Statistical Agnostic Mapping: A framework in neuroimaging based on concentration inequalities

Abstract

In the 1970s a novel branch of statistics emerged focusing its effort on the selection of a function for the pattern recognition problem that would fulfill a relationship between the quality of the approximation and its complexity. This theory is mainly devoted to problems of estimating dependencies in the case of limited sample sizes, and comprise all the empirical out-of sample generalization approaches; e.g. cross validation (CV). In this paper a data-driven approach based on concentration inequalities is designed for testing competing hypothesis or comparing different models. In this sense we derive a Statistical Agnostic (non-parametric) Mapping (SAM) for neuroimages at voxel or regional levels which is able to: relieve the problem of instability with limited sample sizes when estimating the actual risk via CV; and provide an alternative way of Family-wise error (FWE) corrected (p)-value maps in inferential statistics for hypothesis testing. Using several neuroimaging datasets (containing large and small effects) and random task group analyses to compute empirical familywise error rates, this novel framework resulted in a model validation method for small samples over dimension ratios, and a less-conservative procedure than FWE (p)-value correction to determine the significance maps from the inferences made using small upper bounds of the actual risk.