Gradient-based MCMC samplers for dynamic causal modelling.

Area of Science:

• Computational Neuroscience
• Statistical Modeling
• Machine Learning

Background:

• Dynamic Causal Models (DCMs) are essential for inferring directed connectivity in neuroscience.
• Markov chain Monte Carlo (MCMC) methods are crucial for parameter estimation in complex models like DCMs.
• Existing MCMC samplers may struggle with the high dimensionality and dynamical instability inherent in some DCMs.

Purpose of the Study:

• To derive and evaluate novel MCMC samplers for dynamic causal models.
• To compare the efficiency and performance of Hamiltonian MCMC (HMC-E) and Langevin Monte Carlo (LMC) algorithms for DCMs.
• To optimize sampler tuning parameters using Gaussian process models for intervention-free inference.

Main Methods:

• Derivation of Hamiltonian MCMC (HMC-E) using Hamilton's equations of motion.
• Implementation of Langevin Monte Carlo (LMC) on Euclidean (LMC-E) and Riemannian (LMC-R) manifolds.
• Optimization of HMC-E tuning parameters via Gaussian process modeling of sample correlations.
• Application of samplers to neural mass models (NMMs), a type of DCM.

Main Results:

• HMC-E demonstrated superior statistical efficiency compared to LMC-R for NMMs.
• Both HMC-E and LMC-R significantly outperformed the random walk Metropolis algorithm.
• The proposed Gaussian process-based optimization provided an effective intervention-free inference scheme for HMC-E tuning.
• LMC-R required minimal tuning, while HMC-E implementation was sensitive to parameter choices.

Conclusions:

• Gradient-based MCMC samplers, particularly HMC-E, offer substantial improvements for DCM inference over traditional methods.
• The developed HMC-E sampler, with optimized tuning, is a statistically efficient tool for analyzing neural mass models.
• The findings highlight the importance of advanced MCMC techniques for robust causal inference in computational neuroscience.