Markov chain Monte Carlo methods for hierarchical clustering of dynamic causal models

In this article, we address technical difficulties that arise when applying Markov chain Monte Carlo (MCMC) to hierarchical models designed to perform clustering in the space of latent parameters of subject-wise generative models. Specifically, we focus on the case where the subject-wise generative model is a dynamic causal model (DCM) for functional magnetic resonance imaging (fMRI) and clusters are defined in terms of effective brain connectivity. While an attractive approach for detecting mechanistically interpretable subgroups in heterogeneous populations, inverting such a hierarchical model represents a particularly challenging case, since DCM is often characterized by high posterior correlations between its parameters. In this context, standard MCMC schemes exhibit poor performance and extremely slow convergence. In this article, we investigate the properties of hierarchical clustering which lead to the observed failure of standard MCMC schemes and propose a solution designed to improve convergence but preserve computational complexity. Specifically, we introduce a class of proposal distributions which aims to capture the interdependencies between the parameters of the clustering and subject-wise generative models and helps to reduce random walk behaviour of the MCMC scheme. Critically, these proposal distributions only introduce a single hyperparameter that needs to be tuned to achieve good performance. For validation, we apply our proposed solution to synthetic and real-world datasets and also compare it, in terms of computational complexity and performance, to Hamiltonian Monte Carlo (HMC), a state-of-the-art Monte Carlo technique. Our results indicate that, for the specific application domain considered here, our proposed solution shows good convergence performance and superior runtime compared to HMC.