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Probably Approximately Correct: Nature’s Algorithms for Learning and Prospering in a Complex World, by Leslie Valiant
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From a leading computer scientist, a unifying theory that will revolutionize our understanding of how life evolves and learns.
How does life prosper in a complex and erratic world? While we know that nature follows patterns—such as the law of gravity—our everyday lives are beyond what known science can predict. We nevertheless muddle through even in the absence of theories of how to act. But how do we do it?
In Probably Approximately Correct, computer scientist Leslie Valiant presents a masterful synthesis of learning and evolution to show how both individually and collectively we not only survive, but prosper in a world as complex as our own. The key is “probably approximately correct” algorithms, a concept Valiant developed to explain how effective behavior can be learned. The model shows that pragmatically coping with a problem can provide a satisfactory solution in the absence of any theory of the problem. After all, finding a mate does not require a theory of mating. Valiant’s theory reveals the shared computational nature of evolution and learning, and sheds light on perennial questions such as nature versus nurture and the limits of artificial intelligence.
Offering a powerful and elegant model that encompasses life’s complexity, Probably Approximately Correct has profound implications for how we think about behavior, cognition, biological evolution, and the possibilities and limits of human and machine intelligence.
- Sales Rank: #420394 in Books
- Brand: Brand: Basic Books
- Published on: 2013-06-04
- Original language: English
- Number of items: 1
- Dimensions: 9.30" h x 1.10" w x 6.40" l, .85 pounds
- Binding: Hardcover
- 208 pages
- Used Book in Good Condition
Review
“Insightful.... This is science at its best, driven not by dogma and blind belief, but by the desire to understand, intellectual integrity and reliance on facts.... The book is written in a lively, accessible style and is surprisingly entertaining. It’s funny how your perception of even mundane tasks can change after reading it—you start thinking algorithmically, confirming Dr. Valiant’s maxim that computer science is ‘more about humans than about computers.’”
—New York Times
“[A]n engaging meditation on complexity and on how living things often unwittingly use math to navigate it.”
—Scientific American
“Computer scientist Leslie Valiant celebrates Alan Turing as the progenitor of a third scientific revolution, potentially as profound as Newton’s and Einstein’s in transforming our understanding of the world. Why not a ‘fourth revolution’—why omit Darwin? Because, Valiant dares to say, Darwin’s theory is radically incomplete, and until it is equipped to make quantitative, verifiable predictions, evolution by natural selection cannot account for the complexity of living things and is not ‘more than a metaphor.’ But Valiant offers no drop of succor to creationists. Rather, he seeks to arm neo-Darwinian theory against their onslaughts by elucidating the mechanistic, quantitative basis it must have in a world ‘without a designer.’ The algorithms of computational learning theory, he posits, will be key—in particular, a special kind he calls ‘ecorithms,’ which incorporate information gathered from the environment to improve an organism’s ‘performance.’ Turing’s heirs have only just begun to plot its equation.”
—The Scientist
“[Probably Approximately Correct] really shines as an introduction to computer science theory to the general public, providing a compact and accessible description of basic, important results … . This is a book that should be on every computer scientist’s shelf so that when someone asks, ‘Why is computer science theory important?’ the three word response can be, ‘Read this book.’”
—SIGACT News
“A scholar at the intersection of computing and evolutionary neuroscience, Valiant explores ‘ecorithms’: algorithms that learn by interacting with their environment, not from their designer—and so are fundamental to the process of evolution. His text is clear and approachable, with some work; the argument is sweeping.”
—Harvard Magazine
“[Valiant’s] major point is that Darwin introduced evolution by natural selection, but the detailed mechanism is still sketchy. A hundred years of genetics has filled in some details, but Valiant sees the computational details as essential and still missing. The goal of this book is to encourage further research and to set a paradigm for such work. As Erwin Schrödinger’s What Is Life? inspired those who built molecular biology, Valiant hopes to inspire those who will build a future computational biology. Highly recommended.”
—Choice
“This remarkable book is carefully constructed to give the lay person a sense of subtle problems in mathematics and artificial intelligence, and offers a framework for biologists and computer scientists to use in jointly investigating the most fascinating and enigmatic biological questions.”
—Marc Kirschner, Chair, Department of Systems Biology, Harvard Medical School, and coauthor of The Plausibility of Life: Resolving Darwin’s Dilemma
“This book contains a lot of fresh thinking and elegant, nuanced ideas. It is more than probably approximately brilliant. I am amazed by how much insight has been packed into relatively few pages. Anyone interested in computation, learning, evolution, or human nature should find these pages extraordinarily stimulating and informative.”
—Stephen M. Kosslyn, Founding Dean, Minerva University, and former director, Center for Advanced Study in the Behavioral Sciences, Stanford University
“Ecorithms are algorithms that learn from interaction with their environment. This book provides a theoretical framework for understanding the power and limits of ecorithms and applies it to human cognition, biological evolution and artificial intelligence. It is elegantly written and will be accessible to a wide circle of readers.”
—Richard Karp, Turing Award winner and director, Simons Institute for the Theory of Computing, University of California, Berkeley
“This little book is hugely ambitious. It takes on the task of creating a quantitative, mathematical theory to explain all essential mechanisms governing the behavior of all living organisms: survival, learning, adaptation, evolution, cognition and intelligence. The suggested theory has all the characteristics of a great one. It is simple, general, and falsifiable, and moreover seems probably, approximately, correct!”
—Avi Wigderson, Nevanlinna Prize winner and Professor of Mathematics, Institute for Advanced Study, Princeton
“The quest for machines (and codes) that never make mistakes was only a first step toward machines (and codes) that learn from them. Leslie Valiant’s Probably Approximately Correct is a detailed, much-needed guide to how nature brought us here, and where technology is taking us next.”
—George Dyson, author of Turing’s Cathedral and Darwin among the Machines
“Probably Approximately Correct is a great book. It was eye-opening to me, as a mathematician, to learn how we think and reason, and as a grandfather, to understand better the development and learning of my four-month-old grandson. Valiant’s book offers deep insights, both for young and old.”
—Shing-Tung Yau, Professor of Mathematics, Harvard University, and coauthor of The Shape of Inner Space
“[Valiant] grounds his hypotheses in solid computational theory, drawing on Alan Turing’s pioneering work on ‘robust’ problem-solving and algorithm design, and in successive chapters he demonstrates how ecorithms can depict evolution as a search for optimized performance, as well as help computer scientists create machine intelligence.... His book offers a broad look at how ecorithms may be applied successfully to a variety of challenging problems.”—Publishers Weekly
About the Author
Leslie Valiant is the T. Jefferson Coolidge Professor of Computer Science and Applied Mathematics at Harvard University. He is a Fellow of the Royal Society and a member of the National Academy of Sciences. He is a winner of the Nevanlinna Prize from the International Mathematical Union, and the Turing Award, known as the Nobel of computing.
Most helpful customer reviews
72 of 85 people found the following review helpful.
Like a computer scientist's cartoon understanding of biology
By Fife not Cawdor
First, the Good: The author introduces a few ideas that are tasty, like the idea of evolution as computation. This notion suggests evolution as a phenomenon in which Nature (to anthropomorphize) explores possibility space. Or, the introduction of a few challenging (to be charitable) notions--evolution as actually goal-directed (in a way), evolution NOT acting on populations, etc. There is also a nice description of P/NP problems (indeed, the first part of the book is strongest). Finally, there is confrontation with that great bugaboo of science philosophy, the Problem of Induction--even more important in the age of Big Data (a phenom now in its "Screw causation, all is correlation! Yippee!" adolescent part of the Hype Cycle. Sigh.)
The Bad: None of these ideas are really developed, much less justified. From an evolutionary science POV, what he is saying is rather provocative (one thinks..see below) but never defended. Contrast with Dawkins' fantastically lucid descriptions of evolutionary mechanisms--this author's do not compare.
The Ugly: after a while, the prose is simply unreadable. The effect is a little hard to describe, but it seems that the author can't find his theme (or cannot show it to us), and cannot BUILD his ideas. In other words, he doesn't take a central idea, build it up, repeat the essentials (to keep us oriented) and push those elements out into concretes for illustration. Even worse, in trying to straddle some path between using math to show and not using math so as to avoid spooking, there is both too much and too little math.
Worst of all: There is no clear, explicit definition of what a PAC algorithm is--there is a very light introduction to venerable machine learning algorithms (e.g. Perceptron) then suddenly references to the PAC algorithm. Is PAC just machine learning? What the hell is he talking about?! I began to wonder if this was just another kind of crackpottery, old (but very cool, useful and provocative) ideas tarted up in new language, like Wolfram's book...
In the end, this book got the Dorthy Parker review in my house--not a book to be tossed aside lightly, but to be hurled with great force! I actually threw it across the room...
25 of 31 people found the following review helpful.
Great thought starter on applying machine learning to evolution
By Mario Schlosser
In short: whether you're a computer scientist familiar with machine learning algorithms, or whether you don't know much about artificial intelligence, this book has profound and novel insights to offer. I've been a practitioner of machine learning for a long time, and yet the book's framework relating machine learning to evolution gave me a whole bunch of "aha" moments. So pick it up and give it a read.
The book's thesis in a few words: cognitive concepts are computational, and they are acquired by a learning process, before and after birth. Nature, the grand designer, uses ecorithms to guide this process - systems whose functioning and whose parameters are learned and evolved, as opposed to written down once (like algorithms). The processes of learning, evolution and reasoning are the building blocks of ecorithms.
This, in and of itself, is not a new framework. Open any artificial intelligence textbook, and the table of contents will be organized into algorithms for "learning" and "reasoning". So nothing new there. But then, the book launches into an excellent, simple and mind-blowing thought experiment: what if nature were simply relying on the same simple learning algorithms that we as humans have been researching, with the same constraints - and evolution is just that formal learning process in action? And then: given all we know about the parameters of these learning algorithms, would evolution have been mathematically possible?
To answer that, the author goes into some detail on computational complexity theory. Computer science has shown that there are many seemingly simple processes that aren't solvable in polynomial time - meaning, if you make them big enough, solving them will take longer than the universe existed. The question of the shortest overall path in visiting all cities in a particular geography is such a problem. So if it is so easy to mathematically prove that so many really simple problems aren't solvable in the time the universe existed, how would it even be remotely possible that evolution build something as complex as the human brain in an even shorter time frame?
The book then essentially explores areas of machine learning just deep enough to show that it probably would be possible. There are enough real-world functions of the "probably approximately correct"-learnable class that are learnable in polynomial time, and algorithms that do the learning that we already know (and use) today, that it's imaginable that nature relies on variants of those. The book has some strong tidbits it throws out in the course of discussing this. For example, it turns out that parity functions (deciding, without counting, whether something is odd or even) aren't PAC-learnable. So far, so satisfying a read.
One of the book's drawbacks is that a lot of the details are left open. In the author's thesis, the genome and our protein networks somehow encode the parameters of the learning algorithms nature uses. But of course we have no idea how that actually happens (and the book doesn't pretend that it knows). Another drawback is that the book seemingly can't quite decide on its audience: is it pop science or more serious work? It oscillates strangely between being very concrete and being hand-wavy: for example, when discussing the limits of machine learning (semantics, brittleness, complexity, grounding), there isn't anything offered in terms of why machine learning is so brittle (just try Apple's Siri). It also somewhat casually throws around ideas that are mind-blowing but totally unproven: for example, it is known that our working memory can only hold 7 +/- 2 objects at any point in time. The author argues that this is by design, so that the subsequent learning algorithms have an easier time picking up features. That's a pretty cool line of thinking, because it would suggest that nature uses the same heuristics that we as computer scientists use when tackling a learning problem (reduction in features and dimensionality). But it's also totally unproven that THIS is why we have limited working memory, or that THIS is what it does. The book also doesn't go into any depths on learning algorithms we already know, even though a lot of the known algorithms actually have pretty simple intuitions underlying them that could nicely be treated for a non-computer science audience.
But overall, there are some awesome thought starters in this book. It is not always an easy read. But certainly worth it.
3 of 3 people found the following review helpful.
Evolution is not a form of learning: learning is a product of evolution
By Tim Tyler
This book is by a machine learning expert. He in interested in models of learning and particularly their assessment in terms of computational complexity theory. It considers seriously the role of evolution itself in the context of knowledge acquisition processes. The book argues that evolution is a subset of learning processes.
Overall, the book is a reasonable one. However, the presentation is a bit dry and boring. The author apparently likes coining terms, and dislikes reviewing the work of others. As Leslie says, there is indeed a close link between the theories of evolution and learning. He correctly argues against the modern dogma of directionless evolution (since evolution and learning are linked and learning is clearly directional). Leslie argues that "fitness" provides such a direction. In fact a much stronger case than the one Leslie gives can be made - based on thermodynamics.
Overall, I am inclined to think that the book has its core thesis backwards. Instead of evolution being a subset of learning processes, learning processes are part of evolution. Most of the rest of this review focuses on this one point, because I think it is an important one.
The idea that learning is a part of evolution is an old one. James Mark Baldwin proposed that organisms could learn a behavioural trait and then see genetic predispositions to learning that behaviour amplified by evolution. This idea was later generalised by Waddington - who proposed that genes could take over the trait completely - via a process known as "genetic assimilation". We see this effect in modern times, with learned milk drinking preceding genetically encoded lactose tolerance. Overall, the course of evolution is altered significantly by individual and social learning processes.
Leslie says that "The idea that evolution is a form of learning sounds implausible to many people when they first hear it." I think this is because he has things backwards - and learning is better seen as one of the products of evolution. How does Leslie argue that evolution is part of learning - and not the other way around? Leslie confines his attention to the case of "Darwinian evolution". According to Leslie, this term refers to evolution without learning. Leslie asserts that, in Darwinian evolution, genetic variations are generated independently of current experiences - a constraint that does not apply to learning systems. Unfortunately for Leslie's thesis, this isn't the kind of evolution that Darwin believed in. Darwin was well aware of the role of learning in evolution. Indeed he formulated a theory to explain how current experiences went on to affect the next generation. Darwin's proposed "gemmules" were subsequently discredited, but they clearly show that Darwin thought that current experiences influenced heritable variation.
Leslie goes on to describe modern cultural evolution, saying that "culture also undergoes change or evolution, but this change is no longer limited by Darwinian principles". However, Darwin was, in fact, a pioneer in the discovery of cultural evolution, writing about how words and languages were subject to natural selection. Leslie argues that human culture introduced learning to evolution. He minimizes the significance of cultural inheritance in other animals and the influence of individual learning on DNA evolution via the Baldwin effect and genetic assimilation. He says that before human culture: "the learning and reasoning carried out by an organism during its life had limited impact that outlived the individual". I think this is a big understatement that is not really consistent with the scientific evidence on the role of learning in evolution. Learning is important, and it's impact on evolution long pre-dates human cultural evolution.
The "Darwinian evolution" described by the author would have been foreign to Darwin. Also, we know that the idea that genetic variations are generated independently of current experiences is wrong - not least because of the role of stress in stimulating the production of mutations. This it isn't the kind of evolutionary theory that is much use for explaining what happens in nature. Why Leslie focuses on this impoverished version of evolutionary theory is not completely clear. Perhaps he really believes that this is what Darwinian evolutionary theory says. Or perhaps making Darwinism look weak makes his own field of learning seem more important.
So far, this has been mostly an argument over terminology - specifically over what the term "Darwinian evolution" refers to. This debate has limited interest - and can mostly be avoided with clear definitions. However the problem with learning theorists placing learning centrally and denigrating the power of Darwinian evolution, is that they then fail to make proper use of the insights evolutionary theory provides. In fact, Darwinism has much to say about how the brain processes responsible for animal learning work. Natural selection acts on synapses. Axon pulses are copied with variation and selection. There's competition between ideas within the brain for attention. The result is a good adaptive fit between an organism's model of its world and its environment. Interesting though these idea are, you won't find anything like them in this book. Indeed, few machine learning experts appear to have looked into the implications of modern versions of Darwinism. Instead, Leslie sees Darwinian evolution as a primitive ladder that led to modern learning systems. He doesn't deal with the more powerful, generalized versions of evolutionary theory that also cover organisms that learn or make use of cultural transmission.
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