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Seven basic rules for causal inference

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Re: Seven basic rules for causal inference

#21

Post by jerf »

lordnacho wrote: post #2

This is brilliant. The whole causal inference thing is something I only came across after university, either I missed it or it is a hole in the curriculum, because it seems incredibly fundamental to our understanding of the world. The thing that made be read into it was a quite interesting sentence from lesswrong, saying that actually the common idea that correlation does not imply causation is wrong. Now it's not wr…

"correlation does not imply causation is wrong"

That's a specific instance of a more general problem in the "logical fallacies", which is that most of them are written to be true in an absolutist, Aristotelian frame. It is true that if two things are correlated you can not therefore infer a rigidly 100% chance that there is a causative relationship there. And that's how Aristotelian logic works; everything is either True or False and if there is anything else it is as most "Indeterminate" and there is absolutely, positively, no in betweens or probabilities or anything else.

However, consider the canonical "logical fallacy":

    1. A -> B.
    2. B
    3. Therefore, A.
It is absolutely a logical fallacy in the Aristotelian sense. Just because B is there does not mean A is. However, probabilistically, if you are uncertain about A, the presence of B can be used to update your expected probability of A. After all, this is exactly what Bayes' rule is for!

Many of the "fallacies" can be rewritten to be useful probabilistically, and aren't quite as fallacious as their many internet devotees fancy.

It is certainly reasonable to be "suspicious" about correlations. There often is a "there" there. Of course, whether you can ever figure out what the "there" is is quite a different question; https://gwern.net/everything really gets in your way. (I also recommend https://gwern.net/causality ).

The upshot is basically 1. the glib dismissal that correlation != causation is, well, too glib and throws away too many things but 2. it is still true you still generally can't assume it either. The reality of the situation is exceedingly complicated.

Re: Seven basic rules for causal inference

#22

Post by dash2 »

ordu wrote: post #14
apwheele wrote: post #9

Earlier quoted context omitted.

This was my thought as well. I don't like showing the scatterplots in these examples, as "correlation" I think is more associated with the correlation coefficient than the more generic independence that the author means in this scenario. E.g. a U shape in the scatterplot may have a zero correlation coefficient but is not conditionally independent.

From the article: > NB: Correlated does not mean linearly correlated > For simplicity, I have used linear correlations in all the example R code. In real life, however, the pattern of correlation/association/mutual information we should expect depends entirely on the functional form of the causal relationships involved.

The standard mathematical definition of correlation means linear correlation. If you are talking about non-independence, it would be better to use that language. This early mistake made me think the author is not really an expert.

Re: Seven basic rules for causal inference

#23

Post by janto »

lordnacho wrote: post #13
Vecr wrote: post #5

Earlier quoted context omitted.

When did you go to university? The terminology here came from Pearl 2000, and it probably took years and years after that to diffuse out.

I thought Pearl was writing from 1984 onwards? I was at university around the millennium.

Causality (2000) made the topic accessible (to students and lecturers) as a single book.

Re: Seven basic rules for causal inference

#24

Post by boxfire »

jerf wrote: post #21
lordnacho wrote: post #2

This is brilliant. The whole causal inference thing is something I only came across after university, either I missed it or it is a hole in the curriculum, because it seems incredibly fundamental to our understanding of the world. The thing that made be read into it was a quite interesting sentence from lesswrong, saying that actually the common idea that correlation does not imply causation is wrong. Now it's not wr…

"correlation does not imply causation is wrong" That's a specific instance of a more general problem in the "logical fallacies", which is that most of them are written to be true in an absolutist, Aristotelian frame. It is true that if two things are correlated you can not therefore infer a rigidly 100% chance that there is a causative relationship there. And that's how Aristotelian logic works; everything is either…

I liked the way Pearl phrased it originally. A calculus of anti-correlations implies causation. That makes the nature of the analysis clear and doesn't set of the classic minds alarm bells.

Re: Seven basic rules for causal inference

#25

Post by currymj »

lordnacho wrote: post #2

This is brilliant. The whole causal inference thing is something I only came across after university, either I missed it or it is a hole in the curriculum, because it seems incredibly fundamental to our understanding of the world. The thing that made be read into it was a quite interesting sentence from lesswrong, saying that actually the common idea that correlation does not imply causation is wrong. Now it's not wr…

Rigorous causal inference methods are just now starting to diffuse into the undergraduate curriculum, after gradually becoming part of the mainstream in a lot of social science fields. But this is just happening.

Judea Pearl is in some respects a little grandiose, but I think he is right to be express shock that it took almost a century to develop to this point, given how long the basic tools of probability and statistics have been fairly mature.

Re: Seven basic rules for causal inference

#26

Post by [deleted] »

currymj wrote: post #3

Rule 2 (“causation creates correlation”) would be strongly disputed by a lot of people. It relies on the assumption of “faithfulness” which is not discussed until the bottom of the article. This is a very innocent sounding assumption but it’s actually quite strong. In particular it may be violated when there are control systems or strategic agents as part of the system you want to study — which is often the case for…

[deleted]

Re: Seven basic rules for causal inference

#27

Post by SpaceManNabs »

currymj wrote: post #3

Rule 2 (“causation creates correlation”) would be strongly disputed by a lot of people. It relies on the assumption of “faithfulness” which is not discussed until the bottom of the article. This is a very innocent sounding assumption but it’s actually quite strong. In particular it may be violated when there are control systems or strategic agents as part of the system you want to study — which is often the case for…

My fav way to intuit this is this example

https://stats.stackexchange.com/questions/85363/simple-examp...

Blew my mind the first time I saw it.

Not the same definitions one to one (author specifically talks about correlation vs linear correlation) but same idea.

Re: Seven basic rules for causal inference

#28

Post by cubefox »

dash2 wrote: post #22
ordu wrote: post #14

Earlier quoted context omitted.

From the article: > NB: Correlated does not mean linearly correlated > For simplicity, I have used linear correlations in all the example R code. In real life, however, the pattern of correlation/association/mutual information we should expect depends entirely on the functional form of the causal relationships involved.

The standard mathematical definition of correlation means linear correlation. If you are talking about non-independence, it would be better to use that language. This early mistake made me think the author is not really an expert.

What is an appropriate measure of (in)dependence though, if not Pearson correlation? Such that you feed a scatter plot into the formula for this measure, and if the measure returns 0 dependence, the variables are independent.

Re: Seven basic rules for causal inference

#29

Post by rlpb »

dash2 wrote: post #22
ordu wrote: post #14

Earlier quoted context omitted.

From the article: > NB: Correlated does not mean linearly correlated > For simplicity, I have used linear correlations in all the example R code. In real life, however, the pattern of correlation/association/mutual information we should expect depends entirely on the functional form of the causal relationships involved.

The standard mathematical definition of correlation means linear correlation. If you are talking about non-independence, it would be better to use that language. This early mistake made me think the author is not really an expert.

That seems a bit harsh. People can independently become experts without being familiar with the terminology used by existing experts. Further, if intended for a non-expert audience, it may even be deliberate to loosen definitions of terms used by experts, and being precise by leaving a note about that instead, which apparently is exactly what this author did.

Re: Seven basic rules for causal inference

#30

Post by abeppu »

At the bottom, the author mentions that by "correlation" they don't mean "linear correlation", but all their diagrams show the presence or absence of a clear linear correlation, and code examples use linear functions of random variables.

They offhandedly say that "correlation" means "association" or "mutual information", so why not just do the whole post in terms of mutual information? I think the main issue with that is just that some of these points become tautologies -- e.g. the first point, "independent variables have zero mutual information" ends up being just one implication of the definition of mutual information.

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