The model has been evaluated in using an independence score between cause and noise. As $\hat{g}_Y$ is assumed to be invertible, the idea is that the noise variable can be recovered from $P_{X , Y}$ as: $\hat{N}_Y = g_Y^{-1}(Y) - f_Y(X)$ The noise variable is then estimated by functions $l_1$ and $l_2$ such as $\hat{Y}_Y = l_1(Y) - l_2(X)$ with $\hat{N}_Y$ independent of X. It comes back to solve a constrained nonlinear ICA problem, that can be achieved by minimizing $I(X,\hat{N}_Y; \theta)$, the mutual information between X and $\hat{N}_Y$ with respect to the parameter of the model θ . Symmetrically, an optimization of $I(X,\hat{N}_Y; \theta)$ is performed. The causal direction X → Y is preferred if $I(X,\hat{N}_Y; \hat{\theta})< I(Y,\hat{N}_X; \hat{\theta)}$, Y → X otherwise.