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“The Book of Why” by Pearl and Mackenzie

155 points by nkurz 8y ago

nkurz 8y ago
My comment on the blog was (at least initially) eaten by the spam filter, so I reproduce it here. --- JP: There is no way to answer causal questions without snapping out of statistical vocabulary. AG: We disagree. That’s fine. Science is full of disagreements, and there’s lots of room for progress using different methods. I'm only an amateur, but from the outside it sure doesn't feel "fine" for the two of you to disagree on what seems like such a fundamental issue. Instead, this seems like a case where two extremely smart individuals should be able to reach an common understanding instead of accepting disagreement as a final outcome. JP: I have tried to demonstrate it to you in the past several years, but was not able to get you to solve ONE toy problem from beginning to end. AG: For me and many others, one can indeed answer causal questions within statistical vocabulary. Pearl obviously disagrees that standard statistical vocabulary is sufficient to answer all simple causal questions. You seem to think he's wrong. I think you'd be doing a great service to encourage him to formulate such a "toy" question that he thinks is unanswerable without resorting to the do-calculus, which you then try to answer to the audiences' satisfaction using more standard techniques. Maybe the two of you turn out to be in agreement but using different terminology, maybe you are right that his tools are optional, or maybe he's right that they are essential. Any of these outcomes would feel much more satisfactory and productive than agreement to disagree. Please consider offering him a platform with which to make his case.
- bachmeier 8y ago
  > it sure doesn't feel "fine" for the two of you to disagree on what seems like such a fundamental issue. Instead, this seems like a case where two extremely smart individuals should be able to reach an common understanding instead of accepting disagreement as a final outcome. Once you've reached the limits of what you can know (after examining all data, worked through all arguments, etc.) this is pretty much the only possible outcome. What works in one situation might not work in others. One person's interpretation of our limited knowledge might very well appear implausible to someone else. I'll admit to being turned off by Pearl's insistence on working with "toy problems". That might be fine for a philosophical discussion, but it's not of much practical value. I want Pearl to write a few empirical papers attacking important issues, then let's have a discussion about putting ideas into practice.
  - nkurz 8y ago
    I have much more sympathy for Pearl. He's constructed "toy" problems that yield different answers depending on the hidden causal structure chosen. He then shows that unless one takes account of the causal structure, it's impossible to correctly answer the problem. The logical conclusion of this is that any technique that doesn't use the causal structure as an explicit assumption is instead using it as an hidden implicit assumption. His hope is that anyone who goes through his exercise will come to the same conclusion. Starting with real-world problems is tricky, because one doesn't know the correct answer in advance, thus it's much harder show the reliance on the assumptions. Consider a parallel with computer programming. A user complains that they fear a program is giving them the wrong answer on a complex real world problem. They report this, and get back the unhelpful answer "Works for me, will not fix". Unable to shake the feeling that the answer is unreliable, they reduce the problem down to a proof of concept that serves as a simple self-contained test case. Two different inputs produce the same answer, but only one of them can be right! But now they are unable to convince the maintainer to even look at the test case, because now the maintainer says "I need to focus on the real world, and don't want to waste my time on toy examples". It's a discouraging position to find oneself in.
    - bachmeier 8y ago
      Oh, I'm completely on board with being explicit about any assumptions you're making, and for thinking deeply about the causal relations, and for thinking about the reliability of the analysis. I've been critical of economists for not thinking things through. And I'm definitely on board with teaching using toy problems. The problem is that, as far as I can tell, Pearl doesn't go beyond making points with toy problems. He hasn't done much empirical work (has he published a single empirical paper?) or even read much of the empirical literature he's criticizing as worthless. Ultimately, the question is whether policy and other decisions will be better using a particular framework. The fact that Pearl writes with the aggressive confidence of a Hacker News commenter does not mean he's right.
      - harperlee 8y ago
        But from a mathematical point of view this insistence of focusing on empirical work is a little bit disheartening isn’t it? And frankly Judea Pearl is hardly a random internet tinfoil hat guy, nor is he asking people to invest a massive effort checking his looong work (as we eg often see with random NP-completeness “proofs”, or was discussed with the time investment needed to check Mochizuki’s ABC proof - no, he just asks Gellman to apply his own familiar techniques to a toy problem. It does not sound unreasonable at all.
- conjectures 8y ago
  "you'd be doing a great service to encourage him to formulate such a "toy" question that he thinks is unanswerable without resorting to the do-calculus, which you then try to answer to the audiences' satisfaction using more standard techniques." This would be very helpful indeed. I think a lot of the issue comes down to how idiosyncratic Pearl's work is. It will have to accumulate quite a lot of victories before enough people will bother with it. Until then I suspect Causality will remain something of a statistical Finnegan's Wake. I'll probably read The Book of Why to try and get a better handle on motivation for the technical material.
  - deleted 8y ago
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  - notafraudster 8y ago
    Thankfully, "Causality: A Primer" is sort of like the CliffNotes to Finnegan's Wake ;)
    - conjectures 8y ago
      Thanks, may check it out. This stuff has long been on my to-do list.
- mycorrhizal 8y ago
  I think you are overstating Judea Pearl's argument. He doesn't claim it is impossible to answer causal questions (on observational data) without resorting to do-calculus. What he does claim is that to answer causal (interventional or counterfactual) questions you need to define a model and reason on that model in a way that transforms the question into conditional probabilities. Do-calculus provides a framework to help you perform that reasoning, but certainly people have been using things like the backdoor criterion before the invention of do-calculus to answer interventional questions. He might claim that any other method can be reduced to do-calculus. I'm not sure. I do believe at the core of his argument is need for an explicit model.
  - nkurz 8y ago
    Yes, that's a better and more accurate phrasing than I used. The issue is that the correctness of the answer depends on the whether the causal structure of the model matches the underlying generative process. Graphs and do-calculus aren't required for this, but can help to make things clearer. In a later comment on the blog post, Pearl links to a paper that describes one of his "toy" examples: http://ftp.cs.ucla.edu/pub/stat_ser/r400-reprint.pdf http://ftp.cs.ucla.edu/pub/stat_ser/r400-reprint.pdf. Section 3 of page 584 is the beginning of the example. I'm sad to say that I'm sufficiently amateur at this that I found even the "toy" example to be at the limits of my reasoning ability, but I thought it still illustrated the argument Pearl is making.
    - mycorrhizal 8y ago
      I absolutely agree if your model is wrong any causal inferences you draw will be wrong. However his framework does provide mechanisms for determining if your data is inconsistent with your model (ie certain independences should or should not exist). So hopefully if your model is wrong your data will tell you so and you can change your model.
      - deleted 8y ago
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- tunesmith 8y ago
  I'm not an expert on this stuff at all, but are the toy problems basically formulations of Simpson's paradox? My sense was that if you have a set of a data, where if you cut it into two slices and each slice suggests the same (identical) conclusion, but then if you look at the data overall it suggests a different conclusion, then how do you know which approach is correct? And it seems the only way to know that is to use your judgment about causal factors that generated the data, and the do-calculus helps make that explicit. For instance, when thinking about gender ratios and grad programs, it's more probable that the choice of what grad program to apply to is affected by what gender you are, but it's less probable that the choice of your grad program affects your gender. Well I just reviewed section 3 of page 584 of that pdf that was shared and it seems different, so I probably have a long way to go before I understand this stuff.
  - xtacy 8y ago
    Not all "paradoxes" are similar to Simpson's paradox. See this PDF for more similar "paradoxes": https://ftp.cs.ucla.edu/pub/stat_ser/r409-corrected-reprint.pdf https://ftp.cs.ucla.edu/pub/stat_ser/r409-corrected-reprint.... (I quote the word paradox, because they aren't really paradoxes once we have an understanding of what's going on.)
DevX101 8y ago
For anyone interested in this book, I'm going through it now but it addresses an important question of how to identify causality. We've all become familiar with the refrain 'correlation does not imply causation'. This book attempts to answer: 'what DOES imply causation'? He introduces a framework for how one can answer this question. Not very mathematically rigorous, but following through the framework does appear to be able to discover non-intuitive causative conclusions. Understanding causation will have important implications for the advancement of A.I. Finding a correlation with the causes hidden in a black box (current state of deep learning) isn't enough for many disciplines. Doctors for example will likely need to know WHY an algorithm made a decision, instead of simply running correlations and telling the operator that a patient has 80% chance of some diagnosis.
- MAXPOOL 8y ago
  It's possible to infer causation from correlation without experiments if you add some general assumptions. One trick in causal discovery is additive noise. If X and Y are noisy correlating variables and X is causing Y, assumption that the noise in X is present in Y but not vice versa may reveal the direction of the causal arrow. Causal Discovery with Continuous Additive Noise Models http://jmlr.org/papers/volume15/peters14a/peters14a.pdf http://jmlr.org/papers/volume15/peters14a/peters14a.pdf Nonlinear causal discovery with additive noise models https://papers.nips.cc/paper/3548-nonlinear-causal-discovery-with-additive-noise-models.pdf https://papers.nips.cc/paper/3548-nonlinear-causal-discovery... Humans seem to have causal reasoning ability that is very ad hoc. It works well in practice but it's not principled. There is not enough time to do experiments to establish facts. Correlation is causality seems to be a good heuristics. I think that that AI will eventually learn to build causal models in the same way. Build a quick and dirty causal models with unfounded assumptions and see what works. Hold multiple effective conflicting causal theories that apply in different situations without any consistent model.
  - ionforce 8y ago
    I feel like I don't have the background to fully understand what you're saying. Could you explain this in a more lay way? > X and Y are noisy correlating variables
baron816 8y ago
I tried to listen to the audiobook of this. Terrible idea. One of the few audiobooks I’ve abandoned.
- lolptdr 8y ago
  Why was it bad? I'm not an audiobook listener so I don't know what's considered bad.
  - DevX101 8y ago
    Audiobooks for dense non-fiction material is usually a bad idea. I'd recommend audio for fiction, or non-fiction with an engaging storyline (ex: Bad Blood), which this is not. Nonetheless, I'd still recommend the book.
  - ffn 8y ago
    It's an user-experience problem: for an audiobook, Book of Why is quite dense in formula that are hard to visualize when spoke as words. For example, consider what happens if we try to describe a causal diagram in words "A points to B, A points to X, B points to Y, and X points to Y. Now, if we apply do(X) to the diagram, we see that we can Y is now no longer a child of..." or even simple formulas in words: "P of A given B times P of B is equal to P of B given A times P of A" For most of us, this sort of deal is hard to "get" and would be much better served if we just looked at a visual diagram or saw the equation. I personally had to repeat many sections over and over again with a notebook and pencil in hand to truly understand what was being read to me... but if I'm taking notes and creating visuals for myself, then I might as well have just gotten the paper variant of this book lol.
  - mindcrime 8y ago
    There are a lot of diagrams and a bit of math, which don't naturally translate to a purely auditory experience very well. Having read The Book of Why I can't imagine how it would translate to a reasonable audio-book. Frankly I'm surprised they even released an audio-book version at all.
- owaty 8y ago
notafraudster 8y ago
As someone who does social science causal inference for a living, I have to say that I didn't really enjoy "The Book of Why". Full disclosure: I mostly practice the Neyman-Rubin potential outcomes form of causal inference rather than the Pearl do-calculus / DAG ("directed acyclic graph") form of causal inference, but the two are in many cases equivalent. The reason I didn't like the book is that I found it insufficiently rigorous to really engage with the "how" of doing causal inference, but excessively mathematical as a theoretical introduction to causality. "Causality: A Primer" (also written by Pearl) is a very short book that I think does a good job of surfacing some of the same theoretical background while also explaining how to use Pearl's causality. If you exhaust that, I'd recommend moving to the full "Causality" book. But otherwise I'd recommend actually looking into the counterfactual / potential outcomes view of causality. The set of questions it answers are about 80% overlapping (although both Pearl and POs have their own 20%), but I find the vocabulary a little more intuitive. Canonical books include Morgan and Winship "Counterfactuals and Causal Inference" or Imbens and Rubin "Causal Inference for Social Scientists". As to the blog post, Pearl is correct that causality requires qualitative assumptions about design to justify assumptions required to do causal inference. In Pearl's work this is often motivated as qualitative knowledge informing the structure of the DAG before any estimation. But recent advances in causal discovery have actually rendered it possible to black box the structure of a DAG from data -- happy to provide citations if this is down the rabbit hole. By contrast, I agree with Gelman that Pearl is an irritating writer and that in "The Book of Why" he gives a sloppy intellectual history of causation.
- breuderink 8y ago
  > But recent advances in causal discovery have actually rendered it possible to black box the structure of a DAG from data -- happy to provide citations if this is down the rabbit hole. I would be very interested in these references.
  - notafraudster 8y ago
    I should say this is not my wing of the world since in social science typically theory precedes estimation and there would be a strong disciplinary norm against "I have no idea what causes what". So I don't actually use this stuff. That being said, I have played with a few of the packages and read a few pieces on causal discovery. Jonas Peters et al. - Elements of Causal Inference is a textbook that covers a little bit of what they called "learning cause-effect models". For algorithms, check SGS (Spirtes-Glymour-Scheines) and PC (Peter Spirtes and Clark Glymour). I believe both these algorithms are implemented in R in the package `pcalg`. There's another R package on BioConductor that implements them too, but I'm far enough afield from biostats I don't remember the name or have any notes I can find. Some recent cites of note: Peters and Buhlmann - "Identifiability of Gaussian structural equation models" (2014), which led to Ghoshal and Honorio - "Learning linear structural equation models in polynomial time" (2018) who generalize the Peters/Buhlmann claim. Other authors to Google: Dominik Janzig; Joris Mooij; Patrik Hoyer -- all of these people write papers with the above people, so you should be able to map out the network. What the pieces all have in common is that they're trying to establish empirical differences in the joint distributions of X and Y between scenarios where X -> Y and where Y -> X. This is only possible in some cases. Hope this helps.
svat 8y ago
A discussion about this book on the statistics StackExchange, with some interesting answers: "The Book of Why by Judea Pearl: Why is he bashing statistics?" https://stats.stackexchange.com/questions/376920/the-book-of-why-by-judea-pearl-why-is-he-bashing-statistics https://stats.stackexchange.com/questions/376920/the-book-of...
- nkurz 8y ago
  Yes, that has lots of great stuff in the comments. One of them (convolutedly just added based on a link provided in a comment on the Gelman blog post) was to this review: https://www.kdnuggets.com/2018/06/gray-pearl-book-of-why.html https://www.kdnuggets.com/2018/06/gray-pearl-book-of-why.htm.... The review, and then back-and-forth at the bottom and in comments between Gray and Pearl are wonderful context.
  - kgwgk 8y ago
    The irony in this comment is priceless: “Simpson’s paradox in its various forms is something that generations of researchers and statisticians have been trained to look out for. And we do. There is nothing mysterious about it. (This debate regarding Simpsons, which appeared in The American Statistician in 2014, and which I link in the article, hopefully will be visible to readers who are not ASA members.)” There is nothing mysterious about Simpson’s paradox but the proper answer is still being debated! Pearl’s response ends as follows: “The next step is to let the community explore: 1) How many statisticians can actually answer Simpson’s question, and 2) How to make that number reach 90%. I believe The Book of Why has already doubled that number, which is some progress. It is in fact something that I was not able to do in the past thirty years through laborious discussions with the leading statisticians of our time. It is some progress, let’s continue.” http://causality.cs.ucla.edu/blog/index.php/2018/06/15/a-statisticians-re-reaction-to-the-book-of-why http://causality.cs.ucla.edu/blog/index.php/2018/06/15/a-sta...
digitalzombie 8y ago
I tried reading Pearl once. I couldn't get over his tone. Andrew Gelman summarize it pretty nicely his take on it. Coming from a statistic background, casual inference is a growing thing now and several government sponsor research have been pushing for it. Casual inference from statistic point of view is base on missing data, basically Rudin stuff. It's pretty dang interesting to me. I'm sure there are many ways of looking at the same thing. Linear regression you can look at it in more of a optimal math problem with cost function or you can look at it in statitic using maximum likelihood estimation. Both have it's pro and con, with MLE you get a confidence interval. In my bias opinion I feel that statistic is only about data and it's a great domain for casual inference. There's no need to put a field down to make yours better. But if it's constructive criticism (pro/con, contrast) I think it make both fields better. Pearl attitude is off putting when you try to read his stuff. We're all human and have vary degree of ego, if you're going to try to convince us that do calculus and your ways is better be objective about it or word things better. If you don't want to convince people then just be blunt as hell.
haberman 8y ago
As a non-statistician with a lot of interest in statistics, I found the Book of Why frustrating. Modeling causation seems like an undeniably important step towards understanding the world better. But the biggest question I had was: how can you actually verify that your causal model is true? This is not clearly explained, or wasn't before I gave up on the book. Models are only useful if we can have some confidence that they correspond to reality. I was especially interested in the answer to this question, because my only exposure to the language of "causal chains" has been on Twitter, where they seemed to serve a distinctly ideological purpose. One (non-mathematical) person says "I think X is caused by Y", and then a statistician chimes in and says "you're missing other parts of the causal chain, the real causes are Z and Q." Where of course, Z and Q are things that one political perspective prefers to blame, and Y are things blamed by the other side. For example: https://twitter.com/gztstatistics/status/1000914269188296709 https://twitter.com/gztstatistics/status/1000914269188296709. Here's a great comment from today about the difficulty of establishing causality in practice: https://news.ycombinator.com/item?id=18886275 https://news.ycombinator.com/item?id=18886275 I want to know how causal chains can be actually proven or falsified, to be convinced that this isn't just highbrow ideological woo.
- kgwgk 8y ago
  > how can you actually verify that your causal model is true? This is addressed in the introduction. See box 4 in the flow-chart (“testable implications”). “The listening pattern prescribed by the paths of the causal model usually results in observable patterns or dependencies in the data. [...] If the data contradict this implication, then we need to revise our model.”
  - haberman 8y ago
    The part you removed with ellipses undermines this point: "These patterns are called "testable implications" because they can be used for testing the model. These are statements like "There is no path connecting D and L," which translates to a statistical statement, "D and L are independent," that is, finding D does not change the likelihood of L." This says nothing about testing causality, or the direction of causality. If two things are uncorrelated, then there is probably not a causal relationship between them, granted. But this is not a very novel or useful observation. However if D and L are correlated, the test above says nothing about how to validate whether D caused L, L caused D, both were caused by a third thing (or set of things), or the correlation is just coincidence. For a book whose entire thesis is "causality is rigorous," I expect a much more rigorous treatment of how to validate causality using more than mere correlation.
stewbrew 8y ago
So, AG writes a sloppy review to complain about a sloppy mischaracterization of (mostly classic) statisticians. "About the exposition of causal inference, I have little to say." That would have been interesting though.
kgwgk 8y ago
Relevant online course: https://www.edx.org/course/causal-diagrams-draw-assumptions-harvardx-ph559x https://www.edx.org/course/causal-diagrams-draw-assumptions-...
owaty 8y ago
To counter some of the comments here, I absolutely loved the book and went on to recommend it to all my scientist friends. While it may get a bit technical for the lay audience, it should be within reach for a typical scientist or IT person. I wish our society had a better understanding of causality—that would raise the level of many important discussions. Being a long-time fan of Gelman (and having studied his Bayesian Data Analysis textbook), I am baffled and disappointed that he doesn't seem to understand Pearl's ideas. In his linked 2009 post[1], he wrote: "I’ve never been able to understand Pearl’s notation: notions such as a “collider of an M-structure” remain completely opaque to me." I wonder if, after reading this book accessible even to non-statisticans, he still doesn't understand it. [1]: https://statmodeling.stat.columbia.edu/2009/07/05/disputes_about/ https://statmodeling.stat.columbia.edu/2009/07/05/disputes_a...
- mindcrime 8y ago
  To counter some of the comments here, I absolutely loved the book and went on to recommend it to all my scientist friends. Likewise (well, other than not really having any "scientist friends"). I loved this book, think Pearl has some amazingly valuable ideas, and found the book relatively accessible even though I'm not a statistician. I won't claim to have understood every detail on the first reading, but I got enough out of it to feel like I'll understand it all after a couple of follow on readings, plus consulting Pearl's other books. I wish our society had a better understanding of causality—that would raise the level of many important discussions. Absolutely.
- sjg007 8y ago
  To be fair Pearl does not speak in the same terms as the statisticians. Collider is a weird word and an M structure is even weirder. Graphical models suffer similarly.
- deleted 8y ago
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banana_man 8y ago
Pearl's causal model is a decent didactic tool, but it seems to have little relevance when it comes to trying to figure out real-world problems. (If any actual scientific breakthroughs have come from Pearl's approach, I'd love to hear about them. I don't think there are any.) I believe the disagreement between Gelman and Pearl may come down to the fact that Gelman often deals with actual estimation problems where you have to find causal parameters using scanty and imperfect data, with no strong theory to guide decisions, while Pearl is focused on toy models where all the limitations and uncertainties of real problems are assumed away. Donald Rubin has said, surely correctly, that design trumps analysis in causal inference. Pearl's approach seems to be the opposite--all focus is on the analytical details. For practicing scientists, I think this article this article provides a much more useful model for causal inference: https://academic.oup.com/ije/article/45/6/1787/2617188 https://academic.oup.com/ije/article/45/6/1787/2617188 See Textbox 3 where different approaches to studying the relation between smoking and low birthweight are described. The various approaches rely on different assumptions and any one study design may not be convincing by itself, but the way their results converge ("triangulation") is very convincing. AFAIK, none of the studies used DAGs, yet the causal evidence provided is stronger than any DAG could provide.
- kgwgk 8y ago
  The formal approach to quantitative causal inference in epidemiology: misguided or misrepresented? https://academic.oup.com/ije/article/45/6/1817/2960059 https://academic.oup.com/ije/article/45/6/1817/2960059 There are other comments, and the authors’ reply: https://academic.oup.com/ije/issue/45/6 https://academic.oup.com/ije/issue/45/6
dmolony 8y ago
"Fisher would lager argue" I can't tell if this is a typo in the original text, or a typo from the person complaining about a lack of care.
ta1234567890 8y ago
Why is not a physical, mathematical or scientific question, but rather a philosophical one. Personally I believe there is no why (no causality at all). Rather we love to think it exists because it reduces our uncertainty. It's too much to accept our whole reality is just a bunch of random coincidences.
srean 8y ago
> "I’ve never been able to understand Pearl’s notation:" -- Gelman. That should not be surprising: "It is difficult to get a man to understand something when his salary depends upon his not understanding it." -- Upton Sinclair Accepting Pearl would amount to stating that some of the procedures we(statisticians) have been using, championing and sourcing funds for, for half a century are seriously flawed. Thats going to have consequences on future funding. Of course there will be resistance. Tony Hoare is worth paraphrasing -- some methods are so crisp and small that they are obviously correct. Others are so complex that one cannot find obvious errors. Piling on a hierarchy of random variables upon random variables and parameters upon prameters lies firmly in the latter class. This is actually a charitable analogy because some uses of statistical methods are incorrect but the error lies in incorrect use -- Using a tool or a technique to answer a question that it cannot answer. Smothering it with complexity and phrases like 'but real world', 'but noisy big data' helps to muddy the waters enough to deflect the attention from the fundamentals difference beween conditioning and intervening. I can be sympathetic to a claim that a method is more effective solving a complicated problem than a simple one. On the otherhand, if it turns out that the body of theory on which the proposed method has been built, the same proposed method that is presumably correct for the complicated case, cannot deal with a pedagogic toy scenario correctly, that raises my eyebrows.
drallison 8y ago
Judea's work and "The Book of Why" ought to be required reading for anyone who draws conclusions from data. People who do not understand statistics well enough to understand the book need to study statistical thinking until they do. Michael Nielson has a nice post (circa 2012) on the topic at http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/ http://www.michaelnielsen.org/ddi/if-correlation-doesnt-impl... with comments at http://www.michaelnielsen.org/ddi/guest-post-judea-pearl-on-correlation-causation-and-the-psychology-of-simpsons-paradox/ http://www.michaelnielsen.org/ddi/guest-post-judea-pearl-on-....

155 points by nkurz 8y ago

My comment on the blog was (at least initially) eaten by the spam filter, so I reproduce it here. --- JP: There is no way to answer causal questions without snapping out of statistical vocabulary. AG: We disagree. That’s fine. Science is full of disagreements, and there’s lots of room for progress using different methods. I'm only an amateur, but from the outside it sure doesn't feel "fine" for the two of you to disagree on what seems like such a fundamental issue. Instead, this seems like a case where two extremely smart individuals should be able to reach an common understanding instead of accepting disagreement as a final outcome. JP: I have tried to demonstrate it to you in the past several years, but was not able to get you to solve ONE toy problem from beginning to end. AG: For me and many others, one can indeed answer causal questions within statistical vocabulary. Pearl obviously disagrees that standard statistical vocabulary is sufficient to answer all simple causal questions. You seem to think he's wrong. I think you'd be doing a great service to encourage him to formulate such a "toy" question that he thinks is unanswerable without resorting to the do-calculus, which you then try to answer to the audiences' satisfaction using more standard techniques. Maybe the two of you turn out to be in agreement but using different terminology, maybe you are right that his tools are optional, or maybe he's right that they are essential. Any of these outcomes would feel much more satisfactory and productive than agreement to disagree. Please consider offering him a platform with which to make his case.

bachmeier 8y ago
> it sure doesn't feel "fine" for the two of you to disagree on what seems like such a fundamental issue. Instead, this seems like a case where two extremely smart individuals should be able to reach an common understanding instead of accepting disagreement as a final outcome. Once you've reached the limits of what you can know (after examining all data, worked through all arguments, etc.) this is pretty much the only possible outcome. What works in one situation might not work in others. One person's interpretation of our limited knowledge might very well appear implausible to someone else. I'll admit to being turned off by Pearl's insistence on working with "toy problems". That might be fine for a philosophical discussion, but it's not of much practical value. I want Pearl to write a few empirical papers attacking important issues, then let's have a discussion about putting ideas into practice.
- nkurz 8y ago
  I have much more sympathy for Pearl. He's constructed "toy" problems that yield different answers depending on the hidden causal structure chosen. He then shows that unless one takes account of the causal structure, it's impossible to correctly answer the problem. The logical conclusion of this is that any technique that doesn't use the causal structure as an explicit assumption is instead using it as an hidden implicit assumption. His hope is that anyone who goes through his exercise will come to the same conclusion. Starting with real-world problems is tricky, because one doesn't know the correct answer in advance, thus it's much harder show the reliance on the assumptions. Consider a parallel with computer programming. A user complains that they fear a program is giving them the wrong answer on a complex real world problem. They report this, and get back the unhelpful answer "Works for me, will not fix". Unable to shake the feeling that the answer is unreliable, they reduce the problem down to a proof of concept that serves as a simple self-contained test case. Two different inputs produce the same answer, but only one of them can be right! But now they are unable to convince the maintainer to even look at the test case, because now the maintainer says "I need to focus on the real world, and don't want to waste my time on toy examples". It's a discouraging position to find oneself in.
  - bachmeier 8y ago
    Oh, I'm completely on board with being explicit about any assumptions you're making, and for thinking deeply about the causal relations, and for thinking about the reliability of the analysis. I've been critical of economists for not thinking things through. And I'm definitely on board with teaching using toy problems. The problem is that, as far as I can tell, Pearl doesn't go beyond making points with toy problems. He hasn't done much empirical work (has he published a single empirical paper?) or even read much of the empirical literature he's criticizing as worthless. Ultimately, the question is whether policy and other decisions will be better using a particular framework. The fact that Pearl writes with the aggressive confidence of a Hacker News commenter does not mean he's right.
    - harperlee 8y ago
      But from a mathematical point of view this insistence of focusing on empirical work is a little bit disheartening isn’t it? And frankly Judea Pearl is hardly a random internet tinfoil hat guy, nor is he asking people to invest a massive effort checking his looong work (as we eg often see with random NP-completeness “proofs”, or was discussed with the time investment needed to check Mochizuki’s ABC proof - no, he just asks Gellman to apply his own familiar techniques to a toy problem. It does not sound unreasonable at all.
conjectures 8y ago
"you'd be doing a great service to encourage him to formulate such a "toy" question that he thinks is unanswerable without resorting to the do-calculus, which you then try to answer to the audiences' satisfaction using more standard techniques." This would be very helpful indeed. I think a lot of the issue comes down to how idiosyncratic Pearl's work is. It will have to accumulate quite a lot of victories before enough people will bother with it. Until then I suspect Causality will remain something of a statistical Finnegan's Wake. I'll probably read The Book of Why to try and get a better handle on motivation for the technical material.
- deleted 8y ago
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- notafraudster 8y ago
  Thankfully, "Causality: A Primer" is sort of like the CliffNotes to Finnegan's Wake ;)
  - conjectures 8y ago
    Thanks, may check it out. This stuff has long been on my to-do list.
mycorrhizal 8y ago
I think you are overstating Judea Pearl's argument. He doesn't claim it is impossible to answer causal questions (on observational data) without resorting to do-calculus. What he does claim is that to answer causal (interventional or counterfactual) questions you need to define a model and reason on that model in a way that transforms the question into conditional probabilities. Do-calculus provides a framework to help you perform that reasoning, but certainly people have been using things like the backdoor criterion before the invention of do-calculus to answer interventional questions. He might claim that any other method can be reduced to do-calculus. I'm not sure. I do believe at the core of his argument is need for an explicit model.
- nkurz 8y ago
  Yes, that's a better and more accurate phrasing than I used. The issue is that the correctness of the answer depends on the whether the causal structure of the model matches the underlying generative process. Graphs and do-calculus aren't required for this, but can help to make things clearer. In a later comment on the blog post, Pearl links to a paper that describes one of his "toy" examples: http://ftp.cs.ucla.edu/pub/stat_ser/r400-reprint.pdf http://ftp.cs.ucla.edu/pub/stat_ser/r400-reprint.pdf. Section 3 of page 584 is the beginning of the example. I'm sad to say that I'm sufficiently amateur at this that I found even the "toy" example to be at the limits of my reasoning ability, but I thought it still illustrated the argument Pearl is making.
  - mycorrhizal 8y ago
    I absolutely agree if your model is wrong any causal inferences you draw will be wrong. However his framework does provide mechanisms for determining if your data is inconsistent with your model (ie certain independences should or should not exist). So hopefully if your model is wrong your data will tell you so and you can change your model.
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tunesmith 8y ago
I'm not an expert on this stuff at all, but are the toy problems basically formulations of Simpson's paradox? My sense was that if you have a set of a data, where if you cut it into two slices and each slice suggests the same (identical) conclusion, but then if you look at the data overall it suggests a different conclusion, then how do you know which approach is correct? And it seems the only way to know that is to use your judgment about causal factors that generated the data, and the do-calculus helps make that explicit. For instance, when thinking about gender ratios and grad programs, it's more probable that the choice of what grad program to apply to is affected by what gender you are, but it's less probable that the choice of your grad program affects your gender. Well I just reviewed section 3 of page 584 of that pdf that was shared and it seems different, so I probably have a long way to go before I understand this stuff.
- xtacy 8y ago
  Not all "paradoxes" are similar to Simpson's paradox. See this PDF for more similar "paradoxes": https://ftp.cs.ucla.edu/pub/stat_ser/r409-corrected-reprint.pdf https://ftp.cs.ucla.edu/pub/stat_ser/r409-corrected-reprint.... (I quote the word paradox, because they aren't really paradoxes once we have an understanding of what's going on.)

DevX101 8y ago

For anyone interested in this book, I'm going through it now but it addresses an important question of how to identify causality. We've all become familiar with the refrain 'correlation does not imply causation'. This book attempts to answer: 'what DOES imply causation'? He introduces a framework for how one can answer this question. Not very mathematically rigorous, but following through the framework does appear to be able to discover non-intuitive causative conclusions. Understanding causation will have important implications for the advancement of A.I. Finding a correlation with the causes hidden in a black box (current state of deep learning) isn't enough for many disciplines. Doctors for example will likely need to know WHY an algorithm made a decision, instead of simply running correlations and telling the operator that a patient has 80% chance of some diagnosis.

MAXPOOL 8y ago
It's possible to infer causation from correlation without experiments if you add some general assumptions. One trick in causal discovery is additive noise. If X and Y are noisy correlating variables and X is causing Y, assumption that the noise in X is present in Y but not vice versa may reveal the direction of the causal arrow. Causal Discovery with Continuous Additive Noise Models http://jmlr.org/papers/volume15/peters14a/peters14a.pdf http://jmlr.org/papers/volume15/peters14a/peters14a.pdf Nonlinear causal discovery with additive noise models https://papers.nips.cc/paper/3548-nonlinear-causal-discovery-with-additive-noise-models.pdf https://papers.nips.cc/paper/3548-nonlinear-causal-discovery... Humans seem to have causal reasoning ability that is very ad hoc. It works well in practice but it's not principled. There is not enough time to do experiments to establish facts. Correlation is causality seems to be a good heuristics. I think that that AI will eventually learn to build causal models in the same way. Build a quick and dirty causal models with unfounded assumptions and see what works. Hold multiple effective conflicting causal theories that apply in different situations without any consistent model.
- ionforce 8y ago
  I feel like I don't have the background to fully understand what you're saying. Could you explain this in a more lay way? > X and Y are noisy correlating variables

baron816 8y ago

I tried to listen to the audiobook of this. Terrible idea. One of the few audiobooks I’ve abandoned.

lolptdr 8y ago
Why was it bad? I'm not an audiobook listener so I don't know what's considered bad.
- DevX101 8y ago
  Audiobooks for dense non-fiction material is usually a bad idea. I'd recommend audio for fiction, or non-fiction with an engaging storyline (ex: Bad Blood), which this is not. Nonetheless, I'd still recommend the book.
- ffn 8y ago
  It's an user-experience problem: for an audiobook, Book of Why is quite dense in formula that are hard to visualize when spoke as words. For example, consider what happens if we try to describe a causal diagram in words "A points to B, A points to X, B points to Y, and X points to Y. Now, if we apply do(X) to the diagram, we see that we can Y is now no longer a child of..." or even simple formulas in words: "P of A given B times P of B is equal to P of B given A times P of A" For most of us, this sort of deal is hard to "get" and would be much better served if we just looked at a visual diagram or saw the equation. I personally had to repeat many sections over and over again with a notebook and pencil in hand to truly understand what was being read to me... but if I'm taking notes and creating visuals for myself, then I might as well have just gotten the paper variant of this book lol.
- mindcrime 8y ago
  There are a lot of diagrams and a bit of math, which don't naturally translate to a purely auditory experience very well. Having read The Book of Why I can't imagine how it would translate to a reasonable audio-book. Frankly I'm surprised they even released an audio-book version at all.
owaty 8y ago

notafraudster 8y ago

As someone who does social science causal inference for a living, I have to say that I didn't really enjoy "The Book of Why". Full disclosure: I mostly practice the Neyman-Rubin potential outcomes form of causal inference rather than the Pearl do-calculus / DAG ("directed acyclic graph") form of causal inference, but the two are in many cases equivalent. The reason I didn't like the book is that I found it insufficiently rigorous to really engage with the "how" of doing causal inference, but excessively mathematical as a theoretical introduction to causality. "Causality: A Primer" (also written by Pearl) is a very short book that I think does a good job of surfacing some of the same theoretical background while also explaining how to use Pearl's causality. If you exhaust that, I'd recommend moving to the full "Causality" book. But otherwise I'd recommend actually looking into the counterfactual / potential outcomes view of causality. The set of questions it answers are about 80% overlapping (although both Pearl and POs have their own 20%), but I find the vocabulary a little more intuitive. Canonical books include Morgan and Winship "Counterfactuals and Causal Inference" or Imbens and Rubin "Causal Inference for Social Scientists". As to the blog post, Pearl is correct that causality requires qualitative assumptions about design to justify assumptions required to do causal inference. In Pearl's work this is often motivated as qualitative knowledge informing the structure of the DAG before any estimation. But recent advances in causal discovery have actually rendered it possible to black box the structure of a DAG from data -- happy to provide citations if this is down the rabbit hole. By contrast, I agree with Gelman that Pearl is an irritating writer and that in "The Book of Why" he gives a sloppy intellectual history of causation.

breuderink 8y ago
> But recent advances in causal discovery have actually rendered it possible to black box the structure of a DAG from data -- happy to provide citations if this is down the rabbit hole. I would be very interested in these references.
- notafraudster 8y ago
  I should say this is not my wing of the world since in social science typically theory precedes estimation and there would be a strong disciplinary norm against "I have no idea what causes what". So I don't actually use this stuff. That being said, I have played with a few of the packages and read a few pieces on causal discovery. Jonas Peters et al. - Elements of Causal Inference is a textbook that covers a little bit of what they called "learning cause-effect models". For algorithms, check SGS (Spirtes-Glymour-Scheines) and PC (Peter Spirtes and Clark Glymour). I believe both these algorithms are implemented in R in the package `pcalg`. There's another R package on BioConductor that implements them too, but I'm far enough afield from biostats I don't remember the name or have any notes I can find. Some recent cites of note: Peters and Buhlmann - "Identifiability of Gaussian structural equation models" (2014), which led to Ghoshal and Honorio - "Learning linear structural equation models in polynomial time" (2018) who generalize the Peters/Buhlmann claim. Other authors to Google: Dominik Janzig; Joris Mooij; Patrik Hoyer -- all of these people write papers with the above people, so you should be able to map out the network. What the pieces all have in common is that they're trying to establish empirical differences in the joint distributions of X and Y between scenarios where X -> Y and where Y -> X. This is only possible in some cases. Hope this helps.

svat 8y ago

A discussion about this book on the statistics StackExchange, with some interesting answers: "The Book of Why by Judea Pearl: Why is he bashing statistics?" https://stats.stackexchange.com/questions/376920/the-book-of-why-by-judea-pearl-why-is-he-bashing-statistics https://stats.stackexchange.com/questions/376920/the-book-of...

nkurz 8y ago
Yes, that has lots of great stuff in the comments. One of them (convolutedly just added based on a link provided in a comment on the Gelman blog post) was to this review: https://www.kdnuggets.com/2018/06/gray-pearl-book-of-why.html https://www.kdnuggets.com/2018/06/gray-pearl-book-of-why.htm.... The review, and then back-and-forth at the bottom and in comments between Gray and Pearl are wonderful context.
- kgwgk 8y ago
  The irony in this comment is priceless: “Simpson’s paradox in its various forms is something that generations of researchers and statisticians have been trained to look out for. And we do. There is nothing mysterious about it. (This debate regarding Simpsons, which appeared in The American Statistician in 2014, and which I link in the article, hopefully will be visible to readers who are not ASA members.)” There is nothing mysterious about Simpson’s paradox but the proper answer is still being debated! Pearl’s response ends as follows: “The next step is to let the community explore: 1) How many statisticians can actually answer Simpson’s question, and 2) How to make that number reach 90%. I believe The Book of Why has already doubled that number, which is some progress. It is in fact something that I was not able to do in the past thirty years through laborious discussions with the leading statisticians of our time. It is some progress, let’s continue.” http://causality.cs.ucla.edu/blog/index.php/2018/06/15/a-statisticians-re-reaction-to-the-book-of-why http://causality.cs.ucla.edu/blog/index.php/2018/06/15/a-sta...

digitalzombie 8y ago

I tried reading Pearl once. I couldn't get over his tone. Andrew Gelman summarize it pretty nicely his take on it. Coming from a statistic background, casual inference is a growing thing now and several government sponsor research have been pushing for it. Casual inference from statistic point of view is base on missing data, basically Rudin stuff. It's pretty dang interesting to me. I'm sure there are many ways of looking at the same thing. Linear regression you can look at it in more of a optimal math problem with cost function or you can look at it in statitic using maximum likelihood estimation. Both have it's pro and con, with MLE you get a confidence interval. In my bias opinion I feel that statistic is only about data and it's a great domain for casual inference. There's no need to put a field down to make yours better. But if it's constructive criticism (pro/con, contrast) I think it make both fields better. Pearl attitude is off putting when you try to read his stuff. We're all human and have vary degree of ego, if you're going to try to convince us that do calculus and your ways is better be objective about it or word things better. If you don't want to convince people then just be blunt as hell.

haberman 8y ago

As a non-statistician with a lot of interest in statistics, I found the Book of Why frustrating. Modeling causation seems like an undeniably important step towards understanding the world better. But the biggest question I had was: how can you actually verify that your causal model is true? This is not clearly explained, or wasn't before I gave up on the book. Models are only useful if we can have some confidence that they correspond to reality. I was especially interested in the answer to this question, because my only exposure to the language of "causal chains" has been on Twitter, where they seemed to serve a distinctly ideological purpose. One (non-mathematical) person says "I think X is caused by Y", and then a statistician chimes in and says "you're missing other parts of the causal chain, the real causes are Z and Q." Where of course, Z and Q are things that one political perspective prefers to blame, and Y are things blamed by the other side. For example: https://twitter.com/gztstatistics/status/1000914269188296709 https://twitter.com/gztstatistics/status/1000914269188296709. Here's a great comment from today about the difficulty of establishing causality in practice: https://news.ycombinator.com/item?id=18886275 https://news.ycombinator.com/item?id=18886275 I want to know how causal chains can be actually proven or falsified, to be convinced that this isn't just highbrow ideological woo.

kgwgk 8y ago
> how can you actually verify that your causal model is true? This is addressed in the introduction. See box 4 in the flow-chart (“testable implications”). “The listening pattern prescribed by the paths of the causal model usually results in observable patterns or dependencies in the data. [...] If the data contradict this implication, then we need to revise our model.”
- haberman 8y ago
  The part you removed with ellipses undermines this point: "These patterns are called "testable implications" because they can be used for testing the model. These are statements like "There is no path connecting D and L," which translates to a statistical statement, "D and L are independent," that is, finding D does not change the likelihood of L." This says nothing about testing causality, or the direction of causality. If two things are uncorrelated, then there is probably not a causal relationship between them, granted. But this is not a very novel or useful observation. However if D and L are correlated, the test above says nothing about how to validate whether D caused L, L caused D, both were caused by a third thing (or set of things), or the correlation is just coincidence. For a book whose entire thesis is "causality is rigorous," I expect a much more rigorous treatment of how to validate causality using more than mere correlation.

stewbrew 8y ago

So, AG writes a sloppy review to complain about a sloppy mischaracterization of (mostly classic) statisticians. "About the exposition of causal inference, I have little to say." That would have been interesting though.

kgwgk 8y ago

Relevant online course: https://www.edx.org/course/causal-diagrams-draw-assumptions-harvardx-ph559x https://www.edx.org/course/causal-diagrams-draw-assumptions-...

owaty 8y ago

To counter some of the comments here, I absolutely loved the book and went on to recommend it to all my scientist friends. While it may get a bit technical for the lay audience, it should be within reach for a typical scientist or IT person. I wish our society had a better understanding of causality—that would raise the level of many important discussions. Being a long-time fan of Gelman (and having studied his Bayesian Data Analysis textbook), I am baffled and disappointed that he doesn't seem to understand Pearl's ideas. In his linked 2009 post[1], he wrote: "I’ve never been able to understand Pearl’s notation: notions such as a “collider of an M-structure” remain completely opaque to me." I wonder if, after reading this book accessible even to non-statisticans, he still doesn't understand it. [1]: https://statmodeling.stat.columbia.edu/2009/07/05/disputes_about/ https://statmodeling.stat.columbia.edu/2009/07/05/disputes_a...

mindcrime 8y ago
To counter some of the comments here, I absolutely loved the book and went on to recommend it to all my scientist friends. Likewise (well, other than not really having any "scientist friends"). I loved this book, think Pearl has some amazingly valuable ideas, and found the book relatively accessible even though I'm not a statistician. I won't claim to have understood every detail on the first reading, but I got enough out of it to feel like I'll understand it all after a couple of follow on readings, plus consulting Pearl's other books. I wish our society had a better understanding of causality—that would raise the level of many important discussions. Absolutely.
sjg007 8y ago
To be fair Pearl does not speak in the same terms as the statisticians. Collider is a weird word and an M structure is even weirder. Graphical models suffer similarly.
deleted 8y ago
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banana_man 8y ago

Pearl's causal model is a decent didactic tool, but it seems to have little relevance when it comes to trying to figure out real-world problems. (If any actual scientific breakthroughs have come from Pearl's approach, I'd love to hear about them. I don't think there are any.) I believe the disagreement between Gelman and Pearl may come down to the fact that Gelman often deals with actual estimation problems where you have to find causal parameters using scanty and imperfect data, with no strong theory to guide decisions, while Pearl is focused on toy models where all the limitations and uncertainties of real problems are assumed away. Donald Rubin has said, surely correctly, that design trumps analysis in causal inference. Pearl's approach seems to be the opposite--all focus is on the analytical details. For practicing scientists, I think this article this article provides a much more useful model for causal inference: https://academic.oup.com/ije/article/45/6/1787/2617188 https://academic.oup.com/ije/article/45/6/1787/2617188 See Textbox 3 where different approaches to studying the relation between smoking and low birthweight are described. The various approaches rely on different assumptions and any one study design may not be convincing by itself, but the way their results converge ("triangulation") is very convincing. AFAIK, none of the studies used DAGs, yet the causal evidence provided is stronger than any DAG could provide.

kgwgk 8y ago
The formal approach to quantitative causal inference in epidemiology: misguided or misrepresented? https://academic.oup.com/ije/article/45/6/1817/2960059 https://academic.oup.com/ije/article/45/6/1817/2960059 There are other comments, and the authors’ reply: https://academic.oup.com/ije/issue/45/6 https://academic.oup.com/ije/issue/45/6

dmolony 8y ago

"Fisher would lager argue" I can't tell if this is a typo in the original text, or a typo from the person complaining about a lack of care.

ta1234567890 8y ago

Why is not a physical, mathematical or scientific question, but rather a philosophical one. Personally I believe there is no why (no causality at all). Rather we love to think it exists because it reduces our uncertainty. It's too much to accept our whole reality is just a bunch of random coincidences.

srean 8y ago

> "I’ve never been able to understand Pearl’s notation:" -- Gelman. That should not be surprising: "It is difficult to get a man to understand something when his salary depends upon his not understanding it." -- Upton Sinclair Accepting Pearl would amount to stating that some of the procedures we(statisticians) have been using, championing and sourcing funds for, for half a century are seriously flawed. Thats going to have consequences on future funding. Of course there will be resistance. Tony Hoare is worth paraphrasing -- some methods are so crisp and small that they are obviously correct. Others are so complex that one cannot find obvious errors. Piling on a hierarchy of random variables upon random variables and parameters upon prameters lies firmly in the latter class. This is actually a charitable analogy because some uses of statistical methods are incorrect but the error lies in incorrect use -- Using a tool or a technique to answer a question that it cannot answer. Smothering it with complexity and phrases like 'but real world', 'but noisy big data' helps to muddy the waters enough to deflect the attention from the fundamentals difference beween conditioning and intervening. I can be sympathetic to a claim that a method is more effective solving a complicated problem than a simple one. On the otherhand, if it turns out that the body of theory on which the proposed method has been built, the same proposed method that is presumably correct for the complicated case, cannot deal with a pedagogic toy scenario correctly, that raises my eyebrows.

drallison 8y ago

Judea's work and "The Book of Why" ought to be required reading for anyone who draws conclusions from data. People who do not understand statistics well enough to understand the book need to study statistical thinking until they do. Michael Nielson has a nice post (circa 2012) on the topic at http://www.michaelnielsen.org/ddi/if-correlation-doesnt-imply-causation-then-what-does/ http://www.michaelnielsen.org/ddi/if-correlation-doesnt-impl... with comments at http://www.michaelnielsen.org/ddi/guest-post-judea-pearl-on-correlation-causation-and-the-psychology-of-simpsons-paradox/ http://www.michaelnielsen.org/ddi/guest-post-judea-pearl-on-....