Discretization-Induced Dirichlet Posterior for Robust Uncertainty Quantification on Regression

TL;DR

This paper introduces a new auxiliary uncertainty estimator for regression tasks that enhances robustness in uncertainty quantification, especially under out-of-distribution conditions, by modeling heteroscedastic noise and a novel Dirichlet posterior approach.

Contribution

It proposes a generalized AuxUE scheme with a Discretization-Induced Dirichlet posterior for improved robustness in uncertainty estimation on regression tasks.

Findings

Robust uncertainty estimates on age, depth, and super-resolution tasks.

Effective handling of noisy inputs and out-of-distribution data.

Scalable to both image-level and pixel-wise applications.

Abstract

Uncertainty quantification is critical for deploying deep neural networks (DNNs) in real-world applications. An Auxiliary Uncertainty Estimator (AuxUE) is one of the most effective means to estimate the uncertainty of the main task prediction without modifying the main task model. To be considered robust, an AuxUE must be capable of maintaining its performance and triggering higher uncertainties while encountering Out-of-Distribution (OOD) inputs, i.e., to provide robust aleatoric and epistemic uncertainty. However, for vision regression tasks, current AuxUE designs are mainly adopted for aleatoric uncertainty estimates, and AuxUE robustness has not been explored. In this work, we propose a generalized AuxUE scheme for more robust uncertainty quantification on regression tasks. Concretely, to achieve a more robust aleatoric uncertainty estimation, different distribution assumptions are considered for heteroscedastic noise, and Laplace distribution is finally chosen to approximate the prediction error. For epistemic uncertainty, we propose a novel solution named Discretization-Induced Dirichlet pOsterior (DIDO), which models the Dirichlet posterior on the discretized prediction error. Extensive experiments on age estimation, monocular depth estimation, and super-resolution tasks show that our proposed method can provide robust uncertainty estimates in the face of noisy inputs and that it can be scalable to both image-level and pixel-wise tasks. Code is available at https://github.com/ENSTA-U2IS/DIDO .