  A connection between the General Linear Model (GLM) in combination with
classical statistical inference and the machine learning (MLE)-based inference
is described in this paper. Firstly, the estimation of the GLM parameters is
expressed as a Linear Regression Model (LRM) of an indicator matrix, that is,
in terms of the inverse problem of regressing the observations. In other words,
both approaches, i.e. GLM and LRM, apply to different domains, the observation
and the label domains, and are linked by a normalization value at the
least-squares solution. Subsequently, from this relationship we derive a
statistical test based on a more refined predictive algorithm, i.e. the
(non)linear Support Vector Machine (SVM) that maximizes the class margin of
separation, within a permutation analysis. The MLE-based inference employs a
residual score and includes the upper bound to compute a better estimation of
the actual (real) error. Experimental results demonstrate how the parameter
estimations derived from each model resulted in different classification
performances in the equivalent inverse problem. Moreover, using real data the
aforementioned predictive algorithms within permutation tests, including such
model-free estimators, are able to provide a good trade-off between type I
error and statistical power.
