On Information-Theoretic Measures of Predictive Uncertainty
Kajetan Schweighofer, Lukas Aichberger, Mykyta Ielanskyi, Sepp Hochreiter
TL;DR
This paper develops a comprehensive framework for information-theoretic measures of predictive uncertainty, evaluating their effectiveness across various models and data distributions to guide better uncertainty quantification in machine learning.
Contribution
It introduces a unified framework categorizing uncertainty measures based on models and distribution approximations, including new measures, and provides extensive evaluation insights.
Findings
Aligning uncertainty measures with in-distribution data improves reliability.
Epistemic uncertainty measures have limitations for out-of-distribution data.
Disentanglement of uncertainty measures varies significantly between ID and OOD data.
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, there is no universal agreement on how to best quantify predictive uncertainty. In this work, we revisit core concepts to propose a framework for information-theoretic measures of predictive uncertainty. 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 extensively evaluate these measures across a broad set of tasks, identifying conditions under which certain measures excel. Our findings show the…
Peer Reviews
Decision·UAI 2025 Poster
The authors clearly show how each uncertainty quantification measure can be related back to cross entropy. This provides a clear categorization and interpretation of existing measures based on different choices of true and predictive models. Making these assumptions explicit is valuable for users to benchmark and choose the appropriate methods. The paper is also easy to follow with a clear summary in Table 1.
The main contribution of the paper seems to be the theoretical framework categorizing uncertainty quantification measures based on cross entropy, but much of the experiments focus on evaluating the effects of different posterior sampling methods. It is unclear why these methods specifically were significant for the comparison, and if there are any theoretical relationships between different posterior sampling choices and uncertainty measures. Moreover, the main theoretical contribution is not qu
The paper provides a good description of the two types of uncertainty, and this gives a good account for the existing literature on uncertainty measures.
My main concern is that the paper looks more like an experiment report rather than a research paper: First, I agree that the proposed cross-entropy loss (5) is a reasonable uncertainty measure. However, there are several issues: - It assumes there exists a true parameter that governs the generation of the data samples, which can be easily violated and hard to verify for a specific dataset. - All the newly proposed uncertainty measures in this paper serve as an approximation of (5). There is no
- Introduces a comprehensive framework for predictive uncertainty based on cross-entropy between the predicting and true models, adding a novel, theoretical foundation to uncertainty quantification. - Expands on existing information-theoretic measures by categorizing them under a unified approach, highlighting relationships and assumptions that were not fully articulated in prior works. - Derives the framework from first principles, establishing robustness in theoretical grounding.
In my opinion, the paper fails to explain how the presented framework can be of help to better understand the different information-theoretic measures that can be derived from it. I am mostly critical about the analysis given in the experimental section. I was expecting, for example, a more insightful discussion about which are the limitations for properly quantifying uncertainty of the different approximation approaches of the true predictive distribution. However, Section 5 provides a lot of
While the paper is overall well-written and easy to follow, it has significant weaknesses (see below).
I see two major drawbacks in the paper under review, both of which are significant enough that addressing them properly would fundamentally alter the paper's selling point. Specifically, these are: 1. The proposal of Cross-Entropy (CE) between the predicted distribution and the true distribution as a measure of total uncertainty, leading to new definitions of aleatoric uncertainty (AU) and epistemic uncertainty (EU). 2. The relation to prior work and the correct positioning of the paper within
This paper is well-crafted, presenting a unified framework for information-based uncertainty measures and offering a thorough analysis of each measure's interpretation and distinctions. The authors clearly outline how each scenario within the framework aligns with existing work in the literature, providing valuable context and insight.
I understand that the primary contribution of the paper is the general framework presented by the authors. However, in practical applications, testing each measure can be computationally intensive and potentially infeasible. The community would greatly benefit from theoretical insights into specific scenarios, such as identifying which measure is optimal for OOD detection under some assumptions.
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Taxonomy
TopicsStatistical and Computational Modeling
MethodsSparse Evolutionary Training