Abstract
Structured sparse methods have received significant attention in neuroimaging. These methods allow the incorporation of domain knowledge through additional spatial and temporal constraints in the predictive model and carry the promise of being more interpretable than non-structured sparse methods, such as LASSO or Elastic Net methods. However, although sparsity has often been advocated as leading to more interpretable models it can also lead to unstable models under subsampling or slight changes of the experimental conditions. In the present work we investigate the impact of using stability/reproducibility as an additional model selection criterion1 on several different sparse (and structured sparse) methods that have been recently applied for fMRI brain decoding. We compare three different model selection criteria: (i) classification accuracy alone; (ii) classification accuracy and overlap between the solutions; (iii) classification accuracy and correlation between the solutions. The methods we consider include LASSO, Elastic Net, Total Variation, sparse Total Variation, Laplacian and Graph Laplacian Elastic Net (GraphNET). Our results show that explicitly accounting for stability/reproducibility during the model optimization can mitigate some of the instability inherent in sparse methods. In particular, using accuracy and overlap between the solutions as a joint optimization criterion can lead to solutions that are more similar in terms of accuracy, sparsity levels and coefficient maps even when different sparsity methods are considered.
Highlights
Supervised machine learning techniques are being increasingly used in neuroimaging analysis for their inherent ability to deal with multivariate data, higher sensibility and possibility of incorporating specific prior-information.Given the high-dimensionality of neuroimaging, and the few number of samples, regularized linear models have been applied in order to produce effective predictive models (Mourao-Miranda et al, 2006, 2007; Grosenick et al, 2011; Michel et al, 2011)
We investigate the role of model selection criteria on different sparsity methods that have been recently applied for decoding fMRI data, including one we proposed in a previous work (Baldassarre et al, 2012b), and assess their performance with respect to accuracy, sparsity and reproducibility
Model selection is performed by a Leave-One-Subject-Out Cross-Validation (LOSO-CV) scheme, which we describe in detail in the methods section
Summary
Supervised machine learning techniques are being increasingly used in neuroimaging analysis for their inherent ability to deal with multivariate data, higher sensibility and possibility of incorporating specific prior-information.Given the high-dimensionality of neuroimaging, and the few number of samples, regularized linear models have been applied in order to produce effective predictive models (Mourao-Miranda et al, 2006, 2007; Grosenick et al, 2011; Michel et al, 2011). Neurosparse as, the Least Squares Ridge Regression (Tikhonov and Arsenin, 1977) or standard Support Vector Machines (SVMs) (Cortes and Vapnik, 1995) employ an l2 regularization scheme, they are incapable of discriminating which areas (or voxels) of the brain mostly contribute to the model’s predictions. Like the LASSO (Tibshirani, 1996) or the Elastic Net (Zou and Hastie, 2005), are able to estimate solutions for which only few voxels are deemed relevant, aiding interpretation Often these models provide overly sparse solutions, where the non-zero coefficients are assigned to disparate regions across the brain, without exploiting any spatial or temporal prior information (Grosenick et al, 2011; Michel et al, 2011; Rasmussen et al, 2012)
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