By Luc Devroye
Pattern acceptance offers essentially the most major demanding situations for scientists and engineers, and lots of assorted techniques were proposed. the purpose of this ebook is to supply a self-contained account of probabilistic research of those ways. The publication encompasses a dialogue of distance measures, nonparametric equipment in response to kernels or nearest buddies, Vapnik-Chervonenkis conception, epsilon entropy, parametric category, errors estimation, unfastened classifiers, and neural networks. anyplace attainable, distribution-free houses and inequalities are derived. a considerable component of the implications 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
Is related to the Bayes error in a general sense. If the Mahalanobis distance between the class-conditional distributions is large, then L * is small. 4. (DEVIJVER AND KIITLER (1982, p. 166)). 2 For a distribution with mean m and covariance matrix :E, the Mahalanobis distance from a point x E 'Rd tom is REMARK. In one dimension, this is simply interpreted as distance from the mean as measured in units of standard deviation. The use of Mahalanobis distance in discrimination is based upon the intuitive notion that we should classify according to the class for which we are within the least units of standard deviations.
6. 3). (I) Let T, B, and E be independent. Merely by changing the distribution of E, show that the Bayes error for classification based upon (T, B) can be made as close as desired to I /2. (2) Let T and B be independent and exponentially distributed. Find a joint distribution of (T, B, E) such that the Bayes classifier is not a linear classifier. (3) LetT and B be independent and exponentially distributed. B 2 < 10, otherwise . 7. 3. Let Y = I (0) denote whether a student passes (fails) a course.
166)). 2 For a distribution with mean m and covariance matrix :E, the Mahalanobis distance from a point x E 'Rd tom is REMARK. In one dimension, this is simply interpreted as distance from the mean as measured in units of standard deviation. The use of Mahalanobis distance in discrimination is based upon the intuitive notion that we should classify according to the class for which we are within the least units of standard deviations. At least, for distributions that look like nice globular clouds, such a recommendation may make sense.
A Probabilistic Theory of Pattern Recognition by Luc Devroye