Classification with correlated features: unreliability of feature ranking and solutions

Classification and feature selection of genomics or transcriptomics data is often hampered by the large number of features as compared with the small number of samples available. Moreover, features represented by probes that either have similar molecular functions (gene expression analysis) or genomic locations (DNA copy number analysis) are highly correlated. Classical model selection methods such as penalized logistic regression or random forest become unstable in the presence of high feature correlations. Sophisticated penalties such as group Lasso or fused Lasso can force the models to assign similar weights to correlated features and thus improve model stability and interpretability. In this article, we show that the measures of feature relevance corresponding to the above-mentioned methods are biased such that the weights of the features belonging to groups of correlated features decrease as the sizes of the groups increase, which leads to incorrect model interpretation and misleading feature ranking.