Vecchia Gaussian Process Ensembles on Internal Representations of Deep Neural Networks

TL;DR

The paper introduces Deep Vecchia Ensemble (DVE), a scalable, non-retraining method for uncertainty quantification in deep neural networks using Gaussian processes on internal representations, effective even with feature collapse.

Contribution

It proposes DVE, a novel approach combining GPs with DNN internal features that handles feature collapse without retraining, enhancing scalability and compatibility with pretrained models.

Findings

DVE effectively quantifies uncertainty on multiple datasets.

DVE is compatible with pretrained networks and has low computational overhead.

Experiments reveal insights into DVE's inner workings.

Abstract

For regression tasks, standard Gaussian processes (GPs) provide natural uncertainty quantification (UQ), while deep neural networks (DNNs) excel at representation learning. Deterministic UQ methods for neural networks have successfully combined the two and require only a single pass through the neural network. However, current methods necessitate changes to network training to address feature collapse, where unique inputs map to identical feature vectors. We propose an alternative solution, the deep Vecchia ensemble (DVE), which allows deterministic UQ to work in the presence of feature collapse, negating the need for network retraining. DVE comprises an ensemble of GPs built on hidden-layer outputs of a DNN, achieving scalability via Vecchia approximations that leverage nearest-neighbor conditional independence. DVE is compatible with pretrained networks and incurs low computational overhead. We demonstrate DVE's utility on several datasets and carry out experiments to understand the inner workings of the proposed method.