SuRF: a New Method for Sparse Variable Selection, with Application in Microbiome Data Analysis

Abstract: In this paper, we present a new variable selection method for regression and classification purposes. Our method, called Subsampling Ranking Forward selection (SuRF), is based on LASSO penalised regression, subsampling and forward-selection methods. SuRF offers major advantages over existing variable selection methods in terms of both sparsity of selected models and model inference. We provide an R package that can implement our method for generalized linear models. We apply our method to classification problems from microbiome data, using a novel agglomeration approach to deal with the special tree-like correlation structure of the variables. Existing methods arbitrarily choose a taxonomic level a priori before performing the analysis, whereas by combining SuRF with these aggregated variables, we are able to identify the key biomarkers at the appropriate taxonomic level, as suggested by the data. We present simulations in multiple sparse settings to demonstrate that our approach performs better than several other popularly used existing approaches in recovering the true variables. We apply SuRF to two microbiome data sets: one about prediction of pouchitis and another for identifying samples from two healthy individuals. We find that SuRF can provide a better or comparable prediction with other methods while controlling the false positive rate of variable selection.