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Uncertainty Evaluation: Bridging Machine Learning and Measurement Science

Dario Petri, Luca Mari

arXiv:2610.18066v1cs.LGcs.AI

TL;DR

Trustworthy ML predictions require uncertainty evaluation, but the conventional aleatoric–epistemic distinction depends on the adopted model and does not provide a unified framework. The paper compares ML with measurement science and argues that a GUM-inspired approach could provide a more rigorous and consistent basis for evaluating individual predictions.

  • Problem

    The aleatoric–epistemic distinction is model-dependent and has not established a unified framework for evaluating uncertainty in ML.

    Source: §V · pp. 4–5, §VIII · p. 6

  • Method

    The paper draws on metrology's transition from error to uncertainty and examines how systematic identification, quantification, and propagation of uncertainty contributions could apply to ML.

    Source: §I · p. 1, §IV · p. 3, §VIII · p. 7

  • Results

    The paper argues that a GUM-inspired framework could provide a more rigorous and consistent basis for uncertainty evaluation in ML.

    Source: §VIII · p. 7

  • Takeaways & Limitations

    The proposed framework could support pragmatic guidelines for identifying uncertainty boundaries in information-enabled decision-making and promote transferable evaluation methods.

    Source: §VIII · p. 7

Abstract

from arXiv · show

Reliable uncertainty evaluation is essential for assessing the trustworthiness of machine learning (ML) predictions, particularly in safety-critical applications. This paper explores conceptual analogies between uncertainty evaluation in ML and measurement science, drawing on the evolution of metrology from error-based approaches to the framework established by the Guide to the Expression of Uncertainty in Measurement (GUM). Particular attention is devoted to the distinction between process-level and result-level quality and to the limitations of the conventional classification of ML uncertainty into aleatoric and epistemic components. It is argued that this dichotomy, similarly to the traditional distinction between random and systematic measurement errors, is inherently model-dependent and provides an insufficient basis for a unified uncertainty evaluation framework. Further analogies between machine learning and measurement field of knowledge are identified concerning distribution shifts, anomalous operating conditions, and the validity of uncertainty evaluation. Building on the proposed considerations, the paper advocates a metrology-inspired approach based on the systematic identification, quantification, and propagation of uncertainty contributions. By extending the methodology already established in measurement science to ML, this approach could offer a potentially rigorous, consistent, and transferable framework for evaluating the trustworthiness of individual predictions.

I. INTRODUCTION

ML predictions in high-stakes settings need uncertainty evaluation to assess trustworthiness. The paper draws on metrology to examine how uncertainty contributions in ML can be identified and evaluated.

I. INTRODUCTION

  • Assessing the trustworthiness of ML inference results is important as ML systems enter high-stakes applications and measuring systems.The introduction highlights autonomous driving, healthcare, climate science, and ML's growing role in measurement.Source: §I · p. 1
  • Uncertainty evaluation is relevant to active learning, distribution-shift robustness, out-of-distribution detection, and learning with scarce data.In these settings, deferring, abstaining, or requesting information can be at least as critical as predictive accuracy.Source: §I · p. 1
  • An ML system maps inputs to labels or values, and its output can be affected by input, parameter, architecture, and training uncertainties.The paper compares this input-output process with measurement, where inputs map to a measured value affected by uncertainty sources.Source: §I · p. 1
  • The paper draws on metrology to offer insights and possible guidelines for evaluating uncertainty in ML systems.It frames measurement science's evolution from error-based approaches toward the GUM uncertainty framework as relevant background.Source: §I · p. 1

FROM PROCESS QUALITY TO PRODUCT QUALITY?

Process quality is informative about product quality but does not fully determine it. Product-level assessment must also account for the specific conditions under which each product is generated.

FROM PROCESS QUALITY TO PRODUCT QUALITY?

  • Process characteristics inform product quality but do not fully determine it; contingent inputs, environments, and operating states can lower an individual product's quality.Process quality can generally be regarded as an upper bound on product quality, with exceptions possible.Source: FROM PROCESS QUALITY TO PRODUCT QUALITY? · p. 2
  • In deployment, reference values needed to assess an individual product against expected outcomes are usually unavailable.This contrasts with laboratory or validation conditions, where suitable references can support comparison.Source: FROM PROCESS QUALITY TO PRODUCT QUALITY? · p. 2
  • Process-level quality is characterized under controlled or test conditions, whereas product-level quality must partly reflect the conditions of its actual generation.The paper treats the two levels as closely related but distinct.Source: FROM PROCESS QUALITY TO PRODUCT QUALITY? · p. 2

III. MEASUREMENT AS A PARADIGMATIC CASE

Because field measurements generally lack an available reference value, measurement science assesses result quality through uncertainty rather than operationalizing error. Measurement uncertainty reflects the evidence supporting a result and includes more than instrument performance alone.

III. MEASUREMENT AS A PARADIGMATIC CASE

  • Field measurements usually lack a reference value for the measurand, so result accuracy or error cannot generally be operationalized.Establishing a reference would require a higher-quality measurement of the same measurand, often technically infeasible or too costly.Source: §III · p. 2
  • Measurement science evaluates result quality by assessing how strongly available information warrants the measurement result, rather than relying on unknown error.The information may concern both the process and measurand, as well as information acquired through measurement.Source: §III · p. 2
  • Measurement uncertainty characterizes the dispersion of quantity values reasonably attributed to the measurand and is an essential component of the result.It quantifies how far the available evidence supports information obtained about the measurand.Source: §III · pp. 2–3
  • Instrumental uncertainty contributes to measurement uncertainty, but is only one of several sources for an individual measurement.It may sometimes dominate; measurement accuracy contributes inversely to measurement uncertainty.Source: §III · p. 3

IV. THE METROLOGICAL TRANSITION FROM ERROR TO UNCERTAINTY

Metrology's shift from error to uncertainty changed the framework for evaluating result quality. The GUM approach identifies and evaluates contributions, combines them, and incorporates both prior and result-specific information.

IV. THE METROLOGICAL TRANSITION FROM ERROR TO UNCERTAINTY

  • The GUM framework organizes result-quality evaluation around identifying uncertainty sources, evaluating their contributions, and combining them into an overall indicator.The transition from error to uncertainty changed the conceptual framework, not merely the numerical indicator.Source: §IV · p. 3
  • Random-versus-systematic classification is not intrinsic to an error source and can depend on the measurement model and context.The true value may be unknown or non-unique, and a contribution can change category with model changes; temperature effects and quantization illustrate this dependence.Source: §IV · p. 3
  • The GUM classifies uncertainty contributions by evaluation method rather than behavior, avoiding ambiguity while permitting purpose-specific grouping.Type A uses statistical analysis of measured-value series; Type B uses other methods, typically drawing on prior information.Source: §IV · p. 3
  • GUM combines evaluated contributions through uncertainty propagation or probability-distribution propagation, often using a first-order Taylor approximation or Monte Carlo methods.These steps follow construction of an uncertainty budget from the identified and evaluated contributions.Source: §IV · p. 3
  • Measurement uncertainty combines prior process information with information about the actual conditions of a particular measurement.Calibration results, instrument specifications, and typical system behavior can be integrated with result-specific conditions.Source: §IV · pp. 3–4
  • Random and systematic behavior can still guide practical uncertainty-reduction strategies, such as averaging or calibration.Systematic contributions may also be mitigated through compensation or measuring-system redesign.Source: §IV · p. 4

V. THE AN ANALOGY BETWEEN MEASUREMENT AND MACHINE LEARNING INFERENCE

Validation characterizes process-level quality, but deployed ML predictions require result-level assessment because their correct values are generally unavailable. The paper argues that the aleatoric–epistemic distinction is model-dependent and insufficient as a basis for a unified uncertainty-evaluation framework.

V. THE AN ANALOGY BETWEEN MEASUREMENT AND MACHINE LEARNING INFERENCE

  • Validation metrics characterize overall system quality, but cannot generally establish the quality of an individual deployment result whose correct value is unavailable.Result quality can also depend on input ambiguity, atypical observations, acquisition problems, or deployment conditions that differ from training.Source: §V · p. 4
  • Existing ML methods address aspects of uncertainty, but the open issue is integrating them into a process-aware, result-centered framework.The paper looks to measurement science's uncertainty-based approach for insights into characterizing individual prediction results.Source: §V · p. 4
  • The aleatoric–epistemic categorization is model-dependent and has not produced a unified framework for ML uncertainty evaluation.Its interpretation depends on the model, training procedure, and information used; the assumed irreducibility of aleatoric uncertainty can overlook model-dependent propagation.Source: §V · pp. 4–5
  • A lack of universally accepted definitions has yielded diverse uncertainty indexes, making meaningful comparison among evaluation methods difficult.The categorization may also fail to capture reducible and irreducible components adequately.Source: §V · p. 5
  • Treating aleatoric uncertainty as inherently irreducible may discourage investigation of its causes and opportunities for model refinement.The categorization is intended to distinguish potentially reducible epistemic uncertainty from generally irreducible aleatoric uncertainty.Source: §V · pp. 4–5

VI. ANALOGIES BETWEEN MEASUREMENT AND MACHINE LEARNING INFERENCE UNDER MISMATCHED OPERATING CONDITION

Changes in inputs, environment, or operating conditions can challenge the assumptions underlying measurement and ML systems. Such changes may compromise the validity and reliability of the information they provide.

VI. ANALOGIES BETWEEN MEASUREMENT AND MACHINE LEARNING INFERENCE

  • Input data, environmental conditions, and operating conditions may vary in both measurement and ML processes.Such variations can challenge system-development assumptions and potentially compromise the validity and reliability of the resulting information.Source: §VI · p. 5
  • Variations in operating conditions can challenge assumptions underlying system development.The passage identifies this as a potential issue across both measurement and ML.Source: §VI · p. 5
  • When these assumptions are challenged, the validity and reliability of provided information may be compromised, partially or completely.The passage frames this as a potential consequence of variations in inputs or operating conditions.Source: §VI · p. 5

A. Dataset or operating condition shift

Operating-condition shifts can leave a measurement or ML model fundamentally valid while reducing the confidence warranted in its output. For ML, shifted inputs may remain within the training distribution's support yet occupy lower-density regions and yield biased predictions.

A. Dataset or operating condition shift

  • In ML, shifted inputs can remain within training-distribution support while moving toward lower-density regions and potentially increasing epistemic uncertainty.Examples include underrepresented writing styles and vision systems trained on daytime images but deployed at night; predictions may be biased despite the same semantic domain.Source: A. Dataset or operating condition shift · p. 5
  • Unlike uncompensated measurement effects, distribution shift can reduce confidence while the ML model remains fundamentally valid and its information meaningful.Measurement examples include influence quantities beyond specified ranges or use beyond a calibration certificate's validity period, when accuracy may deteriorate.Source: A. Dataset or operating condition shift · p. 5

B. Anomalous operating conditions

Anomalous inputs violate the assumptions of the adopted model, unlike shifts within its semantic domain. The paper draws an analogy between measurement gross errors and ML out-of-distribution inputs and argues that model-scope verification should precede output and uncertainty assessment.

B. Anomalous operating conditions

  • Out-of-distribution inputs are semantically different from training data and can produce confident but meaningless predictions because the model lacks an information basis to interpret them.The passage contrasts these inputs with distribution shifts and gives Italian sentences as an example for a model trained exclusively on English-word sequences.Source: B. Anomalous operating conditions · p. 5
  • Gross errors and out-of-distribution inputs violate the assumed model, making uncertainty-component identification and uncertainty evaluation meaningless.Treating them merely as highly uncertain valid data may produce unreliable results and critical or catastrophic failures.Source: B. Anomalous operating conditions · p. 5
  • A two-step procedure first detects and rejects inputs that violate model assumptions, then provides output and evaluates uncertainty only within the model's validity domain.The second step follows verification that the input is consistent with the model's assumptions and validity domain.Source: B. Anomalous operating conditions · pp. 5–6
  • Some anomalous observations may be novel but legitimate, so rejection versus model extension or retraining depends on prior knowledge, causes, and application context.The passage makes this point for both gross errors in measurement and out-of-distribution ML inputs.Source: B. Anomalous operating conditions · p. 6

VII. SUMMARY

The summary compares metrology and ML uncertainty-evaluation approaches and their behavior when operating assumptions are violated.

  • Table I provides a comparative overview of the main characteristics of uncertainty evaluation approaches adopted in metrology and machine learning.Source: Table I · p. 6, §VII · p. 6
  • Table II compares measurement and ML inference behavior when operating conditions violate assumptions underlying their respective models.Source: Table II · p. 6, §VII · p. 6

VIII. CONCLUSIONS

The conclusions argue that aleatoric–epistemic categories depend on the adopted model and information, limiting their use as a unified basis for ML uncertainty evaluation. They advocate a GUM-inspired approach that systematically identifies, quantifies, and propagates uncertainty contributions.

  • The aleatoric–epistemic distinction depends on the model, training procedure, and information used, so contributions can shift between categories.Source: §VIII · p. 6
  • The GUM offers a contrasting unified framework, representing recognized uncertainty sources with probability distributions and propagating them through a measurement model.Source: §VIII · p. 6
  • Metrology evaluates individual uncertainty contributions and their propagation, supporting identification, quantification, and assessment of mitigation strategies.Strategies include improved modeling, refined calibration, or measuring-system redesign.Source: §VIII · pp. 6–7
  • A GUM-inspired ML framework could provide a more rigorous and consistent basis for evaluation, support decision-making boundaries, and promote transferable methods.Source: §VIII · p. 7

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