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Hyper Evidential Deep Learning to Quantify Composite Classification Uncertainty

Changbin Li, Kangshuo Li, Yuzhe Ou, Lance M. Kaplan, Audun Jøsang, Jin-Hee Cho, Dong Hyun Jeong, Feng Chen

TL;DR

This paper tackles uncertainty in image classification when training labels are composite due to ambiguous visuals. It introduces Hyper Evidential Neural Networks (HENN), which predict evidence leading to hyper-opinions modeled by a grouped Dirichlet distribution $\mathtt{GDD}(\boldsymbol{\alpha}, \mathbf{c})$, enabling explicit quantification of vagueness for composite labels. The training objective combines Uncertainty Partial Cross Entropy (UPCE) with a KL-divergence regularizer to stabilize evidence allocation, and is validated across four image datasets showing improved composite and singleton predictions. By capturing vagueness as a first-class uncertainty type, HENN provides a principled framework for uncertainty-aware classification in settings with composite labels, with practical implications for safety-critical and fine-grained recognition tasks.

Abstract

Deep neural networks (DNNs) have been shown to perform well on exclusive, multi-class classification tasks. However, when different classes have similar visual features, it becomes challenging for human annotators to differentiate them. This scenario necessitates the use of composite class labels. In this paper, we propose a novel framework called Hyper-Evidential Neural Network (HENN) that explicitly models predictive uncertainty due to composite class labels in training data in the context of the belief theory called Subjective Logic (SL). By placing a grouped Dirichlet distribution on the class probabilities, we treat predictions of a neural network as parameters of hyper-subjective opinions and learn the network that collects both single and composite evidence leading to these hyper-opinions by a deterministic DNN from data. We introduce a new uncertainty type called vagueness originally designed for hyper-opinions in SL to quantify composite classification uncertainty for DNNs. Our results demonstrate that HENN outperforms its state-of-the-art counterparts based on four image datasets. The code and datasets are available at: https://github.com/Hugo101/HyperEvidentialNN.

Hyper Evidential Deep Learning to Quantify Composite Classification Uncertainty

TL;DR

This paper tackles uncertainty in image classification when training labels are composite due to ambiguous visuals. It introduces Hyper Evidential Neural Networks (HENN), which predict evidence leading to hyper-opinions modeled by a grouped Dirichlet distribution , enabling explicit quantification of vagueness for composite labels. The training objective combines Uncertainty Partial Cross Entropy (UPCE) with a KL-divergence regularizer to stabilize evidence allocation, and is validated across four image datasets showing improved composite and singleton predictions. By capturing vagueness as a first-class uncertainty type, HENN provides a principled framework for uncertainty-aware classification in settings with composite labels, with practical implications for safety-critical and fine-grained recognition tasks.

Abstract

Deep neural networks (DNNs) have been shown to perform well on exclusive, multi-class classification tasks. However, when different classes have similar visual features, it becomes challenging for human annotators to differentiate them. This scenario necessitates the use of composite class labels. In this paper, we propose a novel framework called Hyper-Evidential Neural Network (HENN) that explicitly models predictive uncertainty due to composite class labels in training data in the context of the belief theory called Subjective Logic (SL). By placing a grouped Dirichlet distribution on the class probabilities, we treat predictions of a neural network as parameters of hyper-subjective opinions and learn the network that collects both single and composite evidence leading to these hyper-opinions by a deterministic DNN from data. We introduce a new uncertainty type called vagueness originally designed for hyper-opinions in SL to quantify composite classification uncertainty for DNNs. Our results demonstrate that HENN outperforms its state-of-the-art counterparts based on four image datasets. The code and datasets are available at: https://github.com/Hugo101/HyperEvidentialNN.
Paper Structure (40 sections, 7 theorems, 58 equations, 6 figures, 19 tables, 1 algorithm)

This paper contains 40 sections, 7 theorems, 58 equations, 6 figures, 19 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Hyper-Opinions and Evidential Uncertainty Measures
  4. Hyper-Opinions in Subjective Logic and GDD
  5. Vagueness and Other Evidential Uncertainty Measures by Hyper-Opinions
  6. Hyper Evidential Neural Network
  7. The Loss function and Regularization for HENN Learning
  8. Experiments
  9. Experimental setup
  10. Experimental Results
  11. Conclusion
  12. Notations
  13. Derivatives of Loss Function
  14. Expectation of GDD
  15. UPCE loss of GDD
  16. ...and 25 more sections

Key Result

Proposition 1

Assume that the universal approximation property (UAP) holds for a HENN, i.e., the network can learn an arbitrary mapping function from the input feature vector ${\bf x}$ to the evidence vector ${\bf e}$. Then, the empirical UPCE risk function $R(f) = \frac{1}{N} \sum\nolimits_{i=1}^N \texttt{UPCE}(

Figures (6)

  • Figure 1: Left: Different probability densities corresponding to specific uncertainty type for 3-class classification (Brighter colors mean higher density). Each corner represents a class. (a) A confident prediction. (b) Conflicting evidence exists for two classes (dissonance or data uncertainty). (c) Uniform Dirichlet distribution with no evidence for known classes (i.e., OOD inputs) (vacuity uncertainty). (d) There is enough evidence to exclude one class but still fail to determine the final prediction from the rest of the classes. Right: The first example shows a confident prediction w/o vagueness and low dissonance. The other two examples have the same projected probabilities but different sources of uncertainties. One is caused by conflicting evidence (dissonance), and the other one is caused by vague evidence only for the final decision from the set {Husky, Wolf} (vagueness). Fig.(d) is drawn by grouped Dirichlet distribution, not ordinary Dirichlet distribution.
  • Figure 2: ROC curves of separating composite and singleton examples among different measurements: vagueness of HENN, vacuity and dissonance of ENN, and entropy of DNN on based on kernel size 7$\times$7.
  • Figure 3: OverJS and Accuracy trends vs. the number of composite labels in tinyImageNet.
  • Figure 4: ROC curves of separating composite examples and singleton examples among different measurements: vagueness of HENN, vacurity of ENN, dissonance of ENN, and entropy of DNN on CIFAR100 for different numbers of selected composite classes and kernel sizes ("Ker" represents "kernel size").
  • Figure 5: ROC curves of separating composite examples and singleton examples among different measurements: vagueness of HENN, vacurity of ENN, dissonance of ENN, and entropy of DNN on tinyImageNet for different numbers of selected composite classes and kernel sizes. ("Ker" represents "kernel size")
  • ...and 1 more figures

Theorems & Definitions (11)

  • Proposition 1: Properties of the empirical UPCE risk function
  • Proposition 2: Effectiveness of the regularization term $\texttt{Reg}({\bf x}, \mathbf{\tilde{y}}; \bm{\theta})$
  • Theorem
  • Proposition A1: Analytical form of UPCE
  • proof
  • Proposition A2: Lower Bound of UPCE
  • proof
  • Proposition A2: Properties of the empirical UPCE risk function
  • proof
  • Proposition A2: Effectiveness of the regularization term $\texttt{Reg}({\bf x}, \mathbf{\tilde{y}}; \bm{\theta})$
  • ...and 1 more