Variational Bayesian inversion for hierarchical unsupervised generative embedding (HUGE)

A recently introduced hierarchical generative model unified the inference of effective connectivity in individual subjects and the unsupervised identification of subgroups defined by connectivity patterns. This hierarchical unsupervised generative embedding (HUGE) approach combined a hierarchical formulation of dynamic causal modelling (DCM) for fMRI with Gaussian mixture models and relied on Markov chain Monte Carlo (MCMC) sampling for inference. While well suited for the inversion of complex hierarchical models, MCMC-based sampling suffers from a computational burden that is prohibitive for many applications. To address this problem, this paper derives an efficient variational Bayesian (VB) inversion scheme for HUGE that simultaneously provides approximations to the posterior distribution over model parameters and to the log model evidence. The face validity of the VB scheme was tested using two synthetic fMRI datasets with known ground truth. Additionally, an empirical fMRI dataset of stroke patients and healthy controls was used to evaluate the practical utility of the method in application to real-world problems. Our analyses demonstrate good performance of our VB scheme, with a marked speed-up of model inversion by two orders of magnitude compared to MCMC, while maintaining a similar level of accuracy. Notably, additional acceleration would be possible if parallel computing techniques were applied. Generally, our VB implementation of HUGE is fast enough to support multi-start procedures for whole-group analyses, a useful strategy to ameliorate problems with local extrema. HUGE thus represents a potentially useful practical solution for an important problem in clinical neuromodeling and computational psychiatry, i.e., the unsupervised detection of subgroups in heterogeneous populations that are defined by effective connectivity.