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Risk-aware Classification via Uncertainty Quantification

Murat Sensoy, Lance M. Kaplan, Simon Julier, Maryam Saleki, Federico Cerutti

TL;DR

This work addresses the problem of overconfident misclassifications in deep learning by framing real-world classification as risk-aware decision making under uncertainty. It shows that Evidential Deep Learning (EDL), which predicts Dirichlet-distributed beliefs through evidence counts, satisfies three key desiderata: uncertainty quantification with Dirichlet priors, smooth transfer from pre-trained models, and compositionality to fuse disjoint classifiers. Building on EDL, the authors introduce risk-aware variants (riskEDL, EDL(p), EDL(pg)) that integrate misclassification costs via Dirichlet-based priors and either supervised or bandit-style learning to minimize expected risk while preserving calibrated uncertainty. Empirical results on MNIST and CIFAR10 demonstrate substantial reductions in misclassification costs with competitive accuracy, and the fusion of evidential classifiers shows improved performance when combining disjoint category sets. Overall, the paper advances risk-aware, uncertainty-calibrated classification with practical pathways for transfer learning and compositional system design.

Abstract

Autonomous and semi-autonomous systems are using deep learning models to improve decision-making. However, deep classifiers can be overly confident in their incorrect predictions, a major issue especially in safety-critical domains. The present study introduces three foundational desiderata for developing real-world risk-aware classification systems. Expanding upon the previously proposed Evidential Deep Learning (EDL), we demonstrate the unity between these principles and EDL's operational attributes. We then augment EDL empowering autonomous agents to exercise discretion during structured decision-making when uncertainty and risks are inherent. We rigorously examine empirical scenarios to substantiate these theoretical innovations. In contrast to existing risk-aware classifiers, our proposed methodologies consistently exhibit superior performance, underscoring their transformative potential in risk-conscious classification strategies.

Risk-aware Classification via Uncertainty Quantification

TL;DR

This work addresses the problem of overconfident misclassifications in deep learning by framing real-world classification as risk-aware decision making under uncertainty. It shows that Evidential Deep Learning (EDL), which predicts Dirichlet-distributed beliefs through evidence counts, satisfies three key desiderata: uncertainty quantification with Dirichlet priors, smooth transfer from pre-trained models, and compositionality to fuse disjoint classifiers. Building on EDL, the authors introduce risk-aware variants (riskEDL, EDL(p), EDL(pg)) that integrate misclassification costs via Dirichlet-based priors and either supervised or bandit-style learning to minimize expected risk while preserving calibrated uncertainty. Empirical results on MNIST and CIFAR10 demonstrate substantial reductions in misclassification costs with competitive accuracy, and the fusion of evidential classifiers shows improved performance when combining disjoint category sets. Overall, the paper advances risk-aware, uncertainty-calibrated classification with practical pathways for transfer learning and compositional system design.

Abstract

Autonomous and semi-autonomous systems are using deep learning models to improve decision-making. However, deep classifiers can be overly confident in their incorrect predictions, a major issue especially in safety-critical domains. The present study introduces three foundational desiderata for developing real-world risk-aware classification systems. Expanding upon the previously proposed Evidential Deep Learning (EDL), we demonstrate the unity between these principles and EDL's operational attributes. We then augment EDL empowering autonomous agents to exercise discretion during structured decision-making when uncertainty and risks are inherent. We rigorously examine empirical scenarios to substantiate these theoretical innovations. In contrast to existing risk-aware classifiers, our proposed methodologies consistently exhibit superior performance, underscoring their transformative potential in risk-conscious classification strategies.

Paper Structure

This paper contains 18 sections, 3 theorems, 21 equations, 10 figures, 1 table.

Table of Contents

  1. Introduction
  2. Motivation and Desiderata for Real-World Risk-Aware Classification
  3. The Problem with the Over-Confident Classifier
  4. A Primer in Dirichlet Distribution
  5. Real-World Risk-Aware Classification Desiderata
  6. Evidential Deep Learning (EDL) Revisited
  7. Learning Dirichlet Distributions (D1)
  8. Knowledge Transfer from Pre-trained Models (D2)
  9. Fusion of Evidential Classifiers (D3)
  10. Risk-aware Classification under Uncertainty
  11. riskEDL: Combining EDL loss with a risk-awareness related loss
  12. EDL(p): Minimizing the Risk of Misclassifications
  13. EDL(pg): Policy Gradient for Learning Pignistic Priors
  14. Evaluation
  15. Discussion and Related Work
  16. ...and 3 more sections

Key Result

Proposition 1

For any $\alpha_{ij} \geq 1$, the inequality $\mathcal{L}_{ij}^{var} < \mathcal{L}_{ij}^{err}$ is satisfied.

Figures (10)

  • Figure 1: Classifying a rotated digit $1$ (positioned at the bottom) across various angles spanning from 0 to 180 degrees involves the calculation of classification probabilities through the softmax function.
  • Figure 2: Probability density function of different $\textnormal{Dirichlet} (\bm{\pi}|\bm{\alpha})$ distributions over three possible outcomes.
  • Figure 3: Visual depiction of the plate notation for discriminative evidential classifiers.
  • Figure 4: ROC (left) and PRC (right) for the fusion of pre-trained and EDL-tuned classifiers. We used the entropy of predictions as uncertainty scores, and the area under the curves indicates how useful uncertainties are while discriminating between correct and incorrect predictions.
  • Figure 5: Proposed architecture for risk-aware classification.
  • ...and 5 more figures

Theorems & Definitions (3)

  • Proposition 1
  • Proposition 2
  • Proposition 3