Classifying densities using functional regression trees: Applications in oceanology

The problem of building a regression tree is considered when the response variable is a probability density function. Splitting criteria which are well adapted to measure the dissimilarity between densities are proposed using the Csiszár's f-divergence. The comparison between performances of trees constructed with various criteria is tackled through numerical simulations. Afterwards, a tree is constructed to predict the size distribution of a zooplankton community using a set of explanatory environmental variables. Functional PCA is used in order to interpret the main modes of variation of the size spectra around the predicted density in each terminal node. Finally, a bagging procedure is used to increase the accuracy of the tree-based model.