Bayesian Neural Networks with Latent Variables (BNN+LV's) provide uncertainties in prediction estimates by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between model parameters and input noise while fitting the data equally well. We demonstrate that, as a result, traditional inference methods may yield parameters that reconstruct observed data well but generalize poorly. Next, we develop a novel inference procedure that explicitly mitigates the effects of likelihood non-identifiability during training and yields high quality predictions as well as uncertainty estimates. We demonstrate that our inference method improves upon benchmark methods across a range of synthetic and real datasets.

Bayesian neural networks with latent variables (BNNs LVs) are scalable and flexible probabilistic models: They account for uncertainty in the estimation of the network weights and, by making use of latent variables, they can capture complex noise patterns in the data. In this work, we show how to separate these two forms of uncertainty for decision-making purposes. This decomposition allows us to successfully identify informative points for active learning of functions with heteroskedastic and bimodal noise. We also demonstrate how this decomposition allows us to define a novel risk-sensitive reinforcement learning criterion to identify policies that balance expected cost, model-bias and noise averseness.