Editing Sampling (statistics) (section)

===Minimax sampling===

In imbalanced datasets, where the sampling ratio does not follow the population statistics, one can resample the dataset in a conservative manner called [[minimax|minimax sampling]]. The minimax sampling has its origin in [[Theodore Wilbur Anderson|Anderson]] minimax ratio whose value is proved to be 0.5: in a binary classification, the class-sample sizes should be chosen equally. This ratio can be proved to be minimax ratio only under the assumption of [[Linear Discriminant Analysis|LDA]] classifier with Gaussian distributions. The notion of minimax sampling is recently developed for a general class of classification rules, called class-wise smart classifiers. In this case, the sampling ratio of classes is selected so that the worst case classifier error over all the possible population statistics for class prior probabilities, would be the best.<ref name=sampling-minimax/>