Topic: Contributed on Nonparametric functional data analysis Title: Nearest neighbor ensembles for functional data Authors:  Jan Gertheiss - Georg August University of Goettingen (Germany) [presenting]
Karen Fuchs - LMU Munich - Siemens AG Munich (Germany)
Abstract: An ensemble method for nonparametric classification with functional data is introduced that inherently provides automatic and interpretable feature selection. It is designed for single as well as multiple functional (and non-functional) covariates. The ensemble members are posterior probability estimates that are obtained using $k-$nearest-neighbors based on different semi-metrics, with each of those semi-metrics focusing on a specific curve feature. Each ensemble member, and thus each curve feature, is weighted by a specific coefficient which is estimated using a proper scoring rule with implicit lasso-type penalty, such that some coefficients can be estimated to be exactly zero. Thus, the ensemble automatically provides feature (and variable) selection. The method is illustrated in simulation studies and on real data from water quality monitoring. Besides classification, the presented approach can also be used for regression with functional covariates.