Algorithm 1.

Subsampling MMD Algorithm ($\mathcal{S}\mathbf{}\mathcal{S}\mathbf{}\mathcal{P}$)

1: Divide $X_S$ and $X_T$ separately into $d$ groups by $Z$

2: Decide subsample size $(s_1,s_2,\mathrm{\dots },s_d)$

3: For $b=\mathrm{\hspace{0.17em}1}$ to $B$, do

4: Generate subsamples $X_S^b$ from $d$ groups of $X_S$

5: Generate subsamples $X_T^b$ from $d$ groups of $X_T$

6: $({\widehat{\lambda }}^b,{\widehat{\theta }}^b)=\arg {\min }_{\lambda \in {\mathrm{\Omega }}_{\lambda },\theta \in {\mathrm{\Omega }}_{\theta }}\widehat{\mathcal{M}\mathcal{M}\mathcal{D}}(h^{\lambda }(X_S^b),g^{\theta }(X_T^b))$

7: Calculate and record $g_{u(i,k)}^b$ for all $u,i,k$

8: Set $\widehat{\lambda }=\frac{1}{B}{\sum }_{b=1}^B{\widehat{\lambda }}^b$ and $\widehat{\theta }=\frac{1}{B}{\sum }_{b=1}^B{\widehat{\theta }}^b$ and calculate $𝕍𝔸{ℝ}_{IJ}(\widehat{\lambda })$ and

$𝕍𝔸{ℝ}_{IJ}(\widehat{\theta })$