THE VC - DIMENSION 3 8 . 2 . 2 Definitions

In the PAC Model we assume there exists a distribution D on the examples X that the learner receives, i.e., when choosing an instance from the sample it is drawn according to D. We assume that D is: 1. Fixed throughout the learning process. 2. Unknown to the learner. 3. The instances are chosen independently. The target concept is specified as a computable function c, thus our instances are of the form . Our goal is to find a function h which approximates c with respect to D, in the following sense. Let error(h) = ProbD [c (x) 6= h(x)] . We would like to ensure that error(h) is below a certain threshold ε, which is given as a parameter to the algorithm. This parameter is a measure of the accuracy of the learning process. As a measure of our confidence in the outcome of the learning process, we add another parameter δ. We require that the following hold: