title: Gradient-based MCMC samplers for dynamic causal modelling.
abstract: In this technical note, we derive two MCMC (Markov chain Monte Carlo) samplers for dynamic causal models (DCMs). Specifically, we use (a) Hamiltonian MCMC (HMC-E) where sampling is simulated using Hamilton's equation of motion and (b) Langevin Monte Carlo algorithm (LMC-R and LMC-E) that simulates the Langevin diffusion of samples using gradients either on a Euclidean (E) or on a Riemannian (R) manifold. While LMC-R requires minimal tuning, the implementation of HMC-E is heavily dependent on its tuning parameters. These parameters are therefore optimised by learning a Gaussian process model of the time-normalised sample correlation matrix. This allows one to formulate an objective function that balances tuning parameter exploration and exploitation, furnishing an intervention-free inference scheme. Using neural mass models (NMMs)-a class of biophysically motivated DCMs-we find that HMC-E is statistically more efficient than LMC-R (with a Riemannian metric); yet both gradient-based samplers are far superior to the random walk Metropolis algorithm, which proves inadequate to steer away from dynamical instability.
authors.affiliation: Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12 Queen Square, London WC1N 3BG, UK. Electronic address: b.sengupta@ucl.ac.uk.
authors.forename: Biswa
authors.initials: B
authors.lastname: Sengupta
authors.affiliation: Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12 Queen Square, London WC1N 3BG, UK.
authors.forename: Karl J
authors.initials: KJ
authors.lastname: Friston
authors.affiliation: Wellcome Trust Centre for Neuroimaging, Institute of Neurology, University College London, 12 Queen Square, London WC1N 3BG, UK.
authors.forename: Will D
authors.initials: WD
authors.lastname: Penny
mesh_terms: D000465:Algorithms; D001499:Bayes Theorem; D006801:Humans; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008390:Markov Chains; D008962:Models, Theoretical; D009010:Monte Carlo Method; D059906:Neuroimaging / Q000379:methods*