Testing Classification Rules
Having a dataset consisting in couples x and y, where x is each element of the population and y the class it belongs to, a classification rule can be considered as a function that assigns its class to each element. A binary classification is such that the label y can take only a two values.
A classification rule or classifier is a function h that can be evaluated for any possible value of x, specifically, given the data, h(x) will yields a similar classification as close as possible to the true group label y.
The true labels yi can be known but will not necessarily match their approximations . In a binary classification, the elements that are not correctly classified are named false positives and false negatives.
Some classification rules are static functions. Others can be computer programs. A computer classifier can be able to learn or can implement static classification rules. For a training data-set, the true labels yj are unknown, but it is a prime target for the classification procedure that the approximation : as well as possible, where the quality of this approximation needs to be judged on the basis of the statistical or probabilistic properties of the overall population from which future observations will be drawn.
Given a classification rule, a classification test is the result of applying the rule to a finite sample of the initial data set.
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