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$ECUAS_n$: A family of metrics for principled evaluation of uncertainty-augmented systems

Summary

In high-stakes automated decision-making, predictive uncertainty enables users to accept or reject predictions based on cost trade-offs. Current evaluation methods for uncertainty-augmented (UA) systems are inadequate. This paper proposes ECUAS_n, a family of proper scoring rules with parameter n controlling the trade-off between cost of incorrect predictions and imperfect uncertainties. Experiments on diverse datasets demonstrate advantages.

SourcearXiv AIAuthor: Lautaro Estienne, Erik Ernst, Mat\'ias Vera, Pablo Piantanida, Luciana Ferrer
$ECUAS_n$: A family of metrics for principled evaluation of uncertainty-augmented systems
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[2605.20490] $ECUAS_n$: A family of metrics for principled evaluation of uncertainty-augmented systems

[Submitted on 19 May 2026 (v1), last revised 21 May 2026 (this version, v2)]

Title:$ECUAS_n$: A family of metrics for principled evaluation of uncertainty-augmented systems

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Abstract:In high-stakes automated decision-making, access to predictive uncertainty is essential for enabling users -- human or downstream systems -- to accept or reject predictions based on application-specific cost trade-offs. Such uncertainty-augmented (UA) systems -- i.e., systems that output both predictions and uncertainty scores -- are currently being assessed in the literature in a variety of ways, using separate metrics to evaluate the predictions and the uncertainty scores, setting a cost function with a fixed rejection cost or integrating over a coverage-risk curve. We argue that these evaluation approaches are inadequate for assessing overall performance of the UA system for decision making under uncertainty and propose a novel family of metrics, $ECUAS_n$, formulated as proper scoring rules for the task of interest. The parameter $n$ controls the trade-off between the cost of incorrect predictions and imperfect uncertainties depending on the needs of the use-case. We demonstrate the advantages of the $ECUAS_n$ metrics both theoretically and empirically, through experiments on diverse classification and generation datasets, including a manually annotated subset of TriviaQA.

Comments: pre-print, 9-pages paper, 25 pages total

Subjects:

Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

Cite as: arXiv:2605.20490 [cs.AI]

(or arXiv:2605.20490v2 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2605.20490

arXiv-issued DOI via DataCite

Submission history

From: Erik Ernst [view email] [v1] Tue, 19 May 2026 20:55:41 UTC (181 KB)

[v2] Thu, 21 May 2026 03:50:50 UTC (181 KB)

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Key points and analysis

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Key points

  • Proposes ECUAS_n metric family for holistic UA system evaluation
  • Parameter n allows customizing trade-off between prediction cost and uncertainty quality
  • Demonstrated theoretical and empirical superiority over existing approaches

Highlights and analysis are generated automatically and may contain errors. Check the original source.