A0599
Title: Adaptive functional regression for locally heterogeneous spectroscopic data
Authors: Federico Ferraccioli - University of Padova (Italy)
Marco Stefanucci - University of Rome Tor Vergata (Italy)
Alessandro Casa - Free University of Bozen-Bolzano (Italy) [presenting]
Abstract: Mid-infrared spectroscopy is a valuable tool for collecting vast amounts of data quickly and in a relatively cheap way. These data provide a rich reservoir of information about analyzed samples, which have been used in various scientific fields. However, spectroscopic data present some serious challenges from a statistical viewpoint. In fact, each spectrum is a curve typically consisting of more than 1000 absorbance values measured across different wavelengths, with a large portion of the spectral domain known to be highly noisy and not containing relevant information for the scopes of the analyses. Nonetheless, variable selection procedures are often hindered by redundancies and complex relationships among wavelengths. Additionally, the signal is highly heterogeneous across the spectral domain, often limiting the use of standard functional data analysis tools. To address these challenges, we introduce an adaptive scalar-on-function regression tool that preserves the functional nature of the data while accommodating varying degrees of smoothness and inhomogeneous signals. Our framework allows us to include scalar covariates and to model both Gaussian and non-Gaussian responses, expanding its use to classification tasks and regression for count data. Furthermore, we propose a bootstrap-based inferential procedure to identify the spectral regions most influential in predicting response variables.
