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REVIEW 2 major objections 8 minor 63 references

Classification uncertainty for transient gravitational-wave noise artefacts with optimised conformal prediction

T0 review · 2 major / 8 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Conformal prediction's optimal uncertainty score for glitch classification is not fixed but depends on the metric being optimised.

desk verdict A clean, honest proof-of-concept for conformal prediction on Gravity Spy; the empirical nonconformity-measure ranking is real within the study, but the label it calibrates against is partly produced by the very classifier being recalibrated. read the letter →

arxiv 2412.11801 v2 pith:FY3FXHBX submitted 2024-12-16 gr-qc astro-ph.HEastro-ph.IM

Ann-Kristin Malz , Gregory Ashton , Nicolo Colombo This is my paper · ORCID
classification gr-qcastro-ph.HEastro-ph.IM PACS 04.80.Nn07.05.Mh
keywords conformalpredictionnonconformitymeasureGravitySpyglitchclassificationgravitationalwavesuncertaintymachinelearningsets
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Conformal prediction wraps any classifier's point predictions in a prediction set with a guaranteed coverage probability, but it requires a chosen score function (the nonconformity measure) to do so. This paper asks which nonconformity measure is best for classifying transient noise artefacts (glitches) in gravitational-wave data with the Gravity Spy classifier, and shows that the answer depends on how 'best' is measured. On the full dataset, the standard baseline measure—one minus the classifier's probability for a label—is optimal or tied for optimal under the F1 score and the average prediction-set size, while a new measure the authors call maxscore2 maximises the number of uniquely classified glitches (singletons). For several individual glitch classes, other measures beat the baseline, so the paper concludes that the optimal nonconformity measure is specific to both the application and the metric of interest. The result is practical: choosing a score function is a decision that should be matched to the downstream use of the uncertainty estimates.

What carries the argument

The central object is the nonconformity measure $A(x,y)$, a score function that converts the classifier's heuristic probabilities into a rigorous uncertainty via a calibration quantile. The paper uses Mondrian (label-conditional) conformal prediction, where a separate quantile $\hat{q}_y$ is computed for each glitch class, guaranteeing coverage per class as well as marginally. Eight parameterised families of nonconformity measures are compared: baseline, softmax, entropy, entropy softmax, margin2, maxscore2 (introduced here), CNN-based, and Brier; parameters are optimised by grid search plus L-BFGS-B, with regularisation to break degeneracy along axes. The machinery does the work of turning the question 'which uncertainty score should we use?' into a well-defined optimisation problem that can be solved separately for each performance metric.

What would settle it

Re-run the same optimisation on a glitch sample whose labels have been independently vetted by human experts (or on the 'golden' images) and check whether the baseline still ties for F1 and average set size and maxscore2 still maximises singletons; a change in the ranking would show the result is an artefact of using the final_label as ground truth. Alternatively, repeat the analysis with the improved multi-view Gravity Spy CNN and see if the metric-dependent ranking persists.

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Extended reading notes

Core claim

The central discovery is an empirical answer to an optimisation question in conformal prediction. The authors parameterise eight families of nonconformity measures, optimise their parameters separately for three metrics (F1 score, average prediction-set size, and singleton count) on the Gravity Spy 'retired' dataset, and find that the baseline measure $A(x,y)=1-f_y(x)$ is optimal or comparable under F1 and average set size, whereas all optimised alternatives produce more singletons, with maxscore2 best. This shows that the optimal nonconformity measure is not intrinsic to the algorithm or dataset but is relative to the metric of interest; class-level results confirm this by showing cases where the baseline is not the best. The paper therefore demonstrates both a concrete application of conformal prediction to multi-class glitch classification and a general methodology for optimising nonconformity measures.

Load-bearing premise

The paper treats the Gravity Spy 'final_label'—a blend of volunteer and computer classifications—as the true glitch class; if that label is wrong for a glitch, the coverage guarantee does not protect the actual physical class.

Editorial extensions

If this is right

  • A practitioner using Gravity Spy who cares about F1 or small prediction sets can safely default to the baseline nonconformity measure; no optimised alternative beats it on the full dataset.
  • A practitioner who values unique, high-purity classifications should choose the maxscore2 measure, which returns the highest singleton count at alpha=0.1 and across error rates.
  • Because the rankings change for individual glitch classes, per-class optimisation or mixing of nonconformity measures could improve class-specific F1 scores by up to about 0.2 over the baseline.
  • Conformal prediction converts the CNN's scores into guaranteed-coverage prediction sets; for example, with alpha=0.1 a set of Tomte glitches can be built where each glitch is in the set with 90% certainty relative to the chosen labels.
  • The optimisation recipe transfers to any point-prediction algorithm, but the optimised parameter values themselves do not transfer to other datasets or classifiers.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An implication the authors leave implicit is that the near-tie between F1 and average set size means these two metrics are largely redundant; a user should choose the one that matches the downstream decision rather than optimising both.
  • Because the calibration labels are a fusion of citizen and machine classifications, not ground truth, the coverage guarantee is conditional on those labels; extending calibration to propagate label noise (e.g., confidence-weighted labels) is a natural next test that could alter the observed rankings.
  • A practical extension would be to rerun this optimisation on the improved multi-view Gravity Spy classifier to see whether the metric-dependent ranking persists across model generations; if it changes, the optimal measure is model-dependent as well as metric-dependent.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 8 minor

Summary. The paper applies split conformal prediction (CP) to the Gravity Spy glitch-classification CNN. It introduces a family of parameterized nonconformity measures (baseline, softmax, entropy, entropy softmax, margin2, maxscore2, CNN, Brier), optimizes their parameters on a dedicated optimization split under three metrics (macro-F1, singleton rate, average set size), and evaluates on a held-out split. The main finding is that the optimal nonconformity measure depends on the metric: the baseline is best or tied under F1 and average set size, whereas maxscore2 yields the highest singleton count, with some per-class exceptions. The validity guarantee of Eq. (1) is verified empirically.

Significance. The paper is a useful proof of concept for applying CP to a real scientific ML pipeline, and the optimization protocol (separate optimization/evaluation sets, five repeats, public code) is a methodological strength. The central qualitative claim that optimal NCM choice is application- and metric-dependent is plausible and consistent with the literature. However, because the 'true label' is the Gravity Spy final_label, which incorporates the same ML classifier's output, the quantitative ranking of NCMs is not anchored to an independent physical classification; this limits the astrophysical conclusions and requires a robustness check or a substantially stronger caveat.

major comments (2)
  1. [II.B.1 and Table II] The calibration and evaluation labels are the Gravity Spy final_label, which is a combination of citizen-scientist votes and the ML classifier's classifications, and the ML classifier is the same one whose softmax scores are transformed by the conformal procedure. The paper acknowledges that this true label may be inaccurate but does not address the circularity: a confidently wrong ML prediction can propagate into final_label, and CP then calibrates on exactly those errors. Equation (1)'s coverage guarantee is with respect to these labels, not to the physical glitch class. The claimed singleton advantage of maxscore2 over baseline (0.271 vs 0.179 in Table II) could be partly an artifact of how final_label is generated. Please add a robustness check (e.g., restrict to glitches with high citizen-scientist consensus, or remove the ML contribution from final_label) or, at minimum, state explicitly that all results are conditional on final_label and cannot be read as optimality for the underlying physical classes.
  2. [III.C-III.D and Table II] The statistical significance of the NCM comparison is not established. The evaluation scores in Table II are computed on a single fixed evaluation set, and the quoted uncertainties reflect only the variation of the optimized parameters over the five splits of the optimization set; the finite-sample variance of the evaluation set is not included. As a result, small differences such as F1 = 0.456 (baseline) vs 0.455 (margin2, softmax) cannot be distinguished from noise, and the statement that the baseline is best under F1 needs either an estimate of evaluation-set uncertainty or a paired significance test across the five repeats. This is important for the central claim that the optimum depends on the metric.
minor comments (8)
  1. [Section IV] In the Discussion, 'average set seize' should be 'average set size'.
  2. [Section III.C] The phrase 'it becomes visibly discreet' should read 'visibly discrete'.
  3. [Section III.A] The word 'adaptions' should be 'adaptations'.
  4. [Section II.B.2] The caption of Fig. 2 states that the y-axis is the predicted label, but the plotted y-values are the labels in the prediction set; please clarify the distinction.
  5. [References] Reference [34] contains 'et al.' in the middle of the title, which is a formatting error.
  6. [Section II and III] The text says 'The code for Section II is openly available', but it is unclear whether the optimization code for Section III is also released; please clarify which parts of the analysis are reproducible.
  7. [Table I] The notation for the classification-score vector f and its component f_y is used in the table but only implicitly defined; please define both in the table caption or the main text.
  8. [Fig. 5] The ROC comparison between CP and Gravity Spy sweeps different quantities (alpha for CP, classification threshold for Gravity Spy); please state this explicitly in the caption to avoid an unfair comparison.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the CP validity guarantee is an imported external theorem, the nonconformity measures are pre-specified families, and the optimization is evaluated on held-out data.

full rationale

The paper's derivation chain is self-contained. The validity guarantee in Eq. (1) is a standard conformal-prediction theorem cited to external references [25,26]; the paper does not derive it from its own assumptions. The nonconformity measures in Table I are pre-specified families taken from or generalizing the literature, and the optimization is performed on a dedicated optimization split and evaluated on a held-out evaluation split (Section III.C), so the ranking in Table II is not a fitted input re-labelled as a prediction. The observation that several measures reduce to the baseline for particular parameter values (e.g., gamma=0 or nu=0) is a stated algebraic property of the definitions, not circularity: the optimization genuinely searches over those parameters and finds the baseline on F1 and set-size metrics, while the singleton metric selects different values. The acknowledged use of Gravity Spy final_label as the 'true label' (Section II.B.1) is a limitation for external physical validity, because final_label combines human and ML classifications rather than independent ground truth; however, the paper explicitly flags this, and no equation in the paper exhibits the label-generation rule as an input to the NCM comparison, so it does not constitute a demonstratable circular reduction. Self-citations to prior work by the authors [27,40] are contextual or provide one candidate NCM family and are not load-bearing: the central comparison does not depend on accepting those citations. No step satisfies the requirement of exhibiting a quantity that is equivalent to its input by construction.

Assumptions & free parameters 8 free parameters · 4 assumptions · 0 invented entities

The paper's free parameters are the tunable constants inside the nonconformity measures, explicitly optimised on data; the values are dataset-specific. No new physical entities are introduced. The key assumed input is that the composite final_label can stand in for ground truth.

free parameters (8)
  • Softmax beta = 0.001 (F1), 0.51 (singletons), 0.001 (set size)
    Optimised on the optimisation dataset for each metric (Table II).
  • Entropy gamma, nu = gamma=0, nu=0 for F1 and set size; gamma=0.14, nu=-0.2 for singletons
    Optimised on the optimisation dataset for each metric (Table II).
  • Entropy softmax nu, beta = nu=0, beta=0 for F1 and set size; nu=1.8, beta=-6.5 for singletons
    Optimised on the optimisation dataset for each metric (Table II).
  • Maxscore2 gamma1, gamma2 = 0,0 for F1 and set size; -0.4,-0.4 for singletons
    Optimised on the optimisation dataset for each metric (Table II).
  • Margin2 gamma, nu = gamma=0, nu=-8.8 (F1); gamma=0.2, nu=-7.4 (singletons); gamma=0, nu=-11.9 (set size)
    Optimised on the optimisation dataset for each metric (Table II).
  • CNN gamma = 1.0 for F1 and set size; 0.96 for singletons
    Optimised on the optimisation dataset for each metric (Table II).
  • Brier nu = 1.001 (F1); 1.012 (singletons); 1.002 (set size)
    Optimised on the optimisation dataset for each metric (Table II).
  • Regularisation constant rho = 0.00001
    Chosen by hand to break degeneracy in entropy measures (Section III.C).
assumptions (4)
  • domain assumption Calibration and test data are exchangeable
    Required for Eq. (1); the authors randomly subsample and split the Gravity Spy dataset, which is a reasonable approximation but not verified for the glitch population.
  • domain assumption final_label is an acceptable proxy for ground truth
    Stated in Section II.B.1; the coverage guarantee applies to final_label, not to an independent truth.
  • standard math Conformal prediction validity theorem
    Imported from Refs. [24,25]; used to assert Eq. (1).
  • domain assumption Classification scores fy encode heuristic uncertainty
    The nonconformity measures are all functions of the Gravity Spy output scores; if these scores were meaningless, CP would still be valid but the set sizes would be uninformative.

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Pith. "Pith review of Classification uncertainty for transient gravitational-wave noise artefacts with optimised conformal prediction." pith.science (2026). https://pith.science/paper/FY3FXHBX

@misc{pith2026241211801,
  author       = {Pith},
  title        = {Pith review of: Classification uncertainty for transient gravitational-wave noise artefacts with optimised conformal prediction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FY3FXHBX}},
  note         = {Machine review of arXiv:2412.11801}
}
read the original abstract

With the increasing use of Machine Learning (ML) algorithms in scientific research comes the need for reliable uncertainty quantification. When taking a measurement it is not enough to provide the result, we also have to declare how confident we are in the measurement. This is also true when the results are obtained from a ML algorithm, and arguably more so since the internal workings of ML algorithms are often less transparent compared to traditional statistical methods. Additionally, many ML algorithms do not provide uncertainty estimates and auxiliary algorithms must be applied. Conformal Prediction (CP) is a framework to provide such uncertainty quantifications for ML point predictors. In this paper, we explore the use and properties of CP applied in the context of glitch classification in gravitational wave astronomy. Specifically, we demonstrate the application of CP to the Gravity Spy glitch classification algorithm. CP makes use of a score function, a nonconformity measure, to convert an algorithm's heuristic notion of uncertainty to a rigorous uncertainty. We use the application on Gravity Spy to explore the performance of different nonconformity measures and optimise them for our application. Our results show that the optimal nonconformity measure depends on the specific application, as well as the metric used to quantify the performance.

Figures

Figures reproduced from arXiv: 2412.11801 by the authors.

Figure 1
Figure 1. FIG. 1. Example plots of three different glitches, represented as time-frequency q-scans, as observed by the LIGO Hanford [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. FIG. 4. Average number of labels in the [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figures from the paper (8 more)
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Grid plots with Scipy optimisations (black cross) using the [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]
Figure 7
Figure 7. Figure 7: In fact, all nonconformity measures shown in Fig. 7 [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Example grid plots for four different nonconformity measures with Scipy optimisations (black cross), maximising the [PITH_FULL_IMAGE:figures/full_fig_p010_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Example grid plots for four different nonconformity measures with Scipy optimisations (black cross), minimising the [PITH_FULL_IMAGE:figures/full_fig_p010_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Comparison of all the discussed nonconformity measures, making use of different metrics. [PITH_FULL_IMAGE:figures/full_fig_p011_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Example grid plots of individual glitch classes using the [PITH_FULL_IMAGE:figures/full_fig_p012_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11 [PITH_FULL_IMAGE:figures/full_fig_p012_11.png]

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Pith tools

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