You have read my mind perfectly and understood the demos! But I’ll go ahead and make the post anyway, when I have time, because there are some general implications to draw from the disconnect between causality and correlation. Such as, for example, the impossibility of arriving at A-->B<-->C for this example from any existing algorithms for deriving causal structure from statistical information.
the impossibility of arriving at A-->B<-->C for this example from any existing algorithms for deriving causal structure from statistical information.
Correct me if I’m wrong, but I think I already know the insight behind what you’re going to say.
It’s this: there is no fully general way to detect all mutual information between variables, because that would be equivalent to being able to compute Kolmogorov complexity (minimum length to output a string), which would in turn be equivalent to solving the Halting problem.
You have read my mind perfectly and understood the demos! But I’ll go ahead and make the post anyway, when I have time, because there are some general implications to draw from the disconnect between causality and correlation. Such as, for example, the impossibility of arriving at A-->B<-->C for this example from any existing algorithms for deriving causal structure from statistical information.
Correct me if I’m wrong, but I think I already know the insight behind what you’re going to say.
It’s this: there is no fully general way to detect all mutual information between variables, because that would be equivalent to being able to compute Kolmogorov complexity (minimum length to output a string), which would in turn be equivalent to solving the Halting problem.
You’re wrong. :-)
Kolmogorov complexity will play no part in the exposition.
Check my comment: I was only guessing the underlying insight behind your future post, not its content.
I obviously leave room for the possibility that you’ll present a more limited or more poorly-defended version of what I just stated. ;-)