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

Timothy Randolph, Jimin Ding, Madan G. Kundu, Jaroslaw Harezlak

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Tikhonov regularization was recently proposed for multivariate calibration. 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 preprocessing 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 2-step method that first preprocesses 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.

Original languageEnglish (US)
JournalJournal of Chemometrics
DOIs
StateAccepted/In press - 2016

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Tikhonov Regularization
Statistical Model
Penalized Regression
Penalty
Spectroscopy
Regression Model
Calibration
Magnetic resonance spectroscopy
Regularization
Metabolites
Refining
Multivariate Calibration
Feature extraction
Principal Component Regression
Brain
Magnetic Resonance
Reduced Model
Association reactions
Dimension Reduction
Feature Extraction

Keywords

  • Adaptive penalty
  • Calibration
  • Generalized singular value decomposition
  • Penalized regression
  • Tikhonov regularization

ASJC Scopus subject areas

  • Analytical Chemistry
  • Applied Mathematics

Cite this

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abstract = "Tikhonov regularization was recently proposed for multivariate calibration. 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 preprocessing 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 2-step method that first preprocesses 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.",
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AU - Ding, Jimin

AU - Kundu, Madan G.

AU - Harezlak, Jaroslaw

PY - 2016

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AB - Tikhonov regularization was recently proposed for multivariate calibration. 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 preprocessing 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 2-step method that first preprocesses 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.

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KW - Penalized regression

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