Can POT be used to compute Wasserstein-2 distance between 2D distributions?

[FabianoVeglianti]

It seems to me that, at the moment, POT doesn't have an API to compute the Wasserstein-2 distance, but I would like to have a confirmation from you because I could be wrong.
Specifically, I need to compute the Wasserstein-2 distance between a Gaussian distribution and a set of data.

Obviously if the answer is :"yes, you can compute it", please tell me also how ^^.

[arakotom]

Hi,

yes you can compute it. for 2D data, if you have samples then you can use the code in this examples
https://github.com/PythonOT/POT/blob/master/examples/plot_OT_2D_samples.py

and it also works for higher dimensional data as long as you have samples.

[FabianoVeglianti]

Ah, ok, thank you! I saw the emd2 function but I was deceived by the name "emd" which stands (I think) for "earth mover's distance" and on wikipedia I read that the earth mover's distance is the Wasserstein-1, so I skipped that. Also I didn't think about the fact that the emd2 function accepts a matrix M of costs and that differents costs would lead to differents distances.

Anyway, thank you!