Variable Selection through Correlation Sifting

Many applications of computational biology require a variable selection procedure to sift through a large number of input variables and select some smaller number that influence a target variable of interest. For example, in virology, only some small number of viral protein fragments influence the nature of the immune response during viral infection. Due to the large number of variables to be considered, a brute-force search for the subset of variables is in general intractable. To approximate this, methods based on l1-regularized linear regression have been proposed and have been found to be particularly successful. It is well understood however that such methods fail to choose the correct subset of variables if these are highly correlated with other "decoy" variables. We present a method for sifting through sets of highly correlated variables which leads to higher accuracy in selecting the correct variables. The main innovation is a filtering step that reduces correlations among variables to be selected, making the l1-regularization effective for datasets on which many methods for variable selection fail. The filtering step changes both the values of the predictor variables and output values by projections onto components obtained through a computationally-inexpensive principal components analysis. In this paper we demonstrate the usefulness of our method on synthetic datasets and on novel applications in virology. These include HIV viral load analysis based on patients' HIV sequences and immune types, as well as the analysis of seasonal variation in influenza death rates based on the regions of the influenza genome that undergo diversifying selection in the previous season.