Learning Structured Gaussians to Approximate Deep Ensembles

TL;DR

This paper introduces a method to approximate deep ensemble predictions with a structured Gaussian distribution, enabling explicit uncertainty modeling, efficient sampling, and interpretability for dense image prediction tasks.

Contribution

It presents a novel sparse-structured Gaussian approximation for ensemble outputs, trained via a neural network to capture correlations and uncertainty explicitly.

Findings

Effective approximation of ensemble uncertainty

Enables visualisation of learned correlation structures

Maintains comparable predictive performance

Abstract

This paper proposes using a sparse-structured multivariate Gaussian to provide a closed-form approximator for the output of probabilistic ensemble models used for dense image prediction tasks. This is achieved through a convolutional neural network that predicts the mean and covariance of the distribution, where the inverse covariance is parameterised by a sparsely structured Cholesky matrix. Similarly to distillation approaches, our single network is trained to maximise the probability of samples from pre-trained probabilistic models, in this work we use a fixed ensemble of networks. Once trained, our compact representation can be used to efficiently draw spatially correlated samples from the approximated output distribution. Importantly, this approach captures the uncertainty and structured correlations in the predictions explicitly in a formal distribution, rather than implicitly through sampling alone. This allows direct introspection of the model, enabling visualisation of the learned structure. Moreover, this formulation provides two further benefits: estimation of a sample probability, and the introduction of arbitrary spatial conditioning at test time. We demonstrate the merits of our approach on monocular depth estimation and show that the advantages of our approach are obtained with comparable quantitative performance.