A deep learning method for comparing Bayesian hierarchical models

Area of Science:

• Computational Neuroscience
• Machine Learning
• Statistical Modeling

Background:

• Bayesian model comparison (BMC) is crucial for evaluating computational models but often intractable for hierarchical models due to complex parameter structures.
• Existing methods struggle with high-dimensional nested parameters and implicit likelihoods common in hierarchical models.

Purpose of the Study:

• To develop a deep learning method for performing Bayesian model comparison on hierarchical models.
• To enable efficient amortized inference for posterior model probabilities and fast performance validation.
• To address the intractability of BMC for hierarchical models with implicit likelihoods.

Main Methods:

• Proposed a deep learning approach applicable to hierarchical models representable as probabilistic programs.
• Utilized amortized inference for efficient posterior model probability estimation and validation.
• Benchmarked against state-of-the-art bridge sampling and explored transfer learning for training efficiency.

Main Results:

• Demonstrated excellent amortized inference performance across various BMC settings, outperforming bridge sampling.
• Successfully applied the method to compare four hierarchical evidence accumulation models previously intractable for BMC.
• Showcased enhanced training efficiency through transfer learning.

Conclusions:

• The proposed deep learning method effectively addresses the intractability of BMC for hierarchical models.
• This approach offers efficient and scalable solutions for model comparison and uncertainty propagation in complex statistical models.
• Reproducible code and an open-source implementation are provided for broader accessibility.