Introducing an Improved Information-Theoretic Measure of Predictive Uncertainty (2311.08309v1)

Abstract: Applying a machine learning model for decision-making in the real world requires to distinguish what the model knows from what it does not. A critical factor in assessing the knowledge of a model is to quantify its predictive uncertainty. Predictive uncertainty is commonly measured by the entropy of the Bayesian model average (BMA) predictive distribution. Yet, the properness of this current measure of predictive uncertainty was recently questioned. We provide new insights regarding those limitations. Our analyses show that the current measure erroneously assumes that the BMA predictive distribution is equivalent to the predictive distribution of the true model that generated the dataset. Consequently, we introduce a theoretically grounded measure to overcome these limitations. We experimentally verify the benefits of our introduced measure of predictive uncertainty. We find that our introduced measure behaves more reasonably in controlled synthetic tasks. Moreover, our evaluations on ImageNet demonstrate that our introduced measure is advantageous in real-world applications utilizing predictive uncertainty.

• The paper critiques conventional BMA entropy measures and introduces a novel metric based on expected pairwise KL-divergence to quantify epistemic uncertainty.
• It decomposes total uncertainty into aleatoric and epistemic components, providing a more accurate and interpretable framework for risk assessment.
• Empirical evaluations on synthetic tasks and ImageNet demonstrate improved AUROC in out-of-distribution and adversarial detection scenarios.

An Improved Information-Theoretic Measure of Predictive Uncertainty: A Critical Evaluation

The paper "Introducing an Improved Information-Theoretic Measure of Predictive Uncertainty" by Kajetan Schweighofer et al. addresses the prevalent concern of accurately measuring predictive uncertainty in machine learning models, particularly in decision-making contexts requiring robust risk assessment. The authors critique the conventional use of the entropy of the Bayesian model average (BMA) predictive distribution as a measure of predictive uncertainty, highlighting its shortcomings and introducing an alternative measure that ostensibly overcomes these limitations.

Key Contributions

Central to the paper’s contributions is the identification of flaws in the common approach of using the entropy of the BMA predictive distribution. The authors argue that the traditional measure makes the erroneous assumption that the BMA distribution equates to the true model that generated the observed data. They propose a novel information-theoretic measure spotlighting the expected pairwise Kullback-Leibler (KL) divergence as the epistemic component, which is theoretically grounded and provides a more comprehensive insight into uncertainty.

The paper makes several specific contributions:

1. Critical Analysis of Current Measures: The authors dissect the limitations inherent in the conventional mutual information-based measures of predictive uncertainty. They reveal that these measures mistakenly equate the BMA predictive distribution to the true predictive distribution of the model.
2. Introduction of a New Measure: By utilizing the expected pairwise KL-divergence, the paper introduces a method that directly accounts for the reducible epistemic uncertainty without relying on the BMA predictive distribution.
3. Experimental Verification: Through both illustrative examples and empirical evaluations on synthetic tasks and ImageNet datasets, the paper demonstrates that the proposed measure offers superior utility over traditional methods, particularly in tasks demanding robust uncertainty quantification like out-of-distribution and adversarial example detection.

Analytical Insights and Numerical Results

Theoretical arguments in the paper articulate that the new measure, which decomposes total uncertainty into aleatoric and epistemic components with the latter characterized by the expected pairwise KL-divergence, provides a tighter and more interpretively sound framework for uncertainty. Empirical results corroborate this claim, revealing that the new measure not only aligns better with intuitive expectations of epistemic uncertainty, particularly in ambiguous model configurations, but also enhances practical metrics like the area under the receiver operating characteristic curve (AUROC) in diverse detection tasks.

Theoretical and Practical Implications

The transition towards using expected pairwise KL-divergence as described in this paper could significantly enhance both theoretical understanding and practical implementations of uncertainty quantification in machine learning. By embracing a measure that does not hinge on the assumption of equivalence between BMA predictive and true distributions, the approach stands to reduce unjustified confidence in model predictions, thus fostering more cautious and accurate decision-making in high-stakes applications.

Speculation on Future Developments

The insights from this research open possible avenues for future work. Notably, the improved uncertainty measures could be pivotal in optimizing active learning workflows where data point informativeness guides sampling. Moreover, this advancement in understanding and measuring predictive uncertainty might spark further investigation into dynamic deployment strategies where model oversight and interactive learning environments necessitate swift and precise uncertainty quantification.

In conclusion, this paper presents a methodologically rigorous and empirically validated improvement in measuring predictive uncertainty, promising enhancements in the deployment and trustworthiness of AI models across industries. As such, it stands as a pertinent contribution to the ongoing refinement of uncertainty principles in artificial intelligence.