The authors note $θ_X$ and $θ_Y$ the vectors of parameters of the estimated mechanisms $\hat{f}_X$ and $\hat{f}_Y$. Note respectively $\theta_{N_X}$ and $\theta_{N_Y}$ the vectors of parameters of the distribution of the modeled noise variables $Q_{N_X}$ and $Q_{N_Y}$. The noise variables are independent. The global vector of parameters of the model is noted $\theta = (\theta_X, \theta_Y, \theta_{N_X}, \theta_{N_Y})$ .

When mathcal{G} = Xrightarrow Y, this candidate generative model (depicted on the figure) generates a distribution $Q_{X,Y}(\theta) = Q_X(\theta_X, \theta_{N_X})Q_{Y|X}(\theta_Y, \theta_{N_Y})$.

When mathcal{G} =Yrightarrow X, this candidate model generates a distribution $Q_{X,Y}(\theta) = Q_Y(\theta_Y, \theta_{N_Y})Q_{X|Y}(\theta_X, \theta_{N_X})$.