In the Additive Noise Model (ANM), the fit score is based on an independence test between the estimated noise and the cause. For the two causal alternatives, X rightarrow Y and Y rightarrow X, the estimated mechanisms $\hat{f}_Y$ and $\hat{f}_X$ are obtained via Gaussian process regressions. These regression functions are used to calculate the residuals $\hat{n}_Y = y - \hat{f}_Y(x)$ and $\hat{n}_X = x - \hat{f}_X(y)$. The scores S_{X rightarrow Y} and S_{Y rightarrow X} correspond to the kernel HSIC independence test between $\hat{n}_Y$ and $x$ (for X rightarrow Y), and between $\hat{n}_X$ and $y$ (for Y rightarrow X). If S_{X rightarrow Y} < S_{Y rightarrow X}, the orientation X rightarrow Y is chosen; if S_{X rightarrow Y} > S_{Y rightarrow X}, Y rightarrow X is chosen.