Max margin general linear modeling for neuroimage analyses

Abstract

General linear modeling (GLM) is one of the most commonly used approaches to perform voxel based analyses (VBA) for hypotheses testing in neuroimaging. In this paper we tie support vector machine based regression (SVR) and classical significance testing to provide the benefits of max margin estimation in the GLM setting. Using Welch-Satterthwaite approximations, we compute degrees of freedom (df) of error (also known as residual df) for ε-SVR. We demonstrate that ε-SVR can result not only in robustness of estimation but also improved residual df compared to the very commonly used ordinary least squares (OLS) estimation. This can result in higher sensitivity to signal in neuroimaging studies and also allow for better control of confounding effects of nuisance covariates. We demonstrate the application of our approach in white matter analyses using diffusion tensor imaging (DTI) data from autism and emotion-regulation studies.

Penalized Likelihood Phenotyping: Unifying Voxelwise Analyses and Multi-Voxel Pattern Analyses in Neuroimaging

“…Of course one could introduce additional penalty to the OLS resulting in for example, ridge regression (Marquardt and Snee, 1975). We can also use other robust loss functions such as the ε -insensitive ℓ 1 -loss function in combination with a || β || 1 as penalty (Adluru et al, 2012). The ε -insensitive ℓ 1 -loss used in the popular support-vector regression (SVR) is defined as…”

“…Testing significance of contrasts of β s using residuals involves using ratios of residuals of nested models resulting in F -tests (please see Adluru et al (2012) for examples and details). Adluru et al (2012) also show that more effective (data-driven) definitions of the df can be used to obtain better sensitivity in rejecting the null-hypotheses.…”