Controlling a confound in predictive models with a test set minimizing its effect

Predictive models applied on brain images can extract imaging biomarkers of pathologies or psychological traits. Yet, a successful prediction may be driven by a confounding effect that is correlated with the effect of interest. For instance fluid intelligence is strongly impacted by age; age is well predicted from brain images; hence successful prediction of fluid intelligence from brain images might have captured nothing more than a biomarker of aging. Here we introduce a non-sparametric approach to control for a confounding effect in a predictive model. It is based on crafting a test set on which the effect of interest is independent from the confounding effect. We name this strategy “anti mutual-information subsampling”. We demonstrate the approach with a large sample resting-state fMRI and psychometric data of healthy aging subjects (n = 608). We show that using a linear model to remove the effect of age on the brain signals (“deconfounding”) leads to pessimistic scores, as previously reported. Anti mutual-information subsampling does not require to remove from the brain signals the shared variance between aging and fluid intelligence, and hence does not display this pessimistic behavior. In addition, it is non-parametric and hence robust to violations of the linear hypothesis.