Inversion of hierarchical Bayesian models using Gaussian processes

Area of Science:

• Computational neuroscience
• Neuroimaging analysis
• Statistical modeling

Background:

• Hierarchical Bayesian models (HBMs) are widely used in neuroimaging for fMRI and behavioral data analysis.
• Standard inversion methods like MCMC are slow, and variational Bayes (VB) can get stuck in local minima.
• Efficient and robust optimization is crucial for complex HBMs in neuroimaging.

Purpose of the Study:

• To investigate Gaussian process optimisation (GPO) as an alternative global optimization technique for HBMs in neuroimaging.
• To introduce a novel hybrid GPO approach combining global search with local gradient-based methods for computational efficiency.
• To evaluate the performance of GPO against MCMC and VB for Dynamic Causal Modelling (DCM) and the Hierarchical Gaussian Filter (HGF).

Main Methods:

• Gaussian Process Optimisation (GPO) for global optimization of objective functions.
• A novel hybrid approach combining GPO with local gradient-based search for high-dimensional problems.
• Comparative analysis using simulated and empirical neuroimaging data (fMRI, behavioral).
• Evaluation against established methods: Markov Chain Monte Carlo (MCMC) and Variational Bayes (VB).

Main Results:

• GPO provides parameter estimates with accuracy equivalent to or better than MCMC and VB.
• The novel GPO implementation significantly reduces computational cost compared to MCMC.
• GPO effectively avoids local minima, ensuring more robust model inversion.
• The hybrid GPO approach demonstrates computational efficiency in high-dimensional neuroimaging models.

Conclusions:

• Gaussian process optimisation (GPO) is a viable, efficient, and accurate method for inverting hierarchical Bayesian models in neuroimaging.
• The hybrid GPO approach offers a significant computational advantage for complex models like DCM and HGF.
• GPO is recommended for robust and efficient analysis of high-dimensional and nonlinear neuroimaging data.
• This method has the potential to accelerate research in computational neuroscience and neuroimaging.