Luc Devroye's A Probabilistic Theory of Pattern Recognition PDF

By Luc Devroye

Pattern acceptance offers some of the most major demanding situations for scientists and engineers, and lots of diverse methods were proposed. the purpose of this booklet is to supply a self-contained account of probabilistic research of those techniques. The booklet features a dialogue of distance measures, nonparametric tools in line with kernels or nearest buddies, Vapnik-Chervonenkis idea, epsilon entropy, parametric category, errors estimation, loose classifiers, and neural networks. anywhere attainable, distribution-free houses and inequalities are derived. a considerable element of the consequences or the research is new. Over 430 difficulties and workouts supplement the material.

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Extra resources for A Probabilistic Theory of Pattern Recognition

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Not only measures how spread out the mass of X is, but also provides us with concrete computational bounds for certain algorithms. In the simple example above, H. is in fact proportional to the expected computational time of the best algorithm. We are not interested in information theory per se, but rather in its usefulness in pattern recognition. For our discussion, if we fix X = x, then Y is Bernoulli (17(x)). (1](X), 1 -7](X)) = -1](X)lOg1](X)- (J -17(X))log(l-7](X)). It measures the amount of uncertainty or chaos in Y given X = x.

11 ). lt also occurs under other guises in mathematical statistics-see, for example, the Hellinger distance literature (Le Cam (1970), Beran (1977)). Clearly, p = 0 if and only if 17(X) E {0, 1} with probability one, that is, if L * = 0. Furthermore, p takes its maximal value 1/2 if and only if 17(X) = 1/2 with probability one. The relationship between p and L * is not linear though. We will show that for all distributions, LNN is more useful than p if it is to be used as an approximation of L *.

The Bayes Error to approximate the Bayes decision. , Van Ryzin (1966), Wolverton and Wagner (1969a), Glick (1973), Csibi (1971), Gyorfi (1975), (1978), Devroye and Wagner (l976b), Devroye (l982b), and Devroye and Gyorfi (1985)) states that if ~(x) is close to the real a posteriori probability in L 1 -sense, then the error probability of decision g is near the optimal decision g*. 2. For the error probability of the plug-in decision g defined above, we have P{g(X) =/ Y}- L * = 2 { lnd l17(x)- 1/211rg

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