On Information-Theoretic Measures of Predictive Uncertainty (2410.10786v1)

Abstract: Reliable estimation of predictive uncertainty is crucial for machine learning applications, particularly in high-stakes scenarios where hedging against risks is essential. Despite its significance, a consensus on the correct measurement of predictive uncertainty remains elusive. In this work, we return to first principles to develop a fundamental framework of information-theoretic predictive uncertainty measures. Our proposed framework categorizes predictive uncertainty measures according to two factors: (I) The predicting model (II) The approximation of the true predictive distribution. Examining all possible combinations of these two factors, we derive a set of predictive uncertainty measures that includes both known and newly introduced ones. We empirically evaluate these measures in typical uncertainty estimation settings, such as misclassification detection, selective prediction, and out-of-distribution detection. The results show that no single measure is universal, but the effectiveness depends on the specific setting. Thus, our work provides clarity about the suitability of predictive uncertainty measures by clarifying their implicit assumptions and relationships.

• The paper introduces a unifying framework for categorizing predictive uncertainty measures based on model assumptions and true distribution approximations.
• The paper derives this framework from first principles using cross-entropy, providing both theoretical rigor and empirical validation on tasks like misclassification detection.
• The paper demonstrates that uncertainty measure effectiveness varies by task, emphasizing the need for tailored approaches in high-stakes applications.

On Information-Theoretic Measures of Predictive Uncertainty

The paper "On Information-Theoretic Measures of Predictive Uncertainty" addresses the pivotal issue of estimating predictive uncertainty in machine learning, particularly in contexts where incorrect predictions could have serious ramifications. Despite the undeniable importance of this topic, a universally accepted standard for measuring predictive uncertainty remains absent. This paper proposes a comprehensive framework, grounded in information theory, to classify and understand different measures of predictive uncertainty.

Framework for Predictive Uncertainty

The authors introduce a framework that categorizes predictive uncertainty measures by considering two main factors: the predicting model and the approximation of the true predictive distribution. By systematically combining these factors, the paper derives a spectrum of predictive uncertainty measures, including both existing and novel ones.

Contributions and Methodology

Key contributions of the paper include:

1. Unifying Framework: A comprehensive framework is proposed for categorizing measures of predictive uncertainty based on the assumptions regarding the predicting model and the true model approximation. This framework not only harmonizes existing measures but also suggests new measures and clarifies their interrelationships.
2. Derivation from First Principles: The framework stems from first principles, specifically the cross-entropy between the predicting and true models, characterized as a fundamental although intractable measure.
3. Empirical Evaluation: The paper empirically evaluates these measures across common uncertainty tasks, such as misclassification detection and out-of-distribution detection, showing that the efficacy of different measures varies across settings.

Empirical Insights

The empirical results emphasize that no universal uncertainty measure exists; rather, the effectiveness is contingent upon the task and the posterior sampling method applied. For instance, total uncertainty measures aligned with the predicting model often yield the best performance in misclassification and selective prediction tasks, especially when using global posterior sampling methods. Conversely, for local posterior sampling methods, some aleatoric measures perform notably well irrespective of the predicting model.

Implications and Future Directions

The implications of this work are multifold. Theoretically, it provides clarity on the relationships among various uncertainty measures, offering a foundation upon which future research can build. Practically, it informs the choice of uncertainty measures suitable for specific machine learning applications, especially those involving high stakes.

Looking forward, several intriguing pathways for further exploration are suggested. One significant avenue involves extending the framework to deterministic methods or autoregressive models prevalent in LLM applications. Additionally, exploring the relation between discussed uncertainty measures and other paradigms, such as distance-based approaches, could be fruitful.

In conclusion, this paper advances the discourse on predictive uncertainty by offering a structured approach to evaluate and select measures based on explicit assumptions, empirical validations, and theoretical underpinnings. As machine learning increasingly permeates critical applications, such insights are invaluable for developing robust models capable of informative uncertainty estimation.