[Question] What does the causal score in the pairwise model really indicate?

[Beliefuture]

Hi, I am new to causal discovery and thanks for your work on this great toolbox.

But I have some questions about (i) the value returned by the predict_proba() function. According to the document, for a pair (X,Y), most of the pairwise model return the score 1 to indicate X -> Y and -1 to Y -> X otherwise. However, when I run those models to get the causation score of my own data, I find that all the models never return simply 1 or -1. Instead, the value sometimes become greater than 1 or less than -1.

Therefore, I wonder if the causation direction between X and Y can be determined just through the sign of value, i.e., if > 0, X -> Y and Y -> X otherwise? If so, I think the corresponding document should be updated as it is certain confused. And the absolute of the score value reflects the significance of the causation judgement?

Lastly, I want to ask (ii) if there exists any metric to determine the performance or the accuracy of the causation model without the labelled (X,Y) pair? And (iii) does this toolbox support the causal discovery of multivariate?