Read e-book online A Probabilistic Theory of Pattern Recognition (Stochastic PDF

By Luc Devroye

ISBN-10: 0387946187

ISBN-13: 9780387946184

A self-contained and coherent account of probabilistic thoughts, overlaying: distance measures, kernel principles, nearest neighbour ideas, Vapnik-Chervonenkis concept, parametric class, and have extraction. every one bankruptcy concludes with difficulties and workouts to additional the readers realizing. either examine staff and graduate scholars will reap the benefits of this wide-ranging and updated account of a quick- relocating box.

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Additional resources for A Probabilistic Theory of Pattern Recognition (Stochastic Modelling and Applied Probability)

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O7 = { ( Ci, Xi), i = 1, ... (J11 + jl2 )T2- 1(jl 2 - jll) as here the likelihood is based on the conditional distribution. As they are based on less information, the direct estimators should be less efficient (that is more variable) although the standard large sample theory applies to show that the estimates are consistent and asymptotically normal. Efron (1975) demonstrates that this is the case, and the loss of efficiency can be appreciable when the class densities overlap, so the classification task is neither easy nor hopeless.

5) continue to hold. l = I:f=I Pk-) Thus some or all of the Pk 's may have discrete components, they may represent normal distributions with singular covariance matrices, and so on. The small piece of theory presented here is fairly standard, although the rigorous derivation of the optimal reject ('doubt') region, by means of the loss function, is less known. 2. 9), in Fisher (1936). 1. Missing values This technique is known as multiple 'hot deck ' imputation in survey sampling. Some problems (such as the Pima Indians data) have examples with missing values for some of the features.

This is the same scenario as a pure significance test in statistical hypothesis testing (Cox & Hinkley, 1974; Lehmann, 1986) and the same ideas apply. Typically we will fix a level rx of acceptable false detections of outliers, and fix a level Pc so that Pr{p(X) < Pc} ~ rx. However, the integration needed here will often be intractable, and in the examples we relate p(x) to its average value on the training set. The two routes lead to the same practical conclusion; declare an outlier when p(x) is small.

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A Probabilistic Theory of Pattern Recognition (Stochastic Modelling and Applied Probability) by Luc Devroye

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