Publication: Gradient-based MCMC samplers for dynamic causal modelling
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Gradient-based MCMC samplers for dynamic causal modelling

- Article in a journal -
 

Area
Neuroscience

Author(s)
Biswa Sengupta , Karl J. Friston , Will D. Penny

Published in
NeuroImage

Year
2016

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.

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ADiMat

BibTeX
@ARTICLE{
         Sengupta2016GbM,
       author = "Biswa Sengupta and Karl J. Friston and Will D. Penny",
       title = "Gradient-based {MCMC} samplers for dynamic causal modelling",
       journal = "NeuroImage",
       volume = "125",
       pages = "1107--1118",
       year = "2016",
       issn = "1053-8119",
       doi = "10.1016/j.neuroimage.2015.07.043",
       url = "http://www.sciencedirect.com/science/article/pii/S1053811915006540",
       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.",
       ad_area = "Neuroscience",
       ad_tools = "ADiMat"
}


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