Adaptive penalties for generalized Tikhonov regularization in statistical regression models with application to spectroscopy data.

Tikhonov regularization was proposed for multivariate calibration by Andries and Kalivas [1]. We use this framework for modeling the statistical association between spectroscopy data and a scalar outcome. In both the calibration and regression settings this regularization process has advantages over methods of spectral pre-processing and dimension-reduction approaches such as feature extraction or principal component regression. We propose an extension of this penalized regression framework by adaptively refining the penalty term to optimally focus the regularization process. We illustrate the approach using simulated spectra and compare it with other penalized regression models and with a two-step method that first pre-processes the spectra then fits a dimension-reduced model using the processed data. The methods are also applied to magnetic resonance spectroscopy data to identify brain metabolites that are associated with cognitive function.