Sparse Uncertainty Representation in Deep Learning with Inducing Weights

Abstract

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 $\le 24.3\%$ of that of a $single$ neural network.

NeurIPS 2021 camera ready

References in corpus (11)

• PyTorch: An Imperative Style, High-Performance Deep Learning Library
• On Calibration of Modern Neural Networks
• Weight Uncertainty in Neural Networks
• Markov Chain Monte Carlo and Variational Inference: Bridging the Gap
• Adversarial Examples, Uncertainty, and Transfer Testing Robustness in Gaussian Process Hybrid Deep Networks
• Functional Variational Bayesian Neural Networks
• BatchEnsemble: An Alternative Approach to Efficient Ensemble and Lifelong Learning
• 'In-Between' Uncertainty in Bayesian Neural Networks
• Subspace Inference for Bayesian Deep Learning
• A Tutorial on Sparse Gaussian Processes and Variational Inference
• Bayesian Deep Learning via Subnetwork Inference

Cited by in corpus (1)

• TyXe: Pyro-based Bayesian neural nets for Pytorch