  There remains an open question about the usefulness and the interpretation of
Machine learning (MLE) approaches for discrimination of spatial patterns of
brain images between samples or activation states. In the last few decades,
these approaches have limited their operation to feature extraction and linear
classification tasks for between-group inference. In this context, statistical
inference is assessed by randomly permuting image labels or by the use of
random effect models that consider between-subject variability. These
multivariate MLE-based statistical pipelines, whilst potentially more effective
for detecting activations than hypotheses-driven methods, have lost their
mathematical elegance, ease of interpretation, and spatial localization of the
ubiquitous General linear Model (GLM). Recently, the estimation of the
conventional GLM has been demonstrated to be connected to an univariate
classification task when the design matrix is expressed as a binary indicator
matrix. In this paper we explore the complete connection between the univariate
GLM and MLE \emph{regressions}. To this purpose we derive a refined statistical
test with the GLM based on the parameters obtained by a linear Support Vector
Regression (SVR) in the \emph{inverse} problem (SVR-iGLM). Subsequently, random
field theory (RFT) is employed for assessing statistical significance following
a conventional GLM benchmark. Experimental results demonstrate how parameter
estimations derived from each model (mainly GLM and SVR) result in different
experimental design estimates that are significantly related to the predefined
functional task. Moreover, using real data from a multisite initiative the
proposed MLE-based inference demonstrates statistical power and the control of
false positives, outperforming the regular GLM.
