Functional Variational Bayesian Neural Networks
This work addresses a bottleneck in Bayesian deep learning for researchers and practitioners by enabling structured priors and better uncertainty quantification, representing a novel method rather than an incremental improvement.
The paper tackles the difficulty of specifying meaningful priors and posteriors in high-dimensional weight spaces for variational Bayesian neural networks by introducing functional variational Bayesian neural networks (fBNNs), which optimize an Evidence Lower Bound defined on stochastic processes, resulting in improved extrapolation, reliable uncertainty estimates, and scalability to large datasets.
Variational Bayesian neural networks (BNNs) perform variational inference over weights, but it is difficult to specify meaningful priors and approximate posteriors in a high-dimensional weight space. We introduce functional variational Bayesian neural networks (fBNNs), which maximize an Evidence Lower BOund (ELBO) defined directly on stochastic processes, i.e. distributions over functions. We prove that the KL divergence between stochastic processes equals the supremum of marginal KL divergences over all finite sets of inputs. Based on this, we introduce a practical training objective which approximates the functional ELBO using finite measurement sets and the spectral Stein gradient estimator. With fBNNs, we can specify priors entailing rich structures, including Gaussian processes and implicit stochastic processes. Empirically, we find fBNNs extrapolate well using various structured priors, provide reliable uncertainty estimates, and scale to large datasets.