Sequential reversible jump MCMC for dynamic Bayesian neural networks

The challenge to automatically select the best among models of varying dimensions remains open, especially in the context of complex models, sparse data, and noisy data. Bayesian neural networks employ Markov chain Monte Carlo (MCMC) and variational inference methods for training (sampling) model parameters. However, the progress of MCMC methods in deep learning has been slow due to high computational requirements and uninformative priors of model parameters. Reversible jump MCMC allows sampling of model parameters of variable lengths; hence, it has the potential to train Bayesian neural networks effectively. In this paper, we implement reversible jump MCMC for training dynamic Bayesian neural networks that feature cascaded neural networks with dynamic hidden and input neurons. We apply the methodology to a wide range of regression and classification problems from the literature. The results show that our proposed framework provides an effective approach for the dynamic exploration of models while featuring uncertainty quantification that not only caters to model parameters but also extends to model topology. This opens up the road for uncertainty quantification in dynamic neural networks where hidden and input neurons can change over time.