Chapter 5 is dedicated to the most important part of predictive modeling for biomarker discovery based on high-dimensional data – multivariate feature selection. When dealing with sparse biomedical data whose dimensionality is much higher than the number of training observations, the crucial issue is to overcome the curse of dimensionality by using methods capable of elevating signal (predictive information) from the overwhelming noise. One way of doing this is to perform many (hundreds or thousands) parallel feature selection experiments based on different random subsamples of the original training data and then aggregating their results (for example, by analyzing the distribution of variables among the results of those parallel experiments). Two designs of such parallel feature selection experiments are discussed in detail: one based on recursive feature elimination, and the other on implementing the stepwise hybrid selection with T2. The chapter includes also descriptions of three evolutionary feature selection algorithms: simulated annealing, genetic algorithms, and particle swarm optimization.

Chapter 17 describes the second real-life study, whose goal is the identification of multivariate biomarkers for liver cancer. This study implements parallel recursive feature elimination experiments coupled with random forests and support vector machines. Included are also considerations for rebalancing class proportions. Three multivariate biomarkers for liver cancer have been identified. The study has been performed in an R environment, and R scripts for all of its steps are provided.