Bias in Random Forest Variable Importance Measures: Illustrations, Sources and a Solution

Variable importance measures for random forests have been receiving
increased attention as a means of variable selection in many
classification tasks in bioinformatics and related scientific
fields, for instance to select a subset of genetic markers relevant
for the prediction of a certain disease. We show that random forest
variable importance measures are a sensible means for variable
selection in many applications, but are not reliable in situations
where potential predictor variables vary in their scale level or
their number of categories. This is particularly important in
genomics and computational biology, where predictors often include
variables of different types, for example when predictors include
both sequence data and continuous variables such as folding energy,
or when amino acid sequence data show different numbers of
categories. Simulation studies are presented illustrating that,
when random forest variable importance measures are used with data
of varying types, the results are misleading because suboptimal
predictor variables may be artificially preferred in variable
selection. The two mechanisms underlying this deficiency are biased
variable selection in the individual classification trees used to
build the random forest on one hand, and effects induced by
bootstrap sampling with replacement on the other hand. We propose
to employ an alternative implementation of random forests, that
provides unbiased variable selection in the individual
classification trees. When this method is applied using subsampling
without replacement, the resulting variable importance measures can
be used reliably for variable selection even in situations where
the potential predictor variables vary in their scale level or
their number of categories. The usage of both random forest
algorithms and their variable importance measures in the R system
for statistical computing is illustrated and documented thoroughly
in an application re-analysing data from a study on RNA editing.
Therefore the suggested method can be applied straightforwardly by
scientists in bioinformatics research.