COT-GAN: Generating Sequential Data via Causal Optimal Transport
This work addresses the challenge of generating realistic time series data for applications in fields like finance or healthcare, representing an incremental improvement by integrating causality constraints into existing optimal transport methods.
The authors tackled the problem of generating sequential data by introducing COT-GAN, an adversarial algorithm based on Causal Optimal Transport, which effectively produces both low- and high-dimensional time series with improved stability and less bias.
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.