Uncertainty Estimation by Density Aware Evidential Deep Learning

TL;DR

This work addresses the challenge of reliable, single-pass uncertainty estimation and OOD detection. It introduces Density Aware Evidential Deep Learning (DAEDL), which combines a novel exponential Dirichlet parameterization with feature-space density estimation via Gaussian discriminant analysis to produce distance-aware uncertainty. Theoretical results show DAEDL yields uniform predictions for distant OOD data, can be interpreted as an input-dependent Dirichlet-Categorical model with an improper prior, and corresponds to adaptive temperature scaled softmax; empirically it achieves state-of-the-art performance on OOD detection, confidence calibration, and distribution shift tasks across MNIST and CIFAR-10 family datasets. The approach requires minimal architectural changes, leverages spectral normalization for stable feature spaces, and offers a practical single-forward-pass uncertainty estimation with strong empirical impact.

Abstract

Evidential deep learning (EDL) has shown remarkable success in uncertainty estimation. However, there is still room for improvement, particularly in out-of-distribution (OOD) detection and classification tasks. The limited OOD detection performance of EDL arises from its inability to reflect the distance between the testing example and training data when quantifying uncertainty, while its limited classification performance stems from its parameterization of the concentration parameters. To address these limitations, we propose a novel method called Density Aware Evidential Deep Learning (DAEDL). DAEDL integrates the feature space density of the testing example with the output of EDL during the prediction stage, while using a novel parameterization that resolves the issues in the conventional parameterization. We prove that DAEDL enjoys a number of favorable theoretical properties. DAEDL demonstrates state-of-the-art performance across diverse downstream tasks related to uncertainty estimation and classification

Figures (8)

• Figure 1: Uncertainty representations on the two moons dataset. (a) Softmax, (b) EDL, and (c) DAEDL (ours).
• Figure 2: Graphical representation of the prediction stage of DAEDL. The process begins with the computation of the logits (blue), followed by the estimation of the normalized feature space density of the testing example (orange). These two components are integrated to derive the concentration parameters (black).
• Figure 3: Relationship between Softmax, EDL+, AdaTS, and DAEDL
• Figure 4: The plot shows the average scores for distribution shift detection in the CIFAR-10-C dataset. The scores were obtained by averaging over 5 independent runs. The score for each run was obtained by averaging over 19 different corruptions. The left-side figures show the results using AUPR, while the right-side figures present the outcomes with AUROC. Additionally, the top row displays the results obtained using aleatoric uncertainty, and the bottom row features the results obtained using epistemic uncertainty.
• Figure 5: AUPR scores for distribution shift detection using aleatoric uncertainty estimates across 19 different corruptions in the CIFAR-10-C dataset

Theorems & Definitions (13)

• Theorem 4.1
• Theorem 4.2
• Theorem 4.3
• Theorem 4.4
• Corollary 4.5
• Lemma 1.3
• proof
• Lemma 1.4
• Lemma 1.5
• proof