Sampling-based inference for large linear models, with application to linearised Laplace
This work addresses the problem of scaling Bayesian uncertainty quantification for large neural networks, which is incremental but impactful for practitioners in machine learning.
The paper tackles the computational limitations of Bayesian linear models in neural network uncertainty quantification, specifically the linearised Laplace method, by introducing a scalable sample-based inference method and hyperparameter selection, enabling application to large networks like ResNet-50 on ImageNet with 50M parameters and 1.2M datapoints.
Large-scale linear models are ubiquitous throughout machine learning, with contemporary application as surrogate models for neural network uncertainty quantification; that is, the linearised Laplace method. Alas, the computational cost associated with Bayesian linear models constrains this method's application to small networks, small output spaces and small datasets. We address this limitation by introducing a scalable sample-based Bayesian inference method for conjugate Gaussian multi-output linear models, together with a matching method for hyperparameter (regularisation) selection. Furthermore, we use a classic feature normalisation method (the g-prior) to resolve a previously highlighted pathology of the linearised Laplace method. Together, these contributions allow us to perform linearised neural network inference with ResNet-18 on CIFAR100 (11M parameters, 100 outputs x 50k datapoints), with ResNet-50 on Imagenet (50M parameters, 1000 outputs x 1.2M datapoints) and with a U-Net on a high-resolution tomographic reconstruction task (2M parameters, 251k output~dimensions).