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The selection of grouped variables using the random forest algorithm isconsidered. First a new importance measure adapted for groups of variables isproposed. Theoretical insights into this criterion are given for additiveregression models. Second, an original method for selecting functionalvariables based on the grouped variable importance measure is developed. Usinga wavelet basis, it is proposed to regroup all of the wavelet coefficients fora given functional variable and use a wrapper selection algorithm with thesegroups. Various other groupings which take advantage of the frequency and timelocalization of the wavelet basis are proposed. An extensive simulation studyis performed to illustrate the use of the grouped importance measure in thiscontext. The method is applied to a real life problem coming from aviationsafety.

Grouped variable importance with random forests and application to multiple functional data analysis