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On the other hand, the following is an algorithm for playing tic-tac-toe:. 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, Poisson’s equation: once we discover it in one field, we can more readily discover it in others; and once we’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.. OK, some say, machine learning can find statistical regularities in data, but it will never discover anything deep, like Newton’s laws. It arguably hasn’t yet, but I bet it will. Stories of falling apples notwithstanding, deep scientific truths are not low-hanging fruit. Science goes through three phases, which we can call the Brahe, Kepler, and Newton phases. In the Brahe phase, we gather lots of data, like Tycho Brahe patiently recording the positions of the planets night after night, year after year. In the Kepler phase, we fit empirical laws to the data, like Kepler did to the planets’ motions. In the Newton phase, we discover the deeper truths. Most science consists of Brahe- and Kepler-like work; Newton moments are rare. Today, big data does the work of billions of Brahes, and machine learning the work of millions of Keplers. If-let’s hope so-there are more Newton moments to be had, they are as likely to come from tomorrow’s learning algorithms as from tomorrow’s even more overwhelmed scientists, or at least from a combination of the two. (Of course, the Nobel prizes will go to the scientists, whether they have the key insights or just push the button. Learning algorithms have no ambitions of their own.) We’ll see in this book what those algorithms might look like and speculate about what they might discover-such as a cure for cancer.. If we knew the first and third rules but not the second, and we had microarray data where at a high temperature B and D were not expressed, we could induce the second rule by inverse deduction. Once we have that rule, and perhaps have verified it using a microarray experiment, we can use it as the basis for further inductive inferences. In a similar manner, we can piece together the sequences of chemical reactions by which proteins do their work.. [Картинка: pic_10.jpg]. If the states and observations are continuous variables instead of discrete ones, the HMM becomes what’s known as a Kalman filter. Economists use Kalman filters to remove noise from time series of quantities like GDP, inflation, and unemployment. The “true” GDP values are the hidden states; at each time step, the true value should be similar to the observed one, but also to the previous true value, since the economy seldom makes abrupt jumps. The Kalman filter trades off these two, yielding a smoother curve that still accords with the observations. When a missile cruises to its target, it’s a Kalman filter that keeps it on track. Without it, there would have been no man on the moon.. Given all this, it’s not surprising that analogy plays a prominent role in machine learning. It got off to a slow start, though, and was initially overshadowed by neural networks. Its first algorithmic incarnation appeared in an obscure technical report written in 1951 by two Berkeley statisticians, Evelyn Fix andJoe Hodges, and was not published in a mainstream journal until decades later. But in the meantime, other papers on Fix and Hodges’s algorithm started to appear and then to multiply until it was one of the most researched in all of computer science. The nearest-neighbor algorithm, as it’s called, is the first stop on our tour of analogy-based learning. The second is support vector machines, an idea that took machine learning by storm around the turn of the millennium and was only recently overshadowed by deep learning. The third and last is full-blown analogical reasoning, which has been a staple of psychology and AI for several decades, and a background theme in machine learning for nearly as long.. The reason lazy learning wins is that forming a global model, such as a decision tree, is much harder than just figuring out where specific query points lie, one at a time. Imagine trying to define what a face is with a decision tree. You could say it has two eyes, a nose, and a mouth, but what is an eye and how do you find it in an image? What if the person’s eyes are closed? Reliably defining a face all the way down to individual pixels is extremely difficult, particularly given all the different expressions, poses, contexts, and lighting conditions a face could appear in. Instead, nearest-neighbor takes a shortcut: if the image in its database most similar to the one Jane just uploaded is of a face, then so is Jane’s. For this to work, the database needs to contain an image that’s similar enough to the new one-for example, a face with similar pose, lighting, and so on-so the bigger the database, the better. For a simple two-dimensional problem like guessing the border between two countries, a tiny database suffices. For a very hard problem like identifying faces, where the color of each pixel is a dimension of variation,

we need a huge database. But these days we have them. Learning from them may be too costly for an eager learner, which explicitly draws the border between faces and nonfaces. For nearest-neighbor, however, the border is implicit in the locations of the data points and the distance measure, and the only cost is at query time.. You’d probably be disappointed if you looked at the principal components of a face data set, though. They’re not what you’d expect, such as facial expressions or features, but more like ghostly faces, blurred beyond recognition. This is because PCA is a linear algorithm, and so all that the principal components can be is weighted pixel-by-pixel averages of real faces. (Also known as eigenfaces because they’re eigenvectors of the centered covariance matrix of the data-but I digress.) To really understand faces, and most shapes in the world, we need something else: nonlinear dimensionalityreduction.. You keep going. The constrained optimization district is a maze of narrow alleys and dead ends, examples of all kinds standing cheek by jowl everywhere, with an occasional clearing around a support vector. Clearly, all you need to do to avoid bumping into examples of the wrong class is add constraints to the optimizer you’ve already assembled. But come to think of it, not even that is necessary. When we learn SVMs, we usually let margins be violated in order to avoid overfitting, provided each violation pays a penalty. In this case the optimal example weights can again be learned by a form of gradient descent. That was easy. You feel like you’re starting to get the hang of it.. After an arduous climb, you reach the top. A wedding is in progress. Praedicatus, First Lord of Logic, ruler of the symbolic realm and Protector of the Programs, says to Markovia, Princess of Probability, Empress of Networks:“Let us unite our realms. To my rules thou shalt add weights, begetting a new representation that will spread far across the land.” The princess says, “And we shall call our progeny Markov logic networks.”. The termsingularity comes from mathematics, where it denotes a point at which a function becomes infinite. For example, the function 1/x has a singularity whenx is 0, because 1 divided by 0 is infinity. In physics, the quintessential example of a singularity is a black hole: a point of infinite density, where a finite amount of matter is crammed into infinitesimal space. The only problem with singularities is that they don’t really exist. (When did you last divide a cake among zero people, and each one got an infinite slice?) In physics, if a theory predicts something is infinite, something’s wrong with the theory. Case in point, general relativity presumably predicts that black holes have infinite density because it ignores quantum effects. Likewise, intelligence cannot continue to increase forever. Kurzweil acknowledges this, but points to a series of exponential curves in technology improvement (processor speed, memory capacity, etc.) and argues that the limits to this growth are so far away that we need not concern ourselves with them.. If this book whetted your appetite for machine learning and the issues surrounding it, you’ll find many suggestions in this section. Its aim is not to be comprehensive but to provide an entrance to machine learning’s garden of forking paths (as Borges put it). Wherever possible, I chose books and articles appropriate for the general reader. Technical publications, which require at least some computational, statistical, or mathematical background, are marked with an asterisk (*). Even these, however, often have large sections accessible to the general reader. I didn’t list volume, issue, or page numbers, since the web renders them superfluous; likewise for publishers’ locations.. Learning Deep Architectures for AI,* by Yoshua Bengio (Now, 2009), is a brief introduction to deep learning. The problem of error signal diffusion in backprop is described in“Learning long-term dependencies with gradient descent is difficult,”* by Yoshua Bengio, Patrice Simard, and Paolo Frasconi (IEEE Transactions on Neural Networks, 1994).“How many computers to identify a cat? 16,000,” by John Markoff (New York Times, 2012), reports on the Google Brain project and its results. Convolutional neural networks, the current deep learning champion, are described in“Gradient-based learning applied to document recognition,”* by Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner (Proceedings of the IEEE, 1998).“The $1.3B quest to build a supercomputer replica of a human brain,” by Jonathon Keats (Wired, 2013), describes the European Union’s brain modeling project. “The NIH BRAIN Initiative,” by Thomas Insel, Story Landis, and Francis Collins (Science, 2013), describes the BRAIN initiative.. “Support vector machines and kernel methods: The new generation of learning machines,”* by Nello Cristianini and Bernhard Schölkopf (AI Magazine, 2002), is a mostly nonmathematical introduction to SVMs. The paper that started the SVM revolution was“A training algorithm for optimal margin classifiers,”* by Bernhard Boser, Isabel Guyon, and Vladimir Vapnik (Proceedings of the Fifth Annual Workshop on Computational Learning Theory, 1992). The first paper applying SVMs to text classification was“Text categorization with support vector machines,”* by Thorsten Joachims (Proceedings of the Tenth European Conference on Machine Learning, 1998). Chapter 5 ofAn Introduction to Support Vector Machines,* by Nello Cristianini and John Shawe-Taylor (Cambridge University Press, 2000), is a brief introduction to constrained optimization in the context of SVMs..

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