[Paper Review] The Unreasonable Effectiveness of Deep Evidential Regression

N. Meinert, Jakob Gawlikowski+1 more|arXiv (Cornell University)|May 20, 2022

Machine Learning and Algorithms4 citations

TL;DR

This paper investigates Deep Evidential Regression (DER), a method that estimates both aleatoric and epistemic uncertainty in deep learning via evidential distributions without sampling. Despite empirical success, the authors reveal DER as a heuristic with theoretical flaws, showing its effectiveness stems from convergence patterns rather than principled uncertainty quantification, and propose corrected definitions for more reliable uncertainty estimation.

ABSTRACT

There is a significant need for principled uncertainty reasoning in machine learning systems as they are increasingly deployed in safety-critical domains. A new approach with uncertainty-aware regression-based neural networks (NNs), based on learning evidential distributions for aleatoric and epistemic uncertainties, shows promise over traditional deterministic methods and typical Bayesian NNs, notably with the capabilities to disentangle aleatoric and epistemic uncertainties. Despite some empirical success of Deep Evidential Regression (DER), there are important gaps in the mathematical foundation that raise the question of why the proposed technique seemingly works. We detail the theoretical shortcomings and analyze the performance on synthetic and real-world data sets, showing that Deep Evidential Regression is a heuristic rather than an exact uncertainty quantification. We go on to discuss corrections and redefinitions of how aleatoric and epistemic uncertainties should be extracted from NNs.

Motivation & Objective

• To investigate the theoretical foundations of Deep Evidential Regression (DER), which claims to disentangle aleatoric and epistemic uncertainty in deep neural networks.
• To identify and analyze mathematical shortcomings in DER that undermine its reliability as a principled uncertainty quantification method.
• To evaluate DER's performance on synthetic and real-world datasets to assess the validity of its uncertainty estimates.
• To propose corrected definitions and redefinitions of aleatoric and epistemic uncertainties for deep neural networks based on evidential reasoning.
• To clarify why DER appears effective despite theoretical inconsistencies, linking its success to convergence behavior of predicted uncertainties.

Proposed method

• The authors derive the theoretical basis of DER using evidential distributions, modeling uncertainty through parameters analogous to those in the normal-inverse-gamma (NIG) distribution.
• They analyze the relationship between predicted uncertainty and model convergence, identifying that DER's performance correlates with training dynamics rather than true uncertainty decomposition.
• The method involves training a deep neural network to predict evidential parameters (e.g., evidence for mean and variance), from which aleatoric and epistemic uncertainties are computed via closed-form expressions.
• The authors compare DER to Bayesian neural networks and Monte Carlo Dropout, highlighting DER’s lack of sampling and computational efficiency but also its theoretical inconsistencies.
• They conduct experiments on synthetic data with known noise and sample size effects to isolate and measure the disentanglement of uncertainty types.
• The study redefines epistemic uncertainty as the variance of the predictive distribution’s mean, and aleatoric uncertainty as the expected variance, based on proper Bayesian principles.

Experimental results

Research questions

• RQ1 Why does Deep Evidential Regression perform well in practice despite lacking a solid theoretical foundation?
• RQ2 To what extent can DER accurately disentangle aleatoric and epistemic uncertainties in the presence of correlated noise and limited data?
• RQ3 How do convergence patterns of uncertainty predictions in DER relate to its empirical performance?
• RQ4 What are the correct theoretical definitions of aleatoric and epistemic uncertainty when using evidential distributions in deep learning?
• RQ5 Can DER be corrected to provide principled uncertainty quantification without requiring sampling or out-of-distribution data?

Key findings

• Deep Evidential Regression is not a principled uncertainty quantification method but rather a heuristic whose success stems from favorable convergence patterns of uncertainty predictions during training.
• The paper identifies that DER’s separation of aleatoric and epistemic uncertainty is mathematically unjustified under standard probabilistic assumptions, particularly due to incorrect parameterization of the evidential distribution.
• On synthetic data, DER fails to properly disentangle uncertainty types when the true data-generating process includes heteroscedastic noise or varying sample sizes, indicating poor generalization of its uncertainty estimates.
• The authors demonstrate that the epistemic uncertainty in DER is not properly calibrated and does not scale with sample size as expected in Bayesian models, undermining its reliability in safety-critical applications.
• The study shows that the original DER formulation overestimates epistemic uncertainty in low-data regions and underestimates it in high-data regions, indicating poor calibration.
• The proposed redefinition of epistemic uncertainty as the variance of the predictive mean and aleatoric uncertainty as the expected variance leads to more consistent and theoretically sound uncertainty estimates in controlled settings.