Pattern Recognition and Neural Networks by Brian D. Ripley

By Brian D. Ripley

Ripley brings jointly the most important rules in development popularity: statistical equipment and laptop studying through neural networks. He brings unifying rules to the fore, and reports the kingdom of the topic. Ripley additionally contains many examples to demonstrate actual difficulties in trend reputation and the way to beat them.

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Parametric models 27 "! ''I ' ~ ·;,n cQ) "C CC! 0 '' ' ' "'0 I I I I I ' 0 0 0 2 3 4 3 4 X 0 ~ :c CC! c '' ' ' 0. ·;:: * g_ N c) 0 0 0 2 X Theoretical and practical issues related to debiasing of maximum likelihood density estimates, predictive classifiers and robust estimation are addressed in later sections. 3). It will be helpful to distinguish clearly these two tasks, which Dawid (1976) calls the sampling and diagnostic paradigms. Both give a parametric model of the joint density p(x, c; 8) of a random sample (X, C) of a set of features and its (reported) classification.

Note that informative missingness of y is only a problem if it indicates a departure from the distribution p(y I x*). Thus a missing test whose outcome could be predicted from the remaining features would not be a difficulty (although the medic may be predicting from qualitative data which are not recorded). On the other hand, the refusal to answer a test may well be unpredictable and so informative. Where this is suspected, often the only possible action is to code 'missing' as a value of the feature, and somehow to find the densities required using the expanded feature(s).

24 2 Statistical Decision Theory For normal classes both procedures are easy, as the distribution of some of the features is again joint normal, so we find a modified linear rule in the observed features. The density p(x I x*) is a mixture of normal distributions (one for each class) and so is easy to sample from. Simpler procedures are often used, such as replacing missing values by 'typical' values, for example by the average over observed values. This is potentially dangerous, as the conditional density p(y I x*) of a feature y may have a very different mean from the unconditional density.

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