Abstract: When dealing with density estimation tasks, we would like to take advantage of intelligent exploration when performing inference. We may be subject to computational constraints, or possess limited training data. To overcome these challenges, we can appeal to a Bayesian approach, leveraging uncertainty as a guiding principle. Uncertainty may determine the choice of data to next show our model, which simulations to run in a simulator-based scenario, or reveal inherent noise in the data observe.
In particular, we look to investigate the capabilities of the Bayesian Density Network (MDN), trained using Hamiltonian Monte Carlo (HMC). Beginning with an examination of such models on simple one-dimensional problems involving heteroscedastic noise, we can also provide a comparison with other approximate Bayesian methods on MDNs. There is also scope for work in the multivariate context, where we might seek a Bayesian version of models like the real-valued neural autoregressive density estimator (RNADE).