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The Book of Why
The New Science of Cause and Effect
By Judea Pearl
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“Correlation is not causation.” This mantra, chanted by scientists for more than a century, has led to a virtual prohibition on causal talk. Today, that taboo is dead. The causal revolution, instigated by Judea Pearl and his colleagues, has cut through a century of confusion and established causality — the study of cause and effect — on a firm scientific basis. His work explains how we can know easy things, like whether it was rain or a sprinkler that made a sidewalk wet; and how to answer hard questions, like whether a drug cured an illness. Pearl’s work enables us to know not just whether one thing causes another: it lets us explore the world that is and the worlds that could have been. It shows us the essence of human thought and key to artificial intelligence. Anyone who wants to understand either needs The Book of Why.
ALMOST two decades ago, when I wrote the preface to my book Causality (2000), I made a rather daring remark that friends advised me to tone down. “Causality has undergone a major transformation,” I wrote, “from a concept shrouded in mystery into a mathematical object with well-defined semantics and well-founded logic. Paradoxes and controversies have been resolved, slippery concepts have been explicated, and practical problems relying on causal information that long were regarded as either metaphysical or unmanageable can now be solved using elementary mathematics. Put simply, causality has been mathematized.”
Reading this passage today, I feel I was somewhat shortsighted. What I described as a “transformation” turned out to be a “revolution” that has changed the thinking in many of the sciences. Many now call it “the Causal Revolution,” and the excitement that it has generated in research circles is spilling over to education and applications. I believe the time is ripe to share it with a broader audience.
This book strives to fulfill a three-pronged mission: first, to lay before you in nonmathematical language the intellectual content of the Causal Revolution and how it is affecting our lives as well as our future; second, to share with you some of the heroic journeys, both successful and failed, that scientists have embarked on when confronted by critical cause-effect questions.
Finally, returning the Causal Revolution to its womb in artificial intelligence, I aim to describe to you how robots can be constructed that learn to communicate in our mother tongue—the language of cause and effect. This new generation of robots should explain to us why things happened, why they responded the way they did, and why nature operates one way and not another. More ambitiously, they should also teach us about ourselves: why our mind clicks the way it does and what it means to think rationally about cause and effect, credit and regret, intent and responsibility.
When I write equations, I have a very clear idea of who my readers are. Not so when I write for the general public—an entirely new adventure for me. Strange, but this new experience has been one of the most rewarding educational trips of my life. The need to shape ideas in your language, to guess your background, your questions, and your reactions, did more to sharpen my understanding of causality than all the equations I have written prior to writing this book.
For this I will forever be grateful to you. I hope you are as excited as I am to see the results.
Los Angeles, October 2017
INTRODUCTION: MIND OVER DATA
Every science that has thriven has thriven upon its own symbols.
—AUGUSTUS DE MORGAN (1864)
THIS book tells the story of a science that has changed the way we distinguish facts from fiction and yet has remained under the radar of the general public. The consequences of the new science are already impacting crucial facets of our lives and have the potential to affect more, from the development of new drugs to the control of economic policies, from education and robotics to gun control and global warming. Remarkably, despite the diversity and apparent incommensurability of these problem areas, the new science embraces them all under a unified framework that was practically nonexistent two decades ago.
The new science does not have a fancy name: I call it simply “causal inference,” as do many of my colleagues. Nor is it particularly high-tech. The ideal technology that causal inference strives to emulate resides within our own minds. Some tens of thousands of years ago, humans began to realize that certain things cause other things and that tinkering with the former can change the latter. No other species grasps this, certainly not to the extent that we do. From this discovery came organized societies, then towns and cities, and eventually the science- and technology-based civilization we enjoy today. All because we asked a simple question: Why?
Causal inference is all about taking this question seriously. It posits that the human brain is the most advanced tool ever devised for managing causes and effects. Our brains store an incredible amount of causal knowledge which, supplemented by data, we could harness to answer some of the most pressing questions of our time. More ambitiously, once we really understand the logic behind causal thinking, we could emulate it on modern computers and create an “artificial scientist.” This smart robot would discover yet unknown phenomena, find explanations to pending scientific dilemmas, design new experiments, and continually extract more causal knowledge from the environment.
But before we can venture to speculate on such futuristic developments, it is important to understand the achievements that causal inference has tallied thus far. We will explore the way that it has transformed the thinking of scientists in almost every data-informed discipline and how it is about to change our lives.
The new science addresses seemingly straightforward questions like these:
• How effective is a given treatment in preventing a disease?
• Did the new tax law cause our sales to go up, or was it our advertising campaign?
• What is the health-care cost attributable to obesity?
• Can hiring records prove an employer is guilty of a policy of sex discrimination?
• I’m about to quit my job. Should I?
These questions have in common a concern with cause-and-effect relationships, recognizable through words such as “preventing,” “cause,” “attributable to,” “policy,” and “should I.” Such words are common in everyday language, and our society constantly demands answers to such questions. Yet, until very recently, science gave us no means even to articulate, let alone answer, them.
By far the most important contribution of causal inference to mankind has been to turn this scientific neglect into a thing of the past. The new science has spawned a simple mathematical language to articulate causal relationships that we know as well as those we wish to find out about. The ability to express this information in mathematical form has unleashed a wealth of powerful and principled methods for combining our knowledge with data and answering causal questions like the five above.
I have been lucky to be part of this scientific development for the past quarter century. I have watched its progress take shape in students’ cubicles and research laboratories, and I have heard its breakthroughs resonate in somber scientific conferences, far from the limelight of public attention. Now, as we enter the era of strong artificial intelligence (AI) and many tout the endless possibilities of Big Data and deep learning, I find it timely and exciting to present to the reader some of the most adventurous paths that the new science is taking, how it impacts data science, and the many ways in which it will change our lives in the twenty-first century.
When you hear me describe these achievements as a “new science,” you may be skeptical. You may even ask, Why wasn’t this done a long time ago? Say when Virgil first proclaimed, “Lucky is he who has been able to understand the causes of things” (29 BC). Or when the founders of modern statistics, Francis Galton and Karl Pearson, first discovered that population data can shed light on scientific questions. There is a long tale behind their unfortunate failure to embrace causation at this juncture, which the historical sections of this book will relate. But the most serious impediment, in my opinion, has been the fundamental gap between the vocabulary in which we cast causal questions and the traditional vocabulary in which we communicate scientific theories.
To appreciate the depth of this gap, imagine the difficulties that a scientist would face in trying to express some obvious causal relationships—say, that the barometer reading B tracks the atmospheric pressure P. We can easily write down this relationship in an equation such as B = kP, where k is some constant of proportionality. The rules of algebra now permit us to rewrite this same equation in a wild variety of forms, for example, P = B/k, k = B/P, or B–kP = 0. They all mean the same thing—that if we know any two of the three quantities, the third is determined. None of the letters k, B, or P is in any mathematical way privileged over any of the others. How then can we express our strong conviction that it is the pressure that causes the barometer to change and not the other way around? And if we cannot express even this, how can we hope to express the many other causal convictions that do not have mathematical formulas, such as that the rooster’s crow does not cause the sun to rise?
My college professors could not do it and never complained. I would be willing to bet that none of yours ever did either. We now understand why: never were they shown a mathematical language of causes; nor were they shown its benefits. It is in fact an indictment of science that it has neglected to develop such a language for so many generations. Everyone knows that flipping a switch will cause a light to turn on or off and that a hot, sultry summer afternoon will cause sales to go up at the local ice-cream parlor. Why then have scientists not captured such obvious facts in formulas, as they did with the basic laws of optics, mechanics, or geometry? Why have they allowed these facts to languish in bare intuition, deprived of mathematical tools that have enabled other branches of science to flourish and mature?
Part of the answer is that scientific tools are developed to meet scientific needs. Precisely because we are so good at handling questions about switches, ice cream, and barometers, our need for special mathematical machinery to handle them was not obvious. But as scientific curiosity increased and we began posing causal questions in complex legal, business, medical, and policy-making situations, we found ourselves lacking the tools and principles that mature science should provide.
Belated awakenings of this sort are not uncommon in science. For example, until about four hundred years ago, people were quite happy with their natural ability to manage the uncertainties in daily life, from crossing a street to risking a fistfight. Only after gamblers invented intricate games of chance, sometimes carefully designed to trick us into making bad choices, did mathematicians like Blaise Pascal (1654), Pierre de Fermat (1654), and Christiaan Huygens (1657) find it necessary to develop what we today call probability theory. Likewise, only when insurance organizations demanded accurate estimates of life annuity did mathematicians like Edmond Halley (1693) and Abraham de Moivre (1725) begin looking at mortality tables to calculate life expectancies. Similarly, astronomers’ demands for accurate predictions of celestial motion led Jacob Bernoulli, Pierre-Simon Laplace, and Carl Friedrich Gauss to develop a theory of errors to help us extract signals from noise. These methods were all predecessors of today’s statistics.
Ironically, the need for a theory of causation began to surface at the same time that statistics came into being. In fact, modern statistics hatched from the causal questions that Galton and Pearson asked about heredity and their ingenious attempts to answer them using cross-generational data. Unfortunately, they failed in this endeavor, and rather than pause to ask why, they declared those questions off limits and turned to developing a thriving, causality-free enterprise called statistics.
This was a critical moment in the history of science. The opportunity to equip causal questions with a language of their own came very close to being realized but was squandered. In the following years, these questions were declared unscientific and went underground. Despite heroic efforts by the geneticist Sewall Wright (1889–1988), causal vocabulary was virtually prohibited for more than half a century. And when you prohibit speech, you prohibit thought and stifle principles, methods, and tools.
Readers do not have to be scientists to witness this prohibition. In Statistics 101, every student learns to chant, “Correlation is not causation.” With good reason! The rooster’s crow is highly correlated with the sunrise; yet it does not cause the sunrise.
Unfortunately, statistics has fetishized this commonsense observation. It tells us that correlation is not causation, but it does not tell us what causation is. In vain will you search the index of a statistics textbook for an entry on “cause.” Students are not allowed to say that X is the cause of Y—only that X and Y are “related” or “associated.”
Because of this prohibition, mathematical tools to manage causal questions were deemed unnecessary, and statistics focused exclusively on how to summarize data, not on how to interpret it. A shining exception was path analysis, invented by geneticist Sewall Wright in the 1920s and a direct ancestor of the methods we will entertain in this book. However, path analysis was badly underappreciated in statistics and its satellite communities and languished for decades in its embryonic status. What should have been the first step toward causal inference remained the only step until the 1980s. The rest of statistics, including the many disciplines that looked to it for guidance, remained in the Prohibition era, falsely believing that the answers to all scientific questions reside in the data, to be unveiled through clever data-mining tricks.
Much of this data-centric history still haunts us today. We live in an era that presumes Big Data to be the solution to all our problems. Courses in “data science” are proliferating in our universities, and jobs for “data scientists” are lucrative in the companies that participate in the “data economy.” But I hope with this book to convince you that data are profoundly dumb. Data can tell you that the people who took a medicine recovered faster than those who did not take it, but they can’t tell you why. Maybe those who took the medicine did so because they could afford it and would have recovered just as fast without it.
Over and over again, in science and in business, we see situations where mere data aren’t enough. Most big-data enthusiasts, while somewhat aware of these limitations, continue the chase after data-centric intelligence, as if we were still in the Prohibition era.
As I mentioned earlier, things have changed dramatically in the past three decades. Nowadays, thanks to carefully crafted causal models, contemporary scientists can address problems that would have once been considered unsolvable or even beyond the pale of scientific inquiry. For example, only a hundred years ago, the question of whether cigarette smoking causes a health hazard would have been considered unscientific. The mere mention of the words “cause” or “effect” would create a storm of objections in any reputable statistical journal.
Even two decades ago, asking a statistician a question like “Was it the aspirin that stopped my headache?” would have been like asking if he believed in voodoo. To quote an esteemed colleague of mine, it would be “more of a cocktail conversation topic than a scientific inquiry.” But today, epidemiologists, social scientists, computer scientists, and at least some enlightened economists and statisticians pose such questions routinely and answer them with mathematical precision. To me, this change is nothing short of a revolution. I dare to call it the Causal Revolution, a scientific shakeup that embraces rather than denies our innate cognitive gift of understanding cause and effect.
The Causal Revolution did not happen in a vacuum; it has a mathematical secret behind it which can be best described as a calculus of causation, which answers some of the hardest problems ever asked about cause-effect relationships. I am thrilled to unveil this calculus not only because the turbulent history of its development is intriguing but even more because I expect that its full potential will be developed one day beyond what I can imagine… perhaps even by a reader of this book.
The calculus of causation consists of two languages: causal diagrams, to express what we know, and a symbolic language, resembling algebra, to express what we want to know. The causal diagrams are simply dot-and-arrow pictures that summarize our existing scientific knowledge. The dots represent quantities of interest, called “variables,” and the arrows represent known or suspected causal relationships between those variables—namely, which variable “listens” to which others. These diagrams are extremely easy to draw, comprehend, and use, and the reader will find dozens of them in the pages of this book. If you can navigate using a map of one-way streets, then you can understand causal diagrams, and you can solve the type of questions posed at the beginning of this introduction.
Though causal diagrams are my tool of choice in this book, as in the last thirty-five years of my research, they are not the only kind of causal model possible. Some scientists (e.g., econometricians) like to work with mathematical equations; others (e.g., hard-core statisticians) prefer a list of assumptions that ostensibly summarizes the structure of the diagram. Regardless of language, the model should depict, however qualitatively, the process that generates the data—in other words, the cause-effect forces that operate in the environment and shape the data generated.
Side by side with this diagrammatic “language of knowledge,” we also have a symbolic “language of queries” to express the questions we want answers to. For example, if we are interested in the effect of a drug (D) on lifespan (L), then our query might be written symbolically as: P(L | do(D)). In other words, what is the probability (P) that a typical patient would survive L years if made to take the drug? This question describes what epidemiologists would call an intervention or a treatment and corresponds to what we measure in a clinical trial. In many cases we may also wish to compare P(L | do(D)) with P(L | do(not-D)); the latter describes patients denied treatment, also called the “control” patients. The do-operator signifies that we are dealing with an intervention rather than a passive observation; classical statistics has nothing remotely similar to this operator.
We must invoke an intervention operator do(D) to ensure that the observed change in Lifespan L is due to the drug itself and is not confounded with other factors that tend to shorten or lengthen life. If, instead of intervening, we let the patient himself decide whether to take the drug, those other factors might influence his decision, and lifespan differences between taking and not taking the drug would no longer be solely due to the drug. For example, suppose only those who were terminally ill took the drug. Such persons would surely differ from those who did not take the drug, and a comparison of the two groups would reflect differences in the severity of their disease rather than the effect of the drug. By contrast, forcing patients to take or refrain from taking the drug, regardless of preconditions, would wash away preexisting differences and provide a valid comparison.
Mathematically, we write the observed frequency of Lifespan L among patients who voluntarily take the drug as P(L | D), which is the standard conditional probability used in statistical textbooks. This expression stands for the probability (P) of Lifespan L conditional on seeing the patient take Drug D. Note that P(L | D) may be totally different from P(L | do(D)). This difference between seeing and doing is fundamental and explains why we do not regard the falling barometer to be a cause of the coming storm. Seeing the barometer fall increases the probability of the storm, while forcing it to fall does not affect this probability.
This confusion between seeing and doing has resulted in a fountain of paradoxes, some of which we will entertain in this book. A world devoid of P(L | do(D)) and governed solely by P(L | D) would be a strange one indeed. For example, patients would avoid going to the doctor to reduce the probability of being seriously ill; cities would dismiss their firefighters to reduce the incidence of fires; doctors would recommend a drug to male and female patients but not to patients with undisclosed gender; and so on. It is hard to believe that less than three decades ago science did operate in such a world: the do-operator did not exist.
One of the crowning achievements of the Causal Revolution has been to explain how to predict the effects of an intervention without actually enacting it. It would never have been possible if we had not, first of all, defined the do-operator so that we can ask the right question and, second, devised a way to emulate it by noninvasive means.
When the scientific question of interest involves retrospective thinking, we call on another type of expression unique to causal reasoning called a counterfactual. For example, suppose that Joe took Drug D and died a month later; our question of interest is whether the drug might have caused his death. To answer this question, we need to imagine a scenario in which Joe was about to take the drug but changed his mind. Would he have lived?
Again, classical statistics only summarizes data, so it does not provide even a language for asking that question. Causal inference provides a notation and, more importantly, offers a solution. As with predicting the effect of interventions (mentioned above), in many cases we can emulate human retrospective thinking with an algorithm that takes what we know about the observed world and produces an answer about the counterfactual world. This “algorithmization of counterfactuals” is another gem uncovered by the Causal Revolution.
Counterfactual reasoning, which deals with what-ifs, might strike some readers as unscientific. Indeed, empirical observation can never confirm or refute the answers to such questions. Yet our minds make very reliable and reproducible judgments all the time about what might be or might have been. We all understand, for instance, that had the rooster been silent this morning, the sun would have risen just as well. This consensus stems from the fact that counterfactuals are not products of whimsy but reflect the very structure of our world model. Two people who share the same causal model will also share all counterfactual judgments.
Counterfactuals are the building blocks of moral behavior as well as scientific thought. The ability to reflect on one’s past actions and envision alternative scenarios is the basis of free will and social responsibility. The algorithmization of counterfactuals invites thinking machines to benefit from this ability and participate in this (until now) uniquely human way of thinking about the world.
My mention of thinking machines in the last paragraph is intentional. I came to this subject as a computer scientist working in the area of artificial intelligence, which entails two points of departure from most of my colleagues in the causal inference arena. First, in the world of AI, you do not really understand a topic until you can teach it to a mechanical robot. That is why you will find me emphasizing and reemphasizing notation, language, vocabulary, and grammar. For example, I obsess over whether we can express a certain claim in a given language and whether one claim follows from others. It is amazing how much one can learn from just following the grammar of scientific utterances. My emphasis on language also comes from a deep conviction that language shapes our thoughts. You cannot answer a question that you cannot ask, and you cannot ask a question that you have no words for. As a student of philosophy and computer science, my attraction to causal inference has largely been triggered by the excitement of seeing an orphaned scientific language making it from birth to maturity.
My background in machine learning has given me yet another incentive for studying causation. In the late 1980s, I realized that machines’ lack of understanding of causal relations was perhaps the biggest roadblock to giving them human-level intelligence. In the last chapter of this book, I will return to my roots, and together we will explore the implications of the Causal Revolution for artificial intelligence. I believe that strong AI is an achievable goal and one not to be feared precisely because causality is part of the solution. A causal reasoning module will give machines the ability to reflect on their mistakes, to pinpoint weaknesses in their software, to function as moral entities, and to converse naturally with humans about their own choices and intentions.
A BLUEPRINT OF REALITY
In our era, readers have no doubt heard terms like “knowledge,” “information,” “intelligence,” and “data,” and some may feel confused about the differences between them or how they interact. Now I am proposing to throw another term, “causal model,” into the mix, and the reader may justifiably wonder if this will only add to the confusion.
It will not! In fact, it will anchor the elusive notions of science, knowledge, and data in a concrete and meaningful setting, and will enable us to see how the three work together to produce answers to difficult scientific questions. Figure I.1 shows a blueprint for a “causal inference engine” that might handle causal reasoning for a future artificial intelligence. It’s important to realize that this is not only a blueprint for the future but also a guide to how causal models work in scientific applications today and how they interact with data.
The inference engine is a machine that accepts three different kinds of inputs—Assumptions, Queries, and Data—and produces three kinds of outputs. The first of the outputs is a Yes/No decision as to whether the given query can in theory be answered under the existing causal model, assuming perfect and unlimited data. If the answer is Yes, the inference engine next produces an Estimand. This is a mathematical formula that can be thought of as a recipe for generating the answer from any hypothetical data, whenever they are available. Finally, after the inference engine has received the Data input, it will use the recipe to produce an actual Estimate for the answer, along with statistical estimates of the amount of uncertainty in that estimate. This uncertainty reflects the limited size of the data set as well as possible measurement errors or missing data.
To dig more deeply into the chart, I have labeled the boxes 1 through 9, which I will annotate in the context of the query “What is the effect of Drug D on Lifespan L?”
- One of Science Friday's "Best Science Books of 2018"
- "Illuminating... The Professor Pearl who emerges from the pages of The Book of Why brims with the joy of discovery and pride in his students and colleagues... [it] not only delivers a valuable lesson on the history of ideas but provides the conceptual tools needed to judge just what big data can and cannot deliver."—New York Times
- "Cause and effect is one of the most heavily debated, difficult-to-prove things in science and medicine. This book really gets you thinking about cause and effect as it applies to issues of our time, such as: How come cigarettes were around for years and we never showed they were causing cancer or heart disease? The authors goes through these cases like an interrogation, and it's just extraordinary."—Science Friday
- "Seriously, everyone should read The Book of Why."—Jeff Witmer, American Mathematical Monthly
- "'Correlation is not causation.' That scientific refrain has had social consequences...Judea Pearl proposes a radical mathematical solution...now bearing fruit in biology, medicine, social science and AI."—Nature
- "Lively and accessible...Pearl was one of the visionary leaders of the causal revolution, and The Book of Why is his crowning achievement."—Jewish Journal
- "Anyone interested in probing connections between cause and effect, and their relevance for the future of AI, will find this a fascinating and provocative book. Highly recommended."—CHOICE
- "Judea Pearl is on a mission to change the way we interpret data. An eminent professor of computer science, Pearl has documented his research and opinions in scholarly books and papers. ... With the release of this historically grounded and thought-provoking book, Pearl leaps from the ivory tower into the real world...Pearl has given us an elegant, powerful, controversial theory of causality."—American Mathematical Society
- "Have you ever wondered about the puzzles of correlation and causation? This wonderful book has illuminating answers and it is fun to read."—Daniel Kahneman, winner of the Nobel Memorial Prize in Economic Sciences and author of Thinking, Fast and Slow
- "Pearl's accomplishments over the last 30 years have provided the theoretical basis for progress in artificial intelligence... and they have redefined the term 'thinking machine.'"—Vint Cerf, Chief Internet Evangelist, Google, Inc.
- "Judea Pearl has been the heart and soul of a revolution in artificial intelligence and in computer science more broadly."—Eric Horvitz, Technical Fellow and Director, Microsoft Research Labs
- "If causation is not correlation, then what is it? Thanks to Judea Pearl's epoch-making research, we now have a precise answer to this question. If you want to understand how the world works, this engrossing and delightful book is the place to start."—Pedro Domingos, professor of computer science, University of Washington, and author of The Master Algorithm
- "The Book of Why ... questions and redefines the building blocks of our AI systems"—theverge.com
- On Sale
- Aug 25, 2020
- Page Count
- 432 pages
- Basic Books