On the other hand, the following is an algorithm for playing tic-tac-toe:. If you or your opponent has two in a row, play on the remaining square.. The larger outcome is that democracy works better because the bandwidth of communication between voters and politicians increases enormously. In these days of high-speed Internet, the amount of information your elected representatives get from you is still decidedly nineteenth century: a hundred bits or so every two years, as much as fits on a ballot. This is supplemented by polling and perhaps the occasional e-mail or town-hall meeting, but thatвЂ™s still precious little. Big data and machine learning change the equation. In the future, provided voter models are accurate, elected officials will be able to ask voters what they want a thousand times a day and act accordingly-without having to pester the actual flesh-and-blood citizens.. In physics, the same equations applied to different quantities often describe phenomena in completely different fields, like quantum mechanics, electromagnetism, and fluid dynamics. The wave equation, the diffusion equation, PoissonвЂ™s equation: once we discover it in one field, we can more readily discover it in others; and once weвЂ™ve learned how to solve it in one field, we know how to solve it in all. Moreover, all these equations are quite simple and involve the same few derivatives of quantities with respect to space and time. Quite conceivably, they are all instances of a master equation, and all the Master Algorithm needs to do is figure out how to instantiate it for different data sets.. A universal learner is sorely needed in many other areas, from life-and-death to mundane situations. Picture the ideal recommender system, one that recommends the books, movies, and gadgets you would pick for yourself if you had the time to check them all out. AmazonвЂ™s algorithm is a very far cry from it. ThatвЂ™s partly because it doesnвЂ™t have enough data-mainly it just knows which items you previously bought from Amazon-but if you went hog wild and gave it access to your complete stream of consciousness from birth, it wouldnвЂ™t know what to do with it. How do you transmute the kaleidoscope of your life, the myriad different choices youвЂ™ve made, into a coherent picture of who you are and what you want? This is well beyond the ken of todayвЂ™s learners, but given enough data, the Master Algorithm should be able to understand you roughly as well asyour best friend.. HumeвЂ™s question is also the departure point for our journey. WeвЂ™ll start by illustrating it with an example from daily life and meeting its modern embodiment in the famous вЂњno free lunchвЂќ theorem. Then weвЂ™ll see the symbolistsвЂ™ answer to Hume. This leads us to the most important problem in machine learning: overfitting, or hallucinating patterns that arenвЂ™t really there. WeвЂ™ll see how the symbolists solve it, and how machine learning is at heart a kind of alchemy, transmuting data into knowledge with the aid of a philosopherвЂ™s stone. For the symbolists, the philosopherвЂ™s stoneis knowledge itself. In the next four chapters weвЂ™ll study the solutions of the other tribesвЂ™ alchemists.. Philosophers have debated HumeвЂ™s problem of induction ever since he posed it, but no one has come up with a satisfactory answer. Bertrand Russell liked to illustrate the problem with the story of the inductivist turkey. On his first morning at the farm, the turkey was fed at 9:00 a.m., but being a good inductivist, he didnвЂ™t jump to conclusions. He first collected many observations on many different days under many different circumstances. Having been fed consistently at 9:00 a.m. for many consecutive days, he finally concluded that yes, he would always be fed at 9:00 a.m. Then came the morning of Christmas eve, and his throat was cut.. How to rule the world. Bottom line: learning is a race between the amount of data you have and the number of hypotheses you consider. More data exponentially reduces the number of hypotheses that survive, but if you start with a lot of them, you may still have some bad ones left at the end. As a rule of thumb, if the learner only considers an exponential number of hypotheses (for example, all possible conjunctive concepts), then the dataвЂ™s exponential payoff cancels it and youвЂ™re OK, provided you have plenty of examples and not too many attributes. On the other hand, if it considers a doubly exponential number (for example, all possible rule sets), then the data cancels only one of the exponentials and youвЂ™re still in trouble. You can even figure out in advance how many examples youвЂ™ll need to be pretty sure that the learnerвЂ™s chosen hypothesis is very close to the true one, provided it fits all the data; in other words, for the hypothesis to be probably approximately correct. HarvardвЂ™s Leslie Valiant received the Turing Award, the Nobel Prize of computer science, for inventing this type of analysis, which he describes in his book entitled, appropriately enough,Probably Approximately Correct.. Your friend Ben is also pretty good, but heвЂ™s had a bit too much to drink. His darts are all over, but he loudly points out that on average heвЂ™s hitting the bullвЂ™s-eye. (Maybe he should have been a statistician.) This is the low-bias, high-variance case, shown in the bottom right corner. BenвЂ™s girlfriend, Ashley, is very steady, butshe has a tendency to aim too high and to the right. She has low variance and high bias (top left corner). Cody, whoвЂ™s visiting from out of town and has never played darts before, is both all over and off center. He has both high bias and high variance (top right).. He who learns fastest wins. [РљР°СЂС‚РёРЅРєР°: pic_23.jpg]. The same idea of forming a local model rather than a global one applies beyond classification. Scientists routinely use linear regression to predict continuous variables, but most phenomena are not linear. Luckily, theyвЂ™re locally linear because smooth curves are locally well approximated by straight lines. So if instead of trying to fit a straight line to all the data, you just fit it to the points near the query point, you now have a very powerful nonlinear regression algorithm. Laziness pays. If Kennedy had needed a complete theory of international relations to decide what to do about the Soviet missiles in Cuba, he would have been in trouble. Instead, he saw an analogy between that crisis and the outbreak of World War I, and that analogy guided him to the right decisions.. [РљР°СЂС‚РёРЅРєР°: pic_25.jpg]. Notice that the network has a separate feature for each pair of people:Alice and Bob both have the flu, Alice and Chris both have the flu, and so on. But we canвЂ™t learn a separate weight for each pair, because we only have one data point per pair (whether itвЂ™s infected or not), and we wouldnвЂ™t be able to generalize to members of the network we havenвЂ™t diagnosed yet (do Yvette and Zach both have the flu?). What we can do instead is learn a single weight for all features of the same form, based on all the instances of it that weвЂ™ve seen. In effect,X and Y have the flu is a template for features that can be instantiated with each pair of acquaintances (Alice and Bob, Alice and Chris, etc.). The weights for all the instances of a template areвЂњtied together,вЂќ in the sense that they all have the same value, and thatвЂ™s how we can generalize despite having only one example (the whole network). In nonrelational learning, the parameters of a model are tied in only one way: across all the independent examples (e.g., all the patients weвЂ™ve diagnosed). In relational learning, every feature template we create ties the parameters of all its instances..