The implementation of wasserstein distance?

[night-chen]

Hello! I found your paper of DT4SR really interesting. However, I found that the implementation of Wasserstein distance is a little bit different from what you described in the paper. I noticed that you comment on those 'real' Wasserstein computation lines and use a simple MSE between the mean and covariance embedding. Are these two equal operations? And which one should I use when I run my own code. Thank you!

[zfan20]

Hi,

Thanks for your interest. When the covariance matrix is diagonal, then Wasserstein computation can be represented as the sum of L2 error between two mean embeds and L2 error of sqrt of covariance embeds. You can check our improved version (published in WWW'22) https://github.com/zfan20/STOSA.

Best.