Structured regression models for high-dimensional spatial spectroscopy data

Abstract

Modeling and analysis of spectroscopy data is an active area of research with applications to chemistry and biology. This paper focuses on modelling high-dimensional spectra for the purpose of noise reduction and prediction in problems where the spectra can be used as covariates. We propose a functional representation of the spectra as well as functional regression model that accommodates multiple spatial dimensions. Both steps emphasize sparsity to reduce the number of parameters and mitigate over-fitting. The motivating application for these models, discussed in some detail, is predicting bone-mineral-density (BMD), an important indicator of fracture healing, from Raman spectra, in both the in vivo and ex vivo settings of a bone fracture healing experiment. To illustrate the general applicability of the method, we also use it to predict lipoprotein concentrations from spectra obtained by nuclear magnetic resonance (NMR) spectroscopy.