The pitfalls of using Gaussian Process Regression for normative modeling

Normative modeling, a group of methods used to quantify an individual's deviation from some expected trajectory relative to observed variability around that trajectory, has been used to characterize subject heterogeneity. Gaussian Processes Regression includes an estimate of variable uncertainty across the input domain, which at face value makes it an attractive method to normalize the cohort heterogeneity where the deviation between predicted value and true observation is divided by the derived uncertainty directly from Gaussian Processes Regression. However, we show that the uncertainty directly from Gaussian Processes Regression is irrelevant to the cohort heterogeneity in general.