The New Science of Causation

http://www.aaronsw.com/weblog/newcausation

by wglb • 17 years ago

96 28 17 years ago

dfranke• 17 years ago

I haven't read any of the cited research, but formalization of causality seems like it should be a straightforward endeavour. The notion of a controlled experiment already embodies a fairly rigorous understanding of what it means: if you have two starting conditions which are identical except for one variable 'A', and the outcomes differ in terms of 'B', then you've established a causal link from A to B. I don't envision any particular difficulty in transcribing this notion into the language of formal logic.

timf• 17 years ago

His comment about statistics (not formal logic?) is mainly about usefulness.

It's not useful to have a pure causality representation because with the real world and other complex systems, you don't know all the variables. Your variable 'A' in 10 years might be shown to be a combination of variables.

I, for example, only 99.99% believe in gravity. One day we might float off the planet. Lack of 100% proof about observations was one of Hume's basic arguments and I think the point of the "do-calculus" for AI that is discussed in this link. We all have an internal "do-calculus" for operating in the world: work with current held beliefs/rules until they're proven to work differently, etc.

darkxanthos• 17 years ago

I'm not convinced of this "truth". Do-calculus might help AI in its current state, but really they may just be making up for fundamental flaws in their neural simulations.

I normally hate to hear people say no one knows how certain things work but in this instance it seems apt. No one has created a self autonomous consciousness yet and so no one really knows exactly what goes into it.

I guess there's also a difference in advancing the study of robots and advancing the study of artificial intelligence.

jerf• 17 years ago

I am reminded of set theory, or perhaps rather, the history of set theory. Creating "a" set theory is easy. Working through all the implications and trying to create a robust set theory took a lot of time, and involved a few unexpected complications. 'Course it all looks simple now from our 21st century perspective, but it didn't happen overnight.

I suspect the theory of causality will be the same way; yeah, a quick approximation that works most of the time is readily available (almost enough information in that post for a mathematically-inclined person to work it out, after all), but working through all the nuances will probably take us somewhere unexpected. For example: What will it mean when someone proves there is no one theory of causality, like there is no one set theory? (Obviously, I don't know this will happen, but from a strictly mathematical point of view it sure wouldn't surprise me much; for a similar example, see Arrow's Impossibility Theorem. (If you (in general, not dfranke specifically) are not math savvy, still, Google it; it's not that hard to follow. Wikipedia's a bit heavy on the math, there are less formal introductions around.)) A branch of math to keep an eye on, I think.

jey4• 17 years ago

Yes, expressing a causal structure is pretty easy (e.g. make a Bayes net). The hard part is inferring a causal structure from a statistical pile of observations. According to Pearl, many statisticians even flatly reject[ed] the notion of causality as just a convenient fiction (iirc; it's been a long time since I read it).

thunk2• 17 years ago

I'd love an explicit ban on pop-sci health articles in the guidelines. Most of them are pure upvote-garbage. They can make HN look like a tabloid.

zackattack• 17 years ago

I agree. In the past year I've probably seen 20 different articles about sleep. In equal amounts they espouse the philosophies that we don't know why we sleep, sleep is for safety from animals, and that sleep is for the consolidation of memories. I would like to see more articles about how to hack sleep -- we hackers have notoriously irregular sleep cycles :).

llimllib• 17 years ago

While it mentions pop-sci health, I think this is not a pop-sci health article.

(I would support a hypothetical ban on those too, FWIW)

thunk2• 17 years ago

Oh, I wasn't suggesting it was. I thought it was a good post.

bokonist• 17 years ago

How is this different than typical multi-variable regressions with control variables?

The problem with social science is that it tries to be a science but in reality its closest relative is product management. Using even the best statistical methods still runs into the keys/lamp post problem. There are too many variables, the variables are not well defined, the variables may have strange interactions, there may be too much noise in the data, etc. In almost all social science situations, you cannot find truth solely through regressions.

For instance, recently I was studying the issue of whether the crash in the stock market caused the fall in consumer spending, or the slow down in consumer spending caused the fall in the stock market. If you run a straight regression you'll have a lot of problems because a) even if the stock market falls first, it could have been because of expectations of future consumption b) the data on expenditures is not collected frequently enough, and c) there are other potentially confounding variables.

But if you take the product management approach you can listen to what people say. And when you listen, you find that people say stuff like, "After the stock market fell, I had to cut back my plans to travel." or "Since the fall in our endowment, we have had to suspend spending on all new projects." By simply asking people you can figure out the causality.

Note that this is how every company in the world makes most of its decisions ( except perhaps Google, because they actually enough controlled data to meaningfully do regressions). When we're trying to figure out what features to build, we do customer interviews, follow-me-homes, surveys, feature requests, talk to customer support, etc. We make very modest use of statistics, because we do not have large amounts of controlled data. Did the customer not use this part of the app because it was not useful, or because we got the label wrong, or because of something else? We could do a bunch of statistics, but what's the point? It won't answer those questions. Asking people may be subjective, but it's the only way (keys/lamppost).

The problem is that social scientists do not get promoted for making accurate judgments and being right. A product manager does. A social scientist/academic can only be judged by his methods. Thus there is the preference within the professions for methods that can be objectively evaluated, and methods that only a select elite can perform. Being right is not part of the selection process for being an academic.

cousin_it2• 17 years ago

How is this different than typical multi-variable regressions with control variables?

I think it is different. Do you understand the smoking/tar/cancer example? See here for the example: http://bayes.cs.ucla.edu/IJCAI99/ijcai-99.pdf (pages 34-38 and 46), and here for a better introductory text: http://cscs.umich.edu/~crshalizi/notebooks/graphical-models.... .

Basically, if the situation allows you to reason that some causal arrows are impossible (e.g. due to time or space separation), you can often infer which of the remaining causal arrows are real and which aren't, using only non-experimental correlation data and some formal inference rules. Of course it doesn't always work - sometimes there really isn't enough data and you have to do a controlled experiment. But on the other hand, people often need to reason about causality in areas where controlled experiments are impossible or unethical, like smoking/tar/cancer.

zby• 17 years ago

The too many variables problem might be more evident in the social sciences - but it is present everywhere in science, even the most 'strict' science branches - like physics. You always need to make some assumptions. Much more eloquently - this idea is laid down in: http://falkenblog.blogspot.com/2009/09/nonscientists-naive-a...

alan-crowe• 17 years ago

> How is this different than typical multi-variable regressions with control variables?

As different as astrology and astronomy. Multi-variable regressions with control variables are known to incapable of supporting causal inference. The network based techniques of Pearl et. al. do permit causal inferences. Notice though that the network based techniques will quite often rigorously prove that the data you have are inadequate to make a causal inference. They do this by discovering multiple causal networks, all consistent with the patterns of correlation and conditional correlation in the data, but with causal links going one way in one net work and the other way in another network.

nazgulnarsil• 17 years ago

http://yudkowsky.net/rational/the-simple-truth

tl;dr: for truth to make any sense you have to postulate how "X being true" would cause a different sensory experience vs it being false.

gregwebs• 17 years ago

The problem with many popular health science articles is not just that the media claims causation from a correlational study, but that the scientists they interview do it also!

MikeCapone• 17 years ago

I know it's stupid, but I'm a bit scared of reading Judea Pearl.

Afraid it's going to be terribly brilliant with lots of maths and I won't understand it.

I know, I should just give it a try...

jey4• 17 years ago

Yes, Pearl's Causality is pretty dense. The trick to reading any research monograph is to realize that you're not supposed to read all of it, nor are you necessarily supposed to read it front-to-back. Once you realize that, Pearl's Causality is actually very accessible -- read the introduction to each chapter, read the text sections in that chapter that look interesting, and study the mathy parts that you find relevant.

ad• 17 years ago

Agreed. MikeCapone, I'd also recommend that you start with the essay at the very end of the book; serves as a good intro/overview.

andreyf2• 17 years ago

The statisticians Aaron cites need an epistemology lesson. Mathematics is not a science. Science is about creating models and testing them, models that involve causality. Mathematics is simply the rigorous definition of things (making it the perfect source of language for said models).

"You must learn to distinguish between what is true and what is real." See: http://www.edge.org/q2005/q05_8.html#kay

jey4• 17 years ago

Mathematics is a science. Mathematicians form hypotheses (guessed theorems, guessed properties, etc) then perform experiments to test their hypothesis (trying to construct a proof). If they end up with a proof, the hypothesis has been confirmed.

I think most mathematicians would disagree with your assertion that math is about "definitions". (I'm no math geek, just a programmer, so take with an appropriately sized grain of salt.)

jibiki• 17 years ago

It's like anything else: some mathematicians see mathematics as a science, and others don't. Most probably don't think about it one way or the other.

> I think most mathematicians would disagree with your assertion that math is about "definitions".

An analogy: math is about definitions in the same sense that go is about placing stones on a grid.

andreyf2• 17 years ago

Mathematicians form hypotheses (guessed theorems, guessed properties, etc) then perform experiments to test their hypothesis (trying to construct a proof).

There's certainly an abstract similarity, but etymologically, constructing a proof is very different from running an experiment. A proof declares a statement as True. An experiment (at best) shows that reality behaves as your model hypothesized it would. Experiments can provide evidence of something, not prove it as True. As Alan Kay says (following former link):

When we guess in science we are guessing about approximations and mappings to languages, we are not guessing about "the truth" (and we are not in a good state of mind for doing science if we think we are guessing "the truth" or "finding the truth"). This is not at all well understood outside of science, and there are unfortunately a few people with degrees in science who don't seem to understand it either.

leecho0• 17 years ago

This is really interesting, does anyone have references to the stuff stated here? I'm trying to read through the stuff from his website: http://bayes.cs.ucla.edu/jp_home.html

ible• 17 years ago

Causation, Prediction, and Search by Spirtes and Glymour is much more accessible than Pearl's Causality, and they cover a lot of similar material.

Video lectures has a workshop from NIPS '08 with talks by Pearl, Spirtes, et al at http://videolectures.net/coa08_whistler/

The UAI and NIPS conferences are a common venue for this research to be published in if you're interested in the latest results.

scott_s• 17 years ago

I took a course which addressed exactly this stuff, and I was going to point out material from that course, but he cites one of the professors who taught the course! Clark Glymour. That doesn't happen to me every day.

yaroslavvb• 17 years ago

Pearl provides a formalism for expressing causality, however it's questionable (to me) whether that formalism corresponds to what we humans consider "causality". Take 3 variables as an example, A,B,C. We observe some instances of A,B,C triples, and try to fit a probability distribution P(A,B,C) to data. If A,B,C are binary, there are 7 parameters, we can fit them directly to training data to get perfect fit, however, when we run it on separate set (validation data), it'll probably not perform very well. To improve fit on new data, you need to reduce number of parameters, so you could make some simplifying assumptions and write P(A,B,C) as P(A)P(B|A)P(C|B). In this form, there are 5 parameters to fit, and the resulting model could perform better with validation data. Alternatively you could fit P(A)P(B)P(C|A,B), 6 parameters, or P(C)(B|C)P(A|B). Select the one that performs the best on your validation data, and is hence the "best" model.

Now comes the cuasality connection -- if the best model is P(A)P(B)P(C|A,B) you read it as A->C<-B. If best model is P(A)P(B|A)P(C|B), you read it as A->B->C. (ie, A causes B, B causes C)

I think causality connection is questionable because the model that corresponds to A->B->C will have the same fit as model for A<-B<-C or A<-B->C. In fact, you could take any causal network without loops and "unshielded colliders" (connections of the form A->B<-C), pick any node as a root, and re-order the arrows to face away from the root to get a model with a different semantic causal structure, but the same mathematical structure, meaning it'll give identical fit to data.

What would be really interesting is if someone deduced causality using Pearl's approach, then verified it using a direct experiment

cousin_it2• 17 years ago

Wow. That's the kind of discussion we should be having. I didn't quite realize that Pearl's causality cannot tell A->B->C from A<-B->C. On the other hand, no other non-experimental statistical technique can do that either. Also, many problems will likely have a very constrained set of causal graphs to choose from, like smoking/tar/cancer.

The New Science of Causation

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