Causal Analysis in Theory and Practice

June 15, 2018

A Statistician’s Re-Reaction to The Book of Why

Filed under: Book (J Pearl),Discussion,Simpson's Paradox — Judea Pearl @ 2:29 am

Responding to my June 11 comment, Kevin Gray posted a reply on kdnuggets.com in which he doubted the possibility that the Causal Revolution has solved problems that generations of statisticians and philosophers have labored over and could not solve. Below is my reply to Kevin’s Re-Reaction, which I have also submitted to kdhuggets.com:

Dear Kevin,
I am not suggesting that you are only superficially acquainted with my works. You actually show much greater acquaintance than most statisticians in my department, and I am extremely appreciative that you are taking the time to comment on The Book of Why. You are showing me what other readers with your perspective would think about the Book, and what they would find unsubstantiated or difficult to swallow. So let us go straight to these two points (i.e., unsubstantiated and difficult to swallow) and give them an in-depth examination.

You say that I have provided no evidence for my claim: “Even today, only a small percentage of practicing statisticians can solve any of the causal toy problems presented in the Book of Why.” I believe that I did provide such evidence, in each of the Book’s chapters, and that the claim is valid once we agree on what is meant by “solve.”

Let us take the first example that you bring, Simpson’s paradox, which is treated in Chapter 6 of the Book, and which is familiar  to every red-blooded statistician. I characterized the paradox in these words: “It has been bothering statisticians for more than sixty years – and it remains vexing to this very day” (p. 201). This was, as you rightly noticed, a polite way of saying: “Even today, the vast majority of statisticians cannot solve Simpson’s paradox,” a fact which I strongly believe to be true.

You find this statement hard to swallow, because: “generations of researchers and statisticians have been trained to look out for it [Simpson’s Paradox]” an observation that seems to contradict my claim. But I beg you to note that “trained to look out for it” does not make the researchers capable of “solving it,” namely capable of deciding what to do when the paradox shows up in the data.

This distinction appears vividly in the debate that took place in 2014 on the pages of The American Statistician, which you and I cite.  However, whereas you see the disagreements in that debate as evidence that statisticians have several ways of resolving Simpson’s paradox, I see it as evidence that they did not even come close. In other words, none of the other participants presented a method for deciding whether the aggregated data or the segregated data give the correct answer to the question: “Is the treatment helpful or harmful?”

Please pay special attention to the article by Keli Liu and Xiao-Li Meng, both are from Harvard’s department of statistics (Xiao-Li is a senior professor and a Dean), so they cannot be accused of misrepresenting the state of statistical knowledge in 2014. Please read their paper carefully and judge for yourself whether it would help you decide whether treatment is helpful or not, in any of the examples presented in the debate.

It would not!! And how do I know? I am listening to their conclusions:

  1. They disavow any connection to causality (p.18), and
  2. They end up with the wrong conclusion. Quoting: “less conditioning is most likely to lead to serious bias when Simpson’s Paradox appears.” (p.17) Simpson himself brings an example where conditioning leads to more bias, not less.

I dont blame Liu and Meng for erring on this point, it is not entirely their fault (Rosenbaum and Rubin made the same error). The correct solution to Simpson’s dilemma rests on the back-door criterion, which is almost impossible to articulate without the aid of DAGs. And DAGs, as you are probably aware, are forbidden from entering a 5 mile no-fly zone around Harvard [North side, where the statistics department is located].

So, here we are. Most statisticians believe that everyone knows how to “watch for” Simpson’s paradox, and those who seek an answer to: “Should we treat or not?” realize that “watching” is far from “solving.” Moreover, the also realize that there is no solution without stepping outside the comfort zone of statistical analysis and entering the forbidden city of causation and graphical models.

One thing I do agree with you — your warning about the implausibility of the Causal Revolution. Quoting: “to this day, philosophers disagree about what causation is, thus to suggest he has found the answer to it is not plausible”.  It is truly not plausible that someone, especially a semi-outsider, has found a Silver Bullet. It is hard to swallow. That is why I am so excited about the Causal Revolution and that is why I wrote the book. The Book does not offer a Silver Bullet to every causal problem in existence, but it offers a solution to a class of problems that centuries of statisticians and Philosophers tried and could not crack. It is implausible, I agree, but it happened. It happened not because I am smarter but because I took Sewall Wright’s idea seriously and milked it to its logical conclusions as much as I could.

It took quite a risk on my part to sound pretentious and call this development a Causal Revolution. I thought it was necessary. Now I am asking you to take a few minutes and judge for yourself whether the evidence does not justify such a risky characterization.

It would be nice if we could alert practicing statisticians, deeply invested in the language of statistics to the possibility that paradigm shifts can occur even in the 21st century, and that centuries of unproductive debates do not make such shifts impossible.

You were right to express doubt and disbelief in the need for a paradigm shift, as would any responsible scientist in your place. 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,
Judea

Comments (4)

June 11, 2018

A Statistician’s Reaction to The Book of Why

Filed under: Book (J Pearl) — Judea Pearl @ 12:37 am

Carlos Cinelli brough to my attention a review of The Book of Why, written by Kevin Gray, who disagrees with my claim that statistics has been  delinquent in neglecting causality. See https://www.kdnuggets.com/2018/06/gray-pearl-book-of-why.html I have received similar reactions from statisticians in the past, and I expect more in the future. These reactions reflect a linguistic dissonance which The Book of Why describes thus: “Many scientists have been quite traumatized to learn that none of the methods they learned in statistics is sufficient even to articulate, let alone answer, a simple question like ‘What happens if we double the price?'” p 31.

I have asked Carlos to post the following response on Kevin’s blog:

————————————————
Kevin’s prediction that many statisticians may find  my views “odd or exaggerated” is accurate. This is exactly what I have found in numerous conversations I have had with statisticians in the past 30 years. However, if you examine my views closely,  you will find that they are not as thoughtless or exaggerated as they may appear at first sight.

Of course many statisticians will scratch their heads and ask: “Isn’t this what we have been doing for years, though perhaps under a different name or not name at all?” And here lies the essence of my views. Doing it informally, under various names, while refraining from doing it mathematically under uniform notation has had a devastating effect on progress in causal inference, both in statistics and in the many disciplines that look to statistics for guidance. The best evidence for this lack of progress is the fact that, even today, only a small percentage of practicing statisticians can solve any of the causal toy problems presented in the Book of Why.

Take for example:

  1. Selecting a sufficient set of covariates to control for confounding
  2. Articulating assumptions that would enable consistent estimates of causal effects
  3. Finding if those assumptions are testable
  4. Estimating causes of effect (as opposed to effects of cause)
  5. More and more.

Every chapter of The Book of Why brings with it a set of problems that statisticians were deeply concerned about, and have been struggling with for years,  albeit under the wrong name (eg. ANOVA or MANOVA) “or not name at all.” The results are many deep concerns but no solution.

A valid question to be asked at this point is what gives humble me the audacity to state so sweepingly that no statistician (in fact no scientist) was able to properly solve those toy problems prior to the 1980’s. How can one be so sure that some bright statistician or philosopher did not come up with the correct resolution of the Simpson’s paradox or a correct way to distinguish direct from indirect effects? The answer is simple: we can see it in the syntax of the equations that scientists used in the 20th century.  To properly define causal problems, let alone solve them, requires a vocabulary that resides outside the language of probability theory. This means that all the smart and brilliant statisticians who used joint density functions, correlation analysis, contingency tables, ANOVA, Entropy, Risk Ratios, etc., etc., and did not enrich them with either diagrams or counterfactual symbols have been laboring in vain — orthogonally to the question — you can’t answer a question if you have no words to ask it. (Book of Why, page 10)

It is this notational litmus test that gives me the confidence to stand behind each one of statements that you were kind enough to cite from the Book of Why. Moreover, if you look closely at this litmus test, you will find that it not just notational but conceptual and practical as well. For example, Fisher’s blunder of using ANOVA to estimate direct effects is still haunting the practices of present day mediation analysts. Numerous other examples are described in the Book of Why and I hope you weigh seriously the lesson that each of them conveys.

Yes, many of your friends and colleagues will be scratching their head saying: “Hmmm… Isn’t this what we have been doing for years, though perhaps under a different name or not name at all?” What I hope you will be able to do after reading “The Book of Why” is to catch some of the head-scratchers and tell them: “Hey, before you scratch further, can you solve any of the toy problems in the Book of Why?” You will be surprised by the results — I was!
————————————————

To me, solving problems is the test of understanding, not head scratching. That is why I wrote this Book.

Judea

Comments (5)

June 7, 2018

Updates on The Book of Why

Filed under: Announcement,Book (J Pearl) — Judea Pearl @ 11:54 pm

Dear friends in causality research,

Three months ago, I sent you a special greeting, announcing the forthcoming publication of The Book of Why (Basic Books, co-authored with Dana MacKenzie). Below please find an update.

The Book came out on May 15, 2018, and has since been featured by the Wall Street Journal, Quanta Magazine, and The Times of London. You can view these articles here:
http://bayes.cs.ucla.edu/WHY/

Eager to allay public fears of the dangers of artificial intelligence, these three articles interpreted my critics of model-blind learning as general impediments to AI and machine learning. This has probably helped put the Book on Amazon’s #1 bestseller lists in several categories.

However, the limitations of current machine learning techniques are only part of the message conveyed in the Book of Why. The second, and more important part of the Book describes how these limitations are circumvented through the use of causal models, however qualitative or incomplete. The impacts that causal modeling has had on the social and health sciences make it only natural that a similar ‘revolution’ will soon be sweeping machine learning research, and liberate it from its current predicaments of opaqueness, forgetfulness and lack of explainability. (See, for example, http://www.sciencemag.org/news/2018/05/ai-researchers-allege-machine-learning-alchemy and https://arxiv.org/pdf/1801.00631.pdf)

I was happy therefore to see that this positive message was understood by many readers who wrote to me about the book, especially readers coming from traditional machine learning background (See, for example, www.inference.vc/untitled). It was also recognized by a more recent review in the New York Times
https://www.nytimes.com/2018/06/01/business/dealbook/review-the-book-of-why-examines-the-science-of-cause-and-effect.html which better reflects my optimism about what artificial intelligence can achieve.

I am hoping that you and your students will find inspiration in the optimistic message of the Book of Why, and that you take active part in the on-going development of “model-assisted machine learning.”

Sincerely,

Judea

Comments (1)
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