In the original paper, the ANM is seen as a discriminative model and the fit score is based on an independence test between noise and cause. More precisely for the two alternatives X → Y and Y → X , the estimated mechanisms and are obtained via Gaussian process regressions. These estimated regression functions are used to estimate the residuals $\hat{n}_Y = y-\hat{f}_Y(x)$ and $\hat{n}_X = x - \hat{f}_X(y)$. The scores $S_{X → Y}$ and $S_{Y → X}$ correspond respectively to kernel HSIC independence test between $\hat{n}_Y$ and x (for X → Y ) and between $\hat{n}_X$ and y (for Y → X ).

If $S_{X → Y} < S_{Y → X}$ it is decided that X → Y . If $S_{X → Y} > S_{Y → X}$ it is decided that Y → X .