t10 - The model we will now introduce is known under a...

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The model we will now introduce is known under a number of different names depending on the discipline concerned. Within statistics it would be known as the study of rates of uniform convergence, or frequentist inference, but within computer science it is generally referred to as the probably approximately correct or pac model, although Vapnik and Chervonenkis applied this style of analysis to statistical inference many years before it became popular in machine learning. The reason for the name will become apparent when we describe the components of the model. The key assumption on which the model is based is that the data used in training and testing are generated independently and identically (i.i.d.) according to an unknown but fixed distribution ?. We assume this is a distribution over input/output pairings (x, y) ? X {-1, 1}, an approach which subsumes the case where the output y is determined by a fixed target function t of the input y = t(x). Adaptations of the model have considered the case where the distribution changes over time, or where there is not full independence in the generation of the examples in the training set, as might be expected in for instance a sequence of examples generated as a time series. The model also ignores the
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