The Post-NonLinear (PNL) model is evaluated using an independence score between the cause and the noise. As $\hat{g}_Y$ is assumed to be invertible, the noise variable can be recovered from the joint distribution $P_{X, Y}$ as: $\hat{N}_Y = \hat{g}_Y^{-1}(Y) - \hat{f}_Y(X)$. The noise variable is then estimated by functions $l_1$ and $l_2$ such as $\hat{N}_Y = l_1(Y) - l_2(X)$ with $\hat{N}_Y$ independent of $X$. This solves a constrained nonlinear Independent Component Analysis (ICA) problem, which can be achieved by minimizing $I(X,\hat{N}_Y; \theta)$, the mutual information between $X$ and $\hat{N}_Y$ with respect to the model parameter $\theta$. Symmetrically, an optimization of $I(Y,\hat{N}_X; \theta)$ is performed. The causal direction X rightarrow Y is preferred if $I(X,\hat{N}_Y; \hat{\theta}) < I(Y,\hat{N}_X; \hat{\theta})$, and Y rightarrow X otherwise.