAN算法应用于产生顺序数据，使用改进的Sinkhorn差异度量学习鉴别器的代价函数，并包括增加的时间因果约束和熵惩罚项。实验表明，该算法在产生低维和高维时间序列数据时具有很好的效率和稳定性。

COT-GAN：通过因果最优传输生成序列数据