Pedro Domingos

The “no free lunch” theorem is a lot like the reason Pascal’s wager fails. In his Pensées, published in 1669, Pascal said we should believe in the Christian God because if he exists that gains us eternal life, and if he doesn’t we lose very little. This was a remarkably sophisticated argument for the time, but as Diderot pointed out, an imam could make the same argument for believing in Allah. And if you pick the wrong god, the price you pay is eternal hell. On balance, considering the wide variety of possible gods, you’re no better off picking a particular one to believe in than you are picking any other. For every god that says “do this,” there’s another that says “no, do that.” You may as well just forget about god and enjoy life without religious constraints. Replace “god” with “learning algorithm” and “eternal life” with “accurate prediction,” and you have the “no free lunch” theorem. Pick your favorite learner. (We’ll see many in this book.) For every world where it does better than random guessing, I, the devil’s advocate, will deviously construct one where it does worse by the same amount. All I have to do is flip the labels of all unseen instances. Since the labels of the observed ones agree, there’s no way your learner can distinguish between the world and the antiworld. On average over the two, it’s as good as random guessing. And therefore, on average over all possible worlds, pairing each world with its antiworld, your learner is equivalent to flipping coins.

For example, consider Naïve Bayes, a learning algorithm that can be expressed as a single short equation. Given a database of patient records— their symptoms, test results, and whether or not they had some particular condition— Naïve Bayes can learn to diagnose the condition in a fraction of a second, often better than doctors who spent many years in medical school. It can also beat medical expert systems that took thousands of person-hours to build. The same algorithm is widely used to learn spam filters, a problem that at first sight has nothing to do with medical diagnosis. Another simple learner, called the nearest-neighbor algorithm, has been used for everything from handwriting recognition to controlling robot hands to recommending books and movies you might like.

Netflix’s algorithm has a deeper (even if still quite limited) understanding of your tastes than Amazon’s, but ironically that doesn’t mean Amazon would be better off using it. Netflix’s business model depends on driving demand into the long tail of obscure movies and TV shows, which cost it little, and away from the blockbusters, which your subscription isn’t enough to pay for. Amazon has no such problem; although it’s well placed to take advantage of the long tail, it’s equally happy to sell you more expensive popular items, which also simplify its logistics. And we, as customers, are more willing to take a chance on an odd item if we have a subscription than if we have to pay for it separately.

The main ones are five in number, and we’ll devote a chapter to each. Symbolists view learning as the inverse of deduction and take ideas from philosophy, psychology, and logic. Connectionists reverse engineer the brain and are inspired by neuroscience and physics. Evolutionaries simulate evolution on the computer and draw on genetics and evolutionary biology. Bayesians believe learning is a form of probabilistic inference and have their roots in statistics. Analogizers learn by extrapolating from similarity judgments and are influenced by psychology and mathematical optimization.

Only engineers and mechanics need to know how a car’s engine works, but every driver needs to know that turning the steering wheel changes the car’s direction and stepping on the brake brings it to a stop. Few people today know what the corresponding elements of a learner even are, let alone how to use them. The psychologist Don Norman coined the term conceptual model to refer to the rough knowledge of a technology we need to have in order to use it effectively. This book provides you with a conceptual model of machine learning.

Your digital future begins with a realization: every time you interact with a computer— whether it’s your smart phone or a server thousands of miles away— you do so on two levels. The first one is getting what you want there and then: an answer to a question, a product you want to buy, a new credit card. The second level, and in the long run the most important one, is teaching the computer about you.

Occam would probably have been perplexed by the notion that we should prefer a theory that does not perfectly account for the evidence on the grounds that it will generalize better. Simple theories are preferable because they incur a lower cognitive cost (for us) and a lower computational cost (for our algorithms), not because we necessarily expect them to be more accurate.

A theory is a set of constraints on what the world could be, not a complete description of it.