Statistical Agnostic Mapping: a Framework in Neuroimaging based on Concentration Inequalities

TL;DR

This paper introduces a new non-parametric framework for neuroimaging analysis that leverages concentration inequalities to improve model validation and statistical inference with limited sample sizes.

Contribution

It develops a statistical agnostic mapping framework based on concentration inequalities, offering a robust alternative to traditional methods in neuroimaging.

Findings

Provides a rigorous model validation method for small sample sizes

Offers a less conservative alternative to FWE p-value correction

Enhances stability of risk estimation in neuroimaging analysis

Abstract

In the 70s a novel branch of statistics emerged focusing its effort in selecting a function in the pattern recognition problem, which fulfils a definite relationship between the quality of the approximation and its complexity. These data-driven approaches are mainly devoted to problems of estimating dependencies with limited sample sizes and comprise all the empirical out-of sample generalization approaches, e.g. cross validation (CV) approaches. Although the latter are \emph{not designed for testing competing hypothesis or comparing different models} in neuroimaging, there are a number of theoretical developments within this theory which could be employed to derive a Statistical Agnostic (non-parametric) Mapping (SAM) at voxel or multi-voxel level. Moreover, SAMs could relieve i) the problem of instability in limited sample sizes when estimating the actual risk via the CV approaches, e.g. large error bars, and provide ii) an alternative way of Family-wise-error (FWE) corrected p-value maps in inferential statistics for hypothesis testing. In this sense, we propose a novel framework in neuroimaging based on concentration inequalities, which results in (i) a rigorous development for model validation with a small sample/dimension ratio, and (ii) a less-conservative procedure than FWE p-value correction, to determine the brain significance maps from the inferences made using small upper bounds of the actual risk.