  Normative modeling has recently been introduced as a promising approach for
modeling variation of neuroimaging measures across individuals in order to
derive biomarkers of psychiatric disorders. Current implementations rely on
Gaussian process regression, which provides coherent estimates of uncertainty
needed for the method but also suffers from drawbacks including poor scaling to
large datasets and a reliance on fixed parametric kernels. In this paper, we
propose a deep normative modeling framework based on neural processes (NPs) to
solve these problems. To achieve this, we define a stochastic process
formulation for mixed-effect models and show how NPs can be adopted for
spatially structured mixed-effect modeling of neuroimaging data. This enables
us to learn optimal feature representations and covariance structure for the
random-effect and noise via global latent variables. In this scheme, predictive
uncertainty can be approximated by sampling from the distribution of these
global latent variables. On a publicly available clinical fMRI dataset, we
compare the novelty detection performance of multivariate normative models
estimated by the proposed NP approach to a baseline multi-task Gaussian process
regression approach and show substantial improvements for certain diagnostic
problems.
