Normative Modeling of Neuroimaging Data Using Scalable Multi-task Gaussian Processes

Normative modeling has recently been proposed as an alternative for the case-control approach in modeling heterogeneity within clinical cohorts. Normative modeling is based on single-output Gaussian process regression that provides coherent estimates of uncertainty required by the method but does not consider spatial covariance structure. Here, we introduce a scalable multi-task Gaussian process regression (S-MTGPR) approach to address this problem. To this end, we exploit a combination of a low-rank approximation of the spatial covariance matrix with algebraic properties of Kronecker product in order to reduce the computational complexity of Gaussian process regression in high-dimensional output spaces. On a public fMRI dataset, we show that S-MTGPR: (1) leads to substantial computational improvements that allow us to estimate normative models for high-dimensional fMRI data whilst accounting for spatial structure in data; (2) by modeling both spatial and across-sample variances, it provides higher sensitivity in novelty detection scenarios.