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This isn't as generally useful as the title suggests... due to these assumptions: "that X and Y are dependent (i.e., PXY=PXPY), there is no confounding (common

This isn't as generally useful as the title suggests... due to these assumptions: "that X and Y are dependent (i.e., PXY=PXPY), there is no confounding (common cause of X and Y), no selection bias (common effect of X and Y that is implicitly conditioned on), and no feedback between X and Y (a two-way causal relationship between X and Y)"

pdabbadabba 12y ago
I must say, I do not understand why they have to assume that there is no common cause. What you're looking for is an asymmetry in the the bleeding of noise from one variable into another, right? I.e., if you're hypothesis is that A causes B, then you want to confirm that noise in A also appears in B, but that noise in B does not also appear in A. The fact that there is a common source of noise in both might make it more difficult to detect this asymmetry (because it weakens your characterization of A or B specific noise) but, on their assumption that noise is typically additive, wouldn't it still be theoretically possible to detect the asymmetry you're looking for? I.e., if A and B have common cause X, then noise from X will appear in A and B, but A noise will not appear in B, and B noise will not appear in A (assuming that A and B also have intrinsic noise sources in addition to the noise they inherit from X). Symmetry is maintained. What am I not getting?
- Tycho 12y ago
  Maybe because you cannot guarantee that noise will bleed? If you detect bleeding, then great, you have a result. If you do not detect bleeding, then it could be that there is a confounding variable or it could just be that the noise doesn't bleed. Similarly if there is a confounding variable then you cannot guarantee that the noise will bleed to both sets of observations. You have know way of knowing. Make sense?
gwern 12y ago
> This isn't as generally useful as the title suggests... My understanding is that the more general case of causal discovery, where you have lots of variables, is already somewhat solved by Pearlian techniques (if you have A/B/C you can conditionalize on each and see what graph fits best - all independent, C confounding A & B, A -> B -> C, etc). But these techniques break down when it's just A and B: A->B and B->A look symmetrical - the problem is so simple that it's hard, because there's no C which can help break the symmetry and suggest something about the underlying causal graph. OP is interesting because it points out that even without a C, A and B often aren't symmetrical in one particular way. So now pairs can be attacked as well as triplets and bigger; and maybe it points the way to new ways to tackle more complicated datasets.
- cafebeen 12y ago
  Certainly interesting--wish the article mentioned the Pearlian techniques. My issue is with the overstated claims, e.g. "Statisticians have always thought it impossible to tell cause and effect apart using observational data. Not any more." Maybe including "bivariate" in the paper's title could have helped.

pdabbadabba 12y ago

I must say, I do not understand why they have to assume that there is no common cause. What you're looking for is an asymmetry in the the bleeding of noise from one variable into another, right? I.e., if you're hypothesis is that A causes B, then you want to confirm that noise in A also appears in B, but that noise in B does not also appear in A. The fact that there is a common source of noise in both might make it more difficult to detect this asymmetry (because it weakens your characterization of A or B specific noise) but, on their assumption that noise is typically additive, wouldn't it still be theoretically possible to detect the asymmetry you're looking for? I.e., if A and B have common cause X, then noise from X will appear in A and B, but A noise will not appear in B, and B noise will not appear in A (assuming that A and B also have intrinsic noise sources in addition to the noise they inherit from X). Symmetry is maintained. What am I not getting?

Tycho 12y ago
Maybe because you cannot guarantee that noise will bleed? If you detect bleeding, then great, you have a result. If you do not detect bleeding, then it could be that there is a confounding variable or it could just be that the noise doesn't bleed. Similarly if there is a confounding variable then you cannot guarantee that the noise will bleed to both sets of observations. You have know way of knowing. Make sense?

gwern 12y ago

> This isn't as generally useful as the title suggests... My understanding is that the more general case of causal discovery, where you have lots of variables, is already somewhat solved by Pearlian techniques (if you have A/B/C you can conditionalize on each and see what graph fits best - all independent, C confounding A & B, A -> B -> C, etc). But these techniques break down when it's just A and B: A->B and B->A look symmetrical - the problem is so simple that it's hard, because there's no C which can help break the symmetry and suggest something about the underlying causal graph. OP is interesting because it points out that even without a C, A and B often aren't symmetrical in one particular way. So now pairs can be attacked as well as triplets and bigger; and maybe it points the way to new ways to tackle more complicated datasets.

cafebeen 12y ago
Certainly interesting--wish the article mentioned the Pearlian techniques. My issue is with the overstated claims, e.g. "Statisticians have always thought it impossible to tell cause and effect apart using observational data. Not any more." Maybe including "bivariate" in the paper's title could have helped.