Introduced by Fonollosa, the standard deviation of the conditional distributions (CDS) is a regression-based feature that captures distribution asymmetry for causality detection. The CDS score measures the spread of the conditional distributions after normalization of the bins:

$CDS(X,Y) = \sqrt{ \frac{1}{M} \sum_{y=0}^{M-1} var_x (p_n(Y=y|X=x)) }$

Here, $p_n(Y=y|X=x)$ represents the normalized conditional probability and $var_x$ is the sample variance over $x$. This feature achieves good performance even when used alone, typically yielding a score of 0.69 on the Tübingen dataset.