A hierarchical model for integrating unsupervised generative embedding and empirical Bayes

- A novel unified hierarchical framework for DCM is presented.
- Simultaneous parameter inference, unsupervised learning and empirical Bayes.
- MCMC sampling for inference.
- Improved model evidence over non-hierarchical DCM.

BackgroundGenerative models of neuroimaging data, such as dynamic causal models (DCMs), are commonly used for inferring effective connectivity from individual subject data. Recently introduced “generative embedding” approaches have used DCM-based connectivity parameters for supervised classification of individual patients or to find unknown subgroups in heterogeneous groups using unsupervised clustering methods.New methodWe present a novel framework which combines DCMs with finite mixture models into a single hierarchical model. This approach unifies the inference of connectivity parameters in individual subjects with inference on population structure, i.e. the existence of subgroups defined by model parameters, and allows for empirical Bayesian estimates of a subject's connectivity based on subgroup-specific prior distributions. We introduce a Markov chain Monte Carlo sampling method for inversion of this hierarchical generative model.ResultsThis paper formally introduces the idea behind our novel concept and demonstrates the face validity of the model in application to both simulated data as well as an empirical fMRI dataset from healthy controls and patients with schizophrenia.Comparison with existing method(s)The analysis of our empirical fMRI data demonstrates that our approach results in superior model evidence than the conventional non-hierarchical inversion of DCMs.ConclusionsIn this paper, we have presented a novel unified framework to jointly infer the effective connectivity parameters in DCMs for multiple subjects and, at the same time, discover connectivity-defined cluster structure of the whole population, using a mixture model approach.