Evidential Deep Learning for Uncertainty Quantification: A Critical Analysis and Reinterpretation as Out-of-Distribution Detection

Core Concepts

Evidential Deep Learning (EDL) methods, while empirically successful in tasks like out-of-distribution detection, do not effectively quantify epistemic and aleatoric uncertainty due to their reliance on fitting a fixed target distribution and the absence of model uncertainty.

Abstract

Bibliographic Information:

Shen, M., Ryu, J. J., Ghosh, S., Bu, Y., Sattigeri, P., Das, S., & Wornell, G. W. (2024). Are Uncertainty Quantification Capabilities of Evidential Deep Learning a Mirage? In Advances in Neural Information Processing Systems (Vol. 38).

Research Objective:

This paper investigates the effectiveness of Evidential Deep Learning (EDL) methods for uncertainty quantification, particularly their ability to accurately represent and distinguish between epistemic and aleatoric uncertainty. The authors aim to reconcile the perceived empirical success of EDL in downstream tasks with recent theoretical critiques highlighting limitations in their uncertainty quantification capabilities.

Methodology:

The authors propose a new taxonomy for EDL methods, unifying various objective functions used in the literature under a single framework. They then provide a theoretical analysis of this unified objective, characterizing the optimal meta-distribution learned by EDL methods. This analysis is complemented by empirical investigations on real-world datasets, examining the behavior of learned uncertainties and the performance of EDL methods on out-of-distribution (OOD) detection tasks.

Key Findings:

• The theoretical analysis reveals that EDL methods essentially force the learned meta-distribution to fit a fixed target distribution, independent of sample size.
• This fixed target distribution leads to spurious epistemic uncertainty, as it does not vanish with increasing data, contradicting the fundamental definition of epistemic uncertainty.
• Similarly, the aleatoric uncertainty quantified by EDL methods is shown to be model-dependent, inconsistent with its definition as irreducible uncertainty inherent in the data.
• Empirical evaluations demonstrate that EDL methods exhibit strong performance in OOD detection, but this performance is not indicative of accurate uncertainty quantification.
• The authors argue that the success of EDL in OOD detection stems from their resemblance to energy-based models, effectively functioning as OOD detectors rather than uncertainty quantifiers.

Main Conclusions:

The authors conclude that while EDL methods can be effective for specific applications like OOD detection, their ability to faithfully quantify and distinguish between epistemic and aleatoric uncertainty is fundamentally limited. They attribute these limitations to the absence of model uncertainty in the EDL framework and suggest that incorporating model uncertainty, potentially through distillation-based methods, could lead to more reliable uncertainty quantification.

Significance:

This research provides a critical analysis of EDL methods, challenging the prevailing notion of their effectiveness for uncertainty quantification. It highlights the importance of considering model uncertainty in uncertainty quantification and suggests potential avenues for improving the reliability of EDL methods in this domain.

Limitations and Future Research:

The authors acknowledge that their analysis primarily focuses on a specific class of EDL methods using the reverse KL divergence objective. Further investigation into other EDL variants and objective functions is warranted. Additionally, exploring the theoretical properties and practical implications of incorporating model uncertainty into EDL methods, particularly through bootstrap distillation, is suggested as a promising direction for future research.

Stats

Epistemic uncertainties quantified by EDL methods are almost constant with respect to the sample size and never vanish to 0, regardless of the increasing test accuracy.
Aleatoric uncertainty quantified by EDL methods vary with λ.
Using smaller values of λ always improves the OOD detection performance.

Quotes

"EDL methods can be better understood as an EBM-based OOD detector with the additional layer of Dirichlet framework for computational convenience rather than a statistically meaningful mechanism that can faithfully distinguish epistemic uncertainty and aleatoric uncertainty."
"This strongly suggests that it is inevitable to assume a stochastic procedure p(ψ|D) to properly define the distributional uncertainty p(π|x, D)."
"Our analyses strongly advocate that considering a stochastic algorithm p(ψ|D) and training a single meta distribution trying to fit the induced distributional uncertainty to expedite the inference time complexity is the best practice for the EDL framework to faithfully capture uncertainties."

Key Insights Distilled From

Are Uncertainty Quantification Capabilities of Evidential Deep Learning a Mirage?

by Maohao Shen,... at arxiv.org 11-04-2024

https://arxiv.org/pdf/2402.06160.pdf

Deeper Inquiries

How can the insights from energy-based models be further leveraged to improve the design and effectiveness of EDL methods for both OOD detection and uncertainty quantification?

The paper reveals a crucial link between EDL methods and energy-based models (EBMs) for OOD detection, highlighting that EDL methods essentially function as EBMs by leveraging the Dirichlet framework for computational efficiency. This insight opens up several avenues for improving EDL methods:

Refined Energy Function Design: Instead of relying solely on the Dirichlet distribution's concentration parameter (α) as a proxy for energy, we can explore more sophisticated energy function designs within the EDL framework. This could involve incorporating features learned by the neural network or leveraging techniques from the EBM literature, such as contrastive learning or score matching, to learn energy functions that better discriminate between ID and OOD data.

Hybrid EDL-EBM Architectures: We can envision hybrid architectures that combine the strengths of both EDL and EBMs. For instance, an EBM could be used to learn a robust energy landscape, while an EDL component could be trained to map this energy landscape to a calibrated uncertainty estimate. This could potentially lead to more accurate uncertainty quantification while retaining the computational efficiency of EDL.

Leveraging EBM Theory for Calibration: The theoretical understanding of EBMs, particularly in terms of their ability to approximate data densities and learn energy landscapes, can be leveraged to improve the calibration of uncertainty estimates in EDL methods. Techniques like temperature scaling or Platt scaling, commonly used in EBM-based OOD detection, could be adapted to calibrate the output of EDL models, leading to more reliable uncertainty quantification.

Beyond OOD Detection: The connection to EBMs suggests that EDL methods could be extended beyond OOD detection to other applications where EBMs excel, such as anomaly detection, generative modeling, and density estimation. By adapting the energy function and training objectives, EDL methods could potentially provide a computationally efficient alternative to traditional EBMs in these domains.

Could the incorporation of alternative uncertainty quantification techniques, such as Bayesian neural networks or Gaussian processes, within the EDL framework address the limitations identified in the paper?

The paper identifies a fundamental limitation of existing EDL methods: the lack of model uncertainty. Incorporating alternative uncertainty quantification techniques like Bayesian neural networks (BNNs) or Gaussian processes (GPs) could potentially address this limitation and improve EDL's fidelity in capturing both epistemic and aleatoric uncertainty.

Bayesian Neural Networks (BNNs): BNNs explicitly model uncertainty over the network's weights, providing a natural mechanism to capture model uncertainty. Integrating BNNs into the EDL framework could involve using the BNN's posterior predictive distribution to define the meta-distribution over predictions. This would allow the EDL model to learn a distributional uncertainty that reflects both data uncertainty and the uncertainty in the learned model parameters.

Gaussian Processes (GPs): GPs offer a non-parametric approach to uncertainty quantification, providing closed-form expressions for predictive uncertainty. Incorporating GPs into EDL could involve using a GP to model the mapping from input features to the parameters of the meta-distribution. This would allow the EDL model to leverage the GP's inherent uncertainty quantification capabilities while retaining the flexibility of neural networks for feature extraction.

Challenges and Considerations: Integrating BNNs or GPs into EDL presents computational challenges. BNNs require approximations for posterior inference, while GPs suffer from cubic complexity with data size. Efficient approximations and scalable inference techniques would be crucial for practical implementation.

Beyond Direct Integration: Instead of direct integration, we can draw inspiration from BNNs and GPs to design novel regularization techniques or architectural modifications within the EDL framework. For instance, we could introduce weight uncertainty in the EDL model or use a GP-inspired kernel function to capture correlations between input data points and improve uncertainty estimates.

What are the broader implications of misinterpreting OOD detection as accurate uncertainty quantification in real-world applications of machine learning, particularly in safety-critical domains?

Misinterpreting OOD detection as accurate uncertainty quantification can have severe consequences in real-world applications, especially in safety-critical domains where reliable uncertainty estimates are paramount for making informed decisions. Here are some broader implications:

Overconfidence in Model Predictions: OOD detection primarily focuses on identifying data points that are different from the training distribution. Mistaking this for accurate uncertainty quantification might lead to overconfidence in the model's predictions, even for ID data points where the model might have high aleatoric uncertainty due to inherent noise or ambiguity in the data.

Compromised Safety and Reliability: In safety-critical applications like autonomous driving or medical diagnosis, relying on miscalibrated uncertainty estimates can lead to catastrophic consequences. For instance, an autonomous vehicle might misjudge its uncertainty about the presence of a pedestrian, leading to an accident. Similarly, a medical diagnosis system might provide a confident but incorrect diagnosis based on a miscalibrated uncertainty estimate.

Erosion of Trust and Ethical Concerns: Deploying machine learning systems that provide misleading uncertainty estimates can erode trust in these systems and raise ethical concerns. Users might make suboptimal or even harmful decisions based on overconfident predictions, leading to negative societal impacts.

Hindered Progress in Uncertainty Quantification Research: Misinterpreting OOD detection as uncertainty quantification can hinder progress in the field. It might lead to a false sense of accomplishment and divert research efforts away from developing methods that can accurately quantify both epistemic and aleatoric uncertainty.

Addressing the Issue: To mitigate these risks, it is crucial to:

Clearly distinguish between OOD detection and uncertainty quantification: Researchers and practitioners should clearly communicate the limitations of OOD detection and emphasize that it does not equate to accurate uncertainty quantification.

Develop and adopt robust evaluation metrics: Metrics that go beyond OOD detection performance, such as calibration error, interval coverage, and out-of-distribution generalization error, are essential for assessing the quality of uncertainty estimates.

Promote research on reliable uncertainty quantification methods: Continued research on methods that can faithfully capture both epistemic and aleatoric uncertainty, such as Bayesian deep learning and ensemble methods, is crucial for building reliable and trustworthy machine learning systems.