CMA package vignette

For the last few years, microarray-based class prediction has been a major topic in statistics and machine learning. Traditional methods often yield unsatisfactory results or are even inapplicable in the p n setting. Hence, microarray studies have stimulated the development of new approaches and motivated the adaptation of known traditional methods to high-dimensional data. Moreover, model selection and evaluation of prediction rules proves to be highly dif-ficult in this situation for several reasons. Firstly, the hazard of overfitting, which is common to all prediction problems, is increased by high dimensionality. Secondly, the usual evaluation scheme based on the splitting into learning and test data sets often applies only partially in the case of small samples. Lastly, modern classification techniques rely on the proper choice of hyperparameters whose optimization is highly computer-intensive, especially in the case of high-dimensional data. 2 Class prediction based high-dimensional data with small samples 2.1 Settings The classification problem can be briefly outlined as follows: we have a predictor space X, here X ⊆ Rp we have a finite set of class labels Y = {0,...,K − 1}, with K denoting the total number of classes P (x, y) denotes the joint probability distribution on X × Y we are given a finite sample S = {(x1, y1),..., (xn, yn)} of n predictor-class pairs