If it exists, the Master Algorithm can derive all knowledge in the world-past, present, and future-from data. Inventing it would be one of the greatest advances in the history of science. It would speed up the progress of knowledge across the board, and change the world in ways that we can barely begin to imagine. The Master Algorithm is to machine learning what the Standard Model is to particle physics or the Central Dogma to molecular biology: a unified theory that makes sense of everything we know to date, and lays the foundation for decades or centuries of future progress. The Master Algorithm is our gateway to solving some of the hardest problems we face, from building domestic robots to curing cancer.. To see the future of science, take a peek inside a lab at the Manchester Institute of Biotechnology, where a robot by the name of Adam is hard at work figuring out which genes encode which enzymes in yeast. Adam has a model of yeast metabolism and general knowledge of genes and proteins. It makes hypotheses, designs experiments to test them, physically carries them out, analyzes the results, and comes up with new hypotheses until itвЂ™s satisfied. Today, human scientists still independently check AdamвЂ™s conclusions before they believe them, but tomorrow theyвЂ™ll leave it to robot scientists to check each otherвЂ™s hypotheses.. The argument from evolution. Rationalists believe that the senses deceive and that logical reasoning is the only sure path to knowledge. Empiricists believe that all reasoning is fallible and that knowledge must come from observation and experimentation. The French are rationalists; the Anglo-Saxons (as the French call them) are empiricists. Pundits, lawyers, and mathematicians are rationalists; journalists, doctors, and scientists are empiricists.Murder, She Wrote is a rationalist TV crime show;CSI: Crime Scene Investigation is an empiricist one. In computer science, theorists and knowledge engineers are rationalists; hackers and machine learners are empiricists.. (If youвЂ™re wondering about the last rule, credit-card thieves used to routinely buy one dollar of gas to check that a stolen credit card was good before data miners caught on to the tactic.). My first direct experience of rule learning in action was when, having just moved to the United States to start graduate school, I applied for a credit card. The bank sent me a letter sayingвЂњWe regret that your application has been rejected due to INSUFFICIENT-TIME-AT-CURRENT-ADDRESS and NO-PREVIOUS-CREDIT-HISTORYвЂќ (or some other all-cap words to that effect). I knew right then that there was much research left to do in machine learning.. The problem is not limited to memorizing instances wholesale. Whenever a learner finds a pattern in the data that is not actually true in the real world, we say that it has overfit the data. Overfitting is the central problem in machine learning. More papers have been written about it than about any other topic. Every powerful learner, whether symbolist, connectionist, or any other, has to worry about hallucinating patterns. The only safe way to avoid it is to severely restrict what the learner can learn, for example by requiring that it be a short conjunctive concept. Unfortunately, that throws out the baby with the bathwater, leaving the learner unable to see most of the true patterns that are visible in the data. Thus a good learner is forever walking the narrow path between blindness and hallucination.. Of course, itвЂ™s not enough to be able to tell when youвЂ™re overfitting; we need to avoid it in the first place. That means stopping short of perfectly fitting the data even if weвЂ™re able to. One method is to use statistical significance tests to make sure the patterns weвЂ™re seeing are really there. For example, a rule covering three hundred positive examples versus one hundred negatives and a rule covering three positives versus one negative are both 75 percent accurate on the training data, but the first rule is almost certainly better than coin flipping, while the second isnвЂ™t, since four flipsof an unbiased coin could easily result in three heads. When constructing a rule, if at some point we canвЂ™t find any conditions that significantly improve its accuracy then we just stop, even if it still covers some negative examples. This reduces the ruleвЂ™s training-set accuracy, but probably makes it a more accurate generalization, which is what we really care about.. If we want to evolve a whole set of spam-filtering rules, not just one, we can represent a candidate set ofn rules by a string ofnГ— 20,000 bits (20,000 for each rule, assuming ten thousand different words in the data, as before). Rules containing 00 for some word effectively disappear from the rule set, since they donвЂ™t match any e-mails, as we saw before. If an e-mail matches any rule in the set, itвЂ™s classified as spam; otherwise itвЂ™s legit. We can still let fitness be the percentage of correctly classified e-mails, but to combat overfitting, weвЂ™ll probably want to subtract from it a penalty proportional to the total number of active conditions in the rule set.. Compared to the simple model in FisherвЂ™s book, genetic algorithms are quite a leap forward. Darwin lamented his lack of mathematical ability, but if he had lived a century later he probably would have yearned for programming prowess instead. Indeed, capturing natural selection by a set of equations is extremely difficult, but expressing it as an algorithm is another matter, and can shed light on many otherwise vexing questions. Why do species appear suddenly in the fossil record? WhereвЂ™s the evidence that they evolved gradually from earlier species? In 1972, Niles Eldredge and Stephen Jay Gould proposed that evolution consists of a series of вЂњpunctuated equilibria,вЂќ alternating long periods of stasis with short bursts of rapid change, like the Cambrian explosion. This sparked a heated debate, with critics of the theory nicknaming it вЂњevolution by jerksвЂќ and Eldredge and Gould retorting that gradualism is вЂњevolution by creeps.вЂќ Experience with genetic algorithms lends support to the jerks. If you run a genetic algorithm for one hundred thousand generations and observe the population at one-thousand-generation intervals, the graph of fitness against time will probably look like an uneven staircase, with sudden improvements followed by flat periods that tend to become longer over time. ItвЂ™s also not hard to see why. Once the algorithm reaches a local maximum of fitness-a peak in the fitness landscape-it will stay there for a long time until a lucky mutation or crossover lands an individual on the slope to a higher peak, at which point that individual will multiply and climb up the slope with each passing generation. And the higher the current peak, the longer before that happens. Of course, natural evolution is more complicated than this: for one, the environment may change, either physically or because other organisms have themselves evolved, and an organism that was on a fitness peak may suddenly find itself under pressure to evolve again. So, while helpful, current genetic algorithms are far from the end of the story.. Eliminating sex would leave evolutionaries with only mutation to power their engine. If the size of the population is substantially larger than the number of genes, chances are that every point mutation is represented in it, and the search becomes a type of hill climbing: try all possible one-step variations, pick the best one, and repeat. (Or pick several of the best variations, in which case itвЂ™s called beam search.) Symbolists, in particular, use this all the time to learn sets of rules, although they donвЂ™t think of it as a form of evolution. To avoid getting trapped in local maxima, hill climbing can be enhanced with randomness (make a downhill move with some probability) and random restarts (after a while, jump to a random state and continue from there). Doing this is enough to find good solutions to problems; whether the benefit of adding crossover to it justifies the extra computational cost remains an open question.. Siri uses the same idea to compute the probability that you just said,вЂњCall the policeвЂќ from the sounds it picked up from the microphone. Think of вЂњCall the policeвЂќ as a platoon of words marching across the page in single file.Police wants to know its probability, but for that it needs to know the probability ofthe; andthe in turn needs to know the probability ofcall. Socall computes its probability and passes it on tothe, which does the same and passes the result topolice. Nowpolice knows its probability, duly influenced by every word in the sentence, but we never had to construct the full table of eight possibilities (the first word iscall or isnвЂ™t, the second isthe or isnвЂ™t, and the third ispolice or isnвЂ™t). In reality, Siri considers all words that could appear in each position, not just whether the first word iscall or not and so on, but the algorithm is the same. Perhaps Siri thinks, based on the sounds, that the first word was eithercall ortell, the second wasthe orher, and the third waspolice orplease. Individually, perhaps the most likely words arecall,the, andplease. But that forms the nonsensical sentenceвЂњCall the please,вЂќ so taking the other words into account, Siri concludes that the sentence is really вЂњCall the police.вЂќ It makes the call, and with luck the police get to your house in time to catch the burglar.. Another reason researchers were initially skeptical of nearest-neighbor was that it wasnвЂ™t clear if it could learn the true borders between concepts. But in 1967 Tom Cover and Peter Hart proved that, given enough data, nearest-neighbor is at worst only twice as error-prone as the best imaginable classifier. If, say, at least 1 percent of test examples will inevitably be misclassified because of noise in the data, then nearest-neighbor is guaranteed to get at most 2 percent wrong. This was a momentous revelation. Up until then, all known classifiers assumed that the frontier had a very specific form, typically a straight line. This was a double-edged sword: on the one hand, it made proofs of correctness possible, as in the case of the perceptron, but it also meant that the classifier was strictly limited in what it could learn. Nearest-neighbor was the first algorithm in history that could take advantage of unlimited amounts of data to learn arbitrarily complex concepts. No human being could hope to trace the frontiers it forms in hyperspace from millions of examples, but because of Cover and HartвЂ™s proof, we know that theyвЂ™re probably not far off the mark. According to Ray Kurzweil, the Singularity begins when we can no longer understand what computers do. By that standard, itвЂ™s not entirely fanciful to say that itвЂ™s already under way-it began all the way back in 1951, when Fix and Hodges invented nearest-neighbor, the little algorithm that could.. The first step accomplished, you hurry on to the Bayesian district. Even from a distance, you can see how it clusters around the Cathedral of BayesвЂ™ Theorem. MCMC Alley zigzags randomly along the way. This is going to take a while. You take a shortcut onto Belief Propagation Street, but it seems to loop around forever. Then you see it: the Most Likely Avenue, rising majestically toward the Posterior Probability Gate. Rather than average over all models, you can head straight for the most probable one, confident that the resulting predictions will be almost the same. And you can let genetic search pick the modelвЂ™s structure and gradient descent its parameters. With a sigh of relief, you realize thatвЂ™s all the probabilistic inference youвЂ™ll need, at least until itвЂ™s time to answer questions using the model.. Actually, I lied: the product of factors is not yet a probability because the probabilities of all pictures must add up to one, and thereвЂ™s no guarantee that the products of factors for all pictures will do so. We need to normalize them, meaning divide each product by the sum of all of them. The sum of all the normalized products is then guaranteed to be one because itвЂ™s just a number divided by itself. The probability of a picture is thus the weighted sum of its features, exponentiated and normalized. If you look back at the equation in the five-pointed star, youвЂ™ll probably start to get an inkling of what it means.P is a probability,w is a vector of weights (notice itвЂ™s in boldface),n is a vector of numbers, and their dot productвЂў is exponentiated and divided byZ, the sum of all products. If we let the first component ofn be one if the first feature of the image is true and zero otherwise, and so on,wвЂўn is just a shorthand for the weighted sum of features weвЂ™ve been talking about all along..