Global inducing point variational posteriors for Bayesian neural networks and deep Gaussian processes
This work addresses the challenge of capturing layer correlations in Bayesian deep learning models, offering a unified inference approach that improves performance for tasks like image classification.
The paper tackles the problem of modeling dependencies across layers in Bayesian neural networks and deep Gaussian processes by introducing a correlated approximate posterior using global inducing points, achieving state-of-the-art performance of 86.7% on CIFAR-10 without data augmentation or tempering.
We consider the optimal approximate posterior over the top-layer weights in a Bayesian neural network for regression, and show that it exhibits strong dependencies on the lower-layer weights. We adapt this result to develop a correlated approximate posterior over the weights at all layers in a Bayesian neural network. We extend this approach to deep Gaussian processes, unifying inference in the two model classes. Our approximate posterior uses learned "global" inducing points, which are defined only at the input layer and propagated through the network to obtain inducing inputs at subsequent layers. By contrast, standard, "local", inducing point methods from the deep Gaussian process literature optimise a separate set of inducing inputs at every layer, and thus do not model correlations across layers. Our method gives state-of-the-art performance for a variational Bayesian method, without data augmentation or tempering, on CIFAR-10 of 86.7%, which is comparable to SGMCMC without tempering but with data augmentation (88% in Wenzel et al. 2020).