Clustered Variable Selection by Regularized Elimination in PLS

Variable selection is a crucial issue in many sciences, including modern biology, where an example is the selection of genomic markers for classification (diagnosing diseases, recognizing pathogenic bacteria, etc.). This becomes complicated as biological variables are in general correlated. For example, genes may be easily correlated, if they provide common biological functions. Variable selection may dissolve the group effects and mislead the focus onto a specific variable instead of a variable cluster. We study the selection and estimation properties of variable clusters in high dimensional settings when the number of variables exceeds the sample size. To address the issue a regularized elimination procedure in multiblock-PLS (mbPLS) is used, where highly correlated variables are clustered together, and whole groups are selected if they establish a relation with the response.