IlyaShpitser comments on Causal Diagrams and Causal Models - Less Wrong

61 Post author: Eliezer_Yudkowsky 12 October 2012 09:49PM

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Comment author: IlyaShpitser 13 October 2012 07:00:31PM 2 points [-]

My suspicion as to why this took so long to develop is that it's worthless when looking at graphs with only two nodes: there, we can only tell the difference between independence and correlation, and there's no way to tell which way the causation goes.

Well, actually...

http://jmlr.csail.mit.edu/papers/volume7/shimizu06a/shimizu06a.pdf http://jmlr.csail.mit.edu/proceedings/papers/v9/peters10a/peters10a.pdf

Comment author: Vaniver 13 October 2012 07:31:09PM *  1 point [-]

Fascinating; thanks for the papers! Those look like they describe continuous and discrete distributions; does my statement hold for binary variables?

Comment author: Kenny 22 October 2012 03:01:44AM *  1 point [-]

Aren't binary variables a discrete distribution?

Comment author: Vaniver 22 October 2012 04:40:35AM *  2 points [-]

Yes, but they contain less information. Check out figure 2 of the Peters paper (which describes discrete distributions). If you have an additive noise model, so Y is X plus noise, then by looking at the joint pdf you can distinguish between X causing Y and Y causing X by the corners. This doesn't seem possible if X and Y can only have 2 values (since you get a square, not a trapezoid).

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