Mitigating the Effects of Non-Identifiability on Inference for Bayesian Neural Networks with Latent Variables
This addresses a critical issue for practitioners using Bayesian deep learning, though it is an incremental improvement focused on a specific bottleneck.
The paper tackles the problem of non-identifiability in Bayesian Neural Networks with Latent Variables, which causes asymptotic bias in posterior modes and poor generalization, and develops a novel inference procedure that improves predictions and uncertainty estimates across synthetic and real datasets.
Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty 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 the model parameters and latent variables while fitting the data equally well. We demonstrate that as a result, in the limit of infinite data, the posterior mode over the network weights and latent variables is asymptotically biased away from the ground-truth. Due to this asymptotic bias, traditional inference methods may in practice yield parameters that generalize poorly and misestimate uncertainty. 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 data-sets.