Hello Azim,

Since we are manipulating empirical probability distributions, p and q are vectors of probability masses
per samples in your distribution. Indeed, it is generally a common choice to consider them as equal 
and set them as 1/(number of samples in the distribution). 

Hope this helps,

Best regards,

Nicolas

Le 8 août 2019 à 21:53, Azim Dehghani Amirabad <azim.dehghani@gmail.com> a écrit :

Hi,

I'm using OT package for GW, and I have a question regarding two arguments of the 
ot.gromov.gromov_wasserstein function. 
What is p and q? I couldn't see them in the objective function of the GW. 


p = ot.unif(n_samples)
q = ot.unif(n_samples)

gw0, log0 = ot.gromov.gromov_wasserstein(
    C1, C2, p, q, 'square_loss', verbose=True, log=True)

gw, log = ot.gromov.entropic_gromov_wasserstein(
    C1, C2, p, q, 'square_loss', epsilon=5e-4, log=True, verbose=True)


print('Gromov-Wasserstein distances: ' + str(log0['gw_dist']))
print('Entropic Gromov-Wasserstein distances: ' + str(log['gw_dist']))
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