Structured Joint Aleatoric and Epistemic Uncertainty for High Dimensional Output Spaces

Leonhard F. Feiner, Manuel Nickel, Laurin Lux, Martin J. Menten, Rickmer Braren, Daniel Rueckert, Georgios Kaissis, Johannes C. Paetzold

Keywords: structured uncertainty, aleatoric, epistemic, high-dimensional data

TL;DR: We introduce an approach to approxmate joint aleatoric and epistemic uncertainty using a low-rank plus diagonal covariance matrix parametrization.

Abstract: Uncertainty estimation plays a vital role in enhancing the reliability of deep learning model predictions, especially in scenarios with high-dimensional output spaces. This paper addresses the dual nature of uncertainty — aleatoric and epistemic — focusing on their joint integration in high-dimensional regression tasks. We introduce an approach to approximate joint uncertainty using a low-rank plus diagonal covariance matrix, which preserves essential output correlations while mitigating the computational complexity associated with full covariance matrices. Specifically, our method reduces memory usage and enhances sampling efficiency and log-likelihood calculations. Simultaneously, our representation matches the true posterior better than factorized joint distributions, offering a clear advancement in reliability and explainability for deep learning model predictions. Furthermore, we empirically show that our method can efficiently enhance out of distribution detection in specific applications.

Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)

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Submission Number: 6647