A Deep Learning Method for Comparing Bayesian Hierarchical Models
This addresses a computational bottleneck for researchers using Bayesian hierarchical models, though it appears incremental as an efficiency improvement over existing methods.
The authors tackled the intractability of Bayesian model comparison for hierarchical models by proposing a deep learning method that enables amortized inference, demonstrating excellent performance against state-of-the-art bridge sampling and successfully comparing previously intractable hierarchical evidence accumulation models.
Bayesian model comparison (BMC) offers a principled approach for assessing the relative merits of competing computational models and propagating uncertainty into model selection decisions. However, BMC is often intractable for the popular class of hierarchical models due to their high-dimensional nested parameter structure. To address this intractability, we propose a deep learning method for performing BMC on any set of hierarchical models which can be instantiated as probabilistic programs. Since our method enables amortized inference, it allows efficient re-estimation of posterior model probabilities and fast performance validation prior to any real-data application. In a series of extensive validation studies, we benchmark the performance of our method against the state-of-the-art bridge sampling method and demonstrate excellent amortized inference across all BMC settings. We then showcase our method by comparing four hierarchical evidence accumulation models that have previously been deemed intractable for BMC due to partly implicit likelihoods. Additionally, we demonstrate how transfer learning can be leveraged to enhance training efficiency. We provide reproducible code for all analyses and an open-source implementation of our method.