Penalized Least Squares Regression Methods and Applications to Neuroimaging

By Florentina Bunea, Yiyuan She, Hernando C. Ombao, Assawin Gongvatana, Kate Devlin, Ronald Cohen. 2010

163 citations recorded by the source corpus.

The goal of this paper is to review the most popular methods of predictor selection in regression models, to explain why some fail when the number P of explanatory variables exceeds the number N of participants, and to discuss alternative statistical methods that can be employed in this case. We focus on penalized least squares methods in regression models, and discuss in detail two such methods that are well established in the statistical literature, the LASSO and Elastic Net. We introduce bootstrap enhancements of these methods, the BE-LASSO and BE-Enet, that allow the user to attach a measure of uncertainty to each variable selected. Our work is motivated by a multimodal neuroimaging dataset that consists of morphometric measures (volumes at several anatomical regions of interest), white matter integrity measures from diffusion weighted data (fractional anisotropy, mean diffusivity, axial diffusivity and radial diffusivity) and clinical and demographic variables (age, education, alcohol and drug history). In this dataset, the number P of explanatory variables exceeds the number N of participants. We use the BE-LASSO and BE-Enet to provide the first statistical analysis that allows the assessment of neurocognitive performance from high dimensional neuroimaging and clinical predictors, including their interactions. The major novelty of this analysis is that biomarker selection and dimension reduction are accomplished with a view towards obtaining good predictions for the outcome of interest (i.e., the neurocognitive indices), unlike principal component analysis that are performed only on the predictors’ space independently of the outcome of interest.

Subfields: Cognitive Neuroscience, Radiology, Nuclear Medicine and Imaging, Statistics and Probability

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Citations in the corpus

Interpreting support vector machine models for multivariate group wise analysis in neuroimaging (2015, positive): “Good examples of using the LASSO in imaging are fMRI analysis presented in Bunea et al. (2011) and shape analysis presented in Kim et al. (2012); Chung (2012).”
Joint variable and rank selection for parsimonious estimation of high-dimensional matrices (2011, methodology): “We refer to Bunea et al. (2011) for details.”
Choosing prediction over explanation in psychology: Lessons from machine learning (2017, background): “Although a full treatment of these issues is beyond the scope of this paper (for excellent full-length introductions, see Browne, 2000; Bunea et al., 2011; Domingos, 2012; McNeish, 2015; an authoritative, freely available textbook is Hastie, Tibshirani, & Friedman, 2009), even a cursory familiarity ”
A Review of Feature Reduction Techniques in Neuroimaging (2013, methodology): “Lastly, we note that the performance of embedded feature reduction methods (LASSO and Elastic Net) strongly depends on the choice of penalization parameters which should be chosen through a cross-validation process (Bunea et al. 2011; Shi et al. 2007).”