I go to some lengths to avoid innumerate discussion online, but it still happens in real life with reasonable frequency. The flavours I seem to encounter most:
1) an all-purpose attempt to refute any statistical finding, even if said finding is not showing correlation, or proposing causation
2) dogged adherence to the belief that the direction of causal relationships are completely impossible to establish
3) the most perverse, that establishing an association between two variables is evidence against a causal relationship
Great answer, thanks. At the same time, I am reminded of gwern’s recent admonitions against “letting the better be the enemy of the good”:
I’m all in favor of giving the “correlation does not imply causation” meme better and more effective Internet visibility, perhaps with a friendly illustrated guide: “A simple explanation of association and causation”.
I’d be dead set against snarky content that runs even the slightest risk of making people feel dumb for knowing something that useful.
Look at almost any reporting of a scientific finding (even something like CNN gets this wrong usually). Chances are, the reporter will claim causality, while the original paper will claim association. This sort of thing is extremely common. Our good friend from slate was not immune to this, sadly.
I don’t get it. How does “journalist reports causation where there is only association” constitute an example of the journalist misapplying “correlation does not imply causation”, as opposed to failing to apply it in the first place?
(In the latter case, it’s good that the phrase “correlation does not imply causation” is floating around them Interwebs. The OP suggests that it’s not an unalloyed good because people “get it wrong”.)
Sorry, I didn’t catch the distinction between misapplying and failing to apply from your original phrasing (“people get this wrong.”)
To add to sixesandsevens list, I have one below, where people think lack of association implies lack of causation, or weak association implies weak causality (it does not in either case, due to effect cancellation, which happens reasonably frequently).
people think lack of association implies lack of causation, or weak association implies weak causality (it does not in either case, due to effect cancellation, which happens reasonably frequently).
Isn’t the Faithfulness assumption the assumption that effect cancellation is rare enough to be ignored? If it happens frequently, that looks like a rather large problem for Pearl’s methods.
I currently have a paper in the submission process about systems which actively perform effect cancellation, and the problems that causes, but I assume that isn’t what you have in mind.
If you pick parameters of your causal model randomly, then almost surely the model will be faithful (formally, in Robins’ phrasing: “in finite dimensional parametric families, the subset of unfaithful distributions typically has Lebesgue measure zero on the parameter space”). People interpret this to mean that faithfulness violations are rare enough to be ignored. It is not so, sadly.
First, Nature doesn’t pick causal models randomly. In fact, cancellations are quite useful (homeostasis, and gene regulation are often “implemented” by faithfulness violations).
Second, we may have a model that is weakly faithful (that is hard to tell from unfaithful with few samples). What is worse is it is difficult to say in advance how many samples one would need to tell apart a faithful vs an unfaithful model. In statistical terms this is sometimes phrased as the existence of “pointwise consistent” but the non-existence of “uniformly consistent” tests.
Kevin Kelly at CMU thinks a lot about “having to change your mind” due to lack of uniform consistency.
Much of what Pearl et al do (identification of causal effects, counterfactual reasoning, actual cause, etc.) does not rely on faithfulness. Faithfulness typically comes up when one wishes to learn causal structure from data. Even in this setting there exist methods which do not require faithfulness (I think the LiNGAM algorithm does not).
First, Nature doesn’t pick causal models randomly. In fact, cancellations are quite useful (homeostasis, and gene regulation are often “implemented” by faithfulness violations).
The very subject of my paper. I don’t think the magnitude of the obstacle has yet been fully appreciated by people who are trying to extend methods of causal discovery in that direction. And in the folklore, there are frequent statements like this one, which is simply false:
“Empirically observed covariation is a necessary but not sufficient condition for causality.”
I think the way causal discovery is sold sometimes is not as a way of establishing causal structure from data, but as a way of narrowing down the set of experiments one would have to run to establish causal structure definitively, in domains which are poorly understood but in which we can experiment (comp. bio., etc).
If phrased in this way, assuming faithfulness is not “so bad.” It is true that many folks in causal inference and related areas are quite skeptical of faithfulness type assumptions and rightly so. To me, it’s the lack of uniform consistency that’s the real killer.
At the risk of being the village idiot today: how do people get this wrong? Point to an example or three?
I go to some lengths to avoid innumerate discussion online, but it still happens in real life with reasonable frequency. The flavours I seem to encounter most:
1) an all-purpose attempt to refute any statistical finding, even if said finding is not showing correlation, or proposing causation
2) dogged adherence to the belief that the direction of causal relationships are completely impossible to establish
3) the most perverse, that establishing an association between two variables is evidence against a causal relationship
Great answer, thanks. At the same time, I am reminded of gwern’s recent admonitions against “letting the better be the enemy of the good”:
I’m all in favor of giving the “correlation does not imply causation” meme better and more effective Internet visibility, perhaps with a friendly illustrated guide: “A simple explanation of association and causation”.
I’d be dead set against snarky content that runs even the slightest risk of making people feel dumb for knowing something that useful.
Your post is valuable enough that it’s worth it to edit it to avoid misinterpretations of your point (like IlyaShpitser’s in reply to Morendil above).
Look at almost any reporting of a scientific finding (even something like CNN gets this wrong usually). Chances are, the reporter will claim causality, while the original paper will claim association. This sort of thing is extremely common. Our good friend from slate was not immune to this, sadly.
I don’t get it. How does “journalist reports causation where there is only association” constitute an example of the journalist misapplying “correlation does not imply causation”, as opposed to failing to apply it in the first place?
(In the latter case, it’s good that the phrase “correlation does not imply causation” is floating around them Interwebs. The OP suggests that it’s not an unalloyed good because people “get it wrong”.)
Sorry, I didn’t catch the distinction between misapplying and failing to apply from your original phrasing (“people get this wrong.”)
To add to sixesandsevens list, I have one below, where people think lack of association implies lack of causation, or weak association implies weak causality (it does not in either case, due to effect cancellation, which happens reasonably frequently).
Isn’t the Faithfulness assumption the assumption that effect cancellation is rare enough to be ignored? If it happens frequently, that looks like a rather large problem for Pearl’s methods.
I currently have a paper in the submission process about systems which actively perform effect cancellation, and the problems that causes, but I assume that isn’t what you have in mind.
If you pick parameters of your causal model randomly, then almost surely the model will be faithful (formally, in Robins’ phrasing: “in finite dimensional parametric families, the subset of unfaithful distributions typically has Lebesgue measure zero on the parameter space”). People interpret this to mean that faithfulness violations are rare enough to be ignored. It is not so, sadly.
First, Nature doesn’t pick causal models randomly. In fact, cancellations are quite useful (homeostasis, and gene regulation are often “implemented” by faithfulness violations).
Second, we may have a model that is weakly faithful (that is hard to tell from unfaithful with few samples). What is worse is it is difficult to say in advance how many samples one would need to tell apart a faithful vs an unfaithful model. In statistical terms this is sometimes phrased as the existence of “pointwise consistent” but the non-existence of “uniformly consistent” tests.
I suggest the following paper for more on this:
http://www.hss.cmu.edu/philosophy/scheines/uniform-consistency.pdf
See also this (the distinction comes from analysis): http://en.wikipedia.org/wiki/Uniform_convergence
Kevin Kelly at CMU thinks a lot about “having to change your mind” due to lack of uniform consistency.
Much of what Pearl et al do (identification of causal effects, counterfactual reasoning, actual cause, etc.) does not rely on faithfulness. Faithfulness typically comes up when one wishes to learn causal structure from data. Even in this setting there exist methods which do not require faithfulness (I think the LiNGAM algorithm does not).
The very subject of my paper. I don’t think the magnitude of the obstacle has yet been fully appreciated by people who are trying to extend methods of causal discovery in that direction. And in the folklore, there are frequent statements like this one, which is simply false:
(Edward Tufte, quoted here.)
I think the way causal discovery is sold sometimes is not as a way of establishing causal structure from data, but as a way of narrowing down the set of experiments one would have to run to establish causal structure definitively, in domains which are poorly understood but in which we can experiment (comp. bio., etc).
If phrased in this way, assuming faithfulness is not “so bad.” It is true that many folks in causal inference and related areas are quite skeptical of faithfulness type assumptions and rightly so. To me, it’s the lack of uniform consistency that’s the real killer.
In Part II of this talk (http://videolectures.net/uai2011_shpitser_causal/) I gave is an example of how you can do completely ridiculous, magical things if you assume a type of faithfulness. See 31:07.