Gradient-based MCMC samplers for dynamic causal modelling

Sengupta, Biswa, Friston, Karl J and Penny, Will D. (2016) Gradient-based MCMC samplers for dynamic causal modelling. NeuroImage, 125. pp. 1107-1118. ISSN 1053-8119

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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.

Item Type: Article
Additional Information: Copyright © 2015. Published by Elsevier Inc.
Uncontrolled Keywords: algorithms,bayes theorem,humans,computer-assisted image interpretation,markov chains,theoretical models,monte carlo method,neuroimaging,comparative study
Faculty \ School: Faculty of Social Sciences > School of Psychology
Depositing User: Pure Connector
Date Deposited: 18 Aug 2017 05:07
Last Modified: 22 Apr 2020 05:21
URI: https://ueaeprints.uea.ac.uk/id/eprint/64568
DOI: 10.1016/j.neuroimage.2015.07.043

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