Algorithm 1: GAN-based auxiliary domain stage 1

for epoch i = 1:L do

for D, steps j = 1:M do

Sample minibatch of size p from the ground truth sample of the distant source dataset

Sample minibatch of size p from the latent space

Applying gradient ascent to D to solve the maximization problem:

$\underset{D}{\max }{F}_D\left(D,G\right)=E_{x,y}\left[\log \left(D\left(x,y\right)\right)\right]+E_{x,z}\left[\log \left(1-D\left(x,G\left(x,z\right)\right)\right)\right]$

end

for G, steps k = 1:N do

Sample minibatch of size p from the latent space

Applying gradient descent to G to solve the minimization problem:

$\underset{G}{\min }{F}_G\left(D,G\right)=E_{x,z}\left[\log \left(1-D\left(x,G\left(x,z\right)\right)\right)\right]+\lambda {\displaystyle {\displaystyle \sum }_i^N}{\beta }_i{\left(1-{\theta }_i\right)}^2$

end

end