Sparse Uncertainty Representation in Deep Learning with Inducing Weights

Bayesian neural networks and deep ensembles represent two modern paradigms of uncertainty quantification in deep learning. Yet these approaches struggle to scale mainly due to memory inefficiency issues, since they require parameter storage several times higher than their deterministic counterparts. To address this, we augment the weight matrix of each layer with a small number of inducing weights, thereby projecting the uncertainty quantification into such low dimensional spaces. We further extend Matheron's conditional Gaussian sampling rule to enable fast weight sampling, which enables our inference method to maintain reasonable run-time as compared with ensembles. Importantly, our approach achieves competitive performance to the state-of-the-art in prediction and uncertainty estimation tasks with fully connected neural networks and ResNets, while reducing the parameter size to $\leq 24.3\%$ of that of a $single$ neural network.