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Unveil Sources of Uncertainty: Feature Contribution to Conformal Prediction Intervals

T0 review · 2 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that the width and boundaries of conformal prediction intervals can be treated as cooperative games, so Shapley and proportional Shapley values attribute predictive uncertainty to individual features, with Monte Carlo…

desk verdict Original idea with a solvent Shapley core; the proportional Shapley approximation is mis-specified as printed, so the paper needs major revision before it supports its headline claims. read the letter →

arxiv 2505.13118 v1 pith:GFLOF46F submitted 2025-05-19 cs.AI cs.LGstat.ML

Marouane Il Idrissi (UQAM , IID) , Agathe Fernandes Machado (UQAM) , Ewen Gallic (AMSE) , Arthur Charpentier (UQAM) This is my paper · ORCID
classification cs.AIcs.LGstat.ML
keywords conformalpredictionuncertaintyattributionShapleyvaluesproportionalHarsanyiallocationsexplainableAIcooperativegametheoryMonteCarloapproximation
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

Existing explanation tools attribute a model's average prediction; this paper tries to establish that predictive uncertainty itself can be attributed to features. It treats the width, lower bound, and upper bound of a conformal prediction interval as cooperative-game value functions, then allocates those values among features using Shapley values and proportional Shapley values, both members of the Harsanyi allocation family. It also claims a Monte Carlo permutation scheme estimates these attributions without bias and with convergence guarantees, making the decomposition feasible when exact computation over all $2^d$ feature subsets is too costly. If the approach works, practitioners in high-stakes settings gain an answer to a different question than usual: not just why the model predicted this, but which features make that prediction more or less trustworthy.

What carries the argument

The machinery is a cooperative game whose value function is a CP-interval property, paired with a Harsanyi allocation that redistributes Harsanyi dividends—the added value attributable to each coalition beyond its subsets—among the coalition's members. The Shapley value uses egalitarian weights $\lambda_j(A)=1/|A|$, splitting each dividend equally; the proportional Shapley value uses weights proportional to individual feature values, $\lambda_j^{\mathrm{PS}}(A)=|v(\{j\})|/\sum_{j'\in A}|v(\{j'\})|$. For computation, the paper exploits the random-order formulation of these allocations: the value of a coalition is read off a permutation as the marginal change in the interval property, and sampling permutations according to the appropriate distribution (uniform for Shapley, proportional to singleton values for P-Shapley) gives the Monte Carlo estimates. An importance-sampling reweighting then recycles one permutation sample into both allocations without retraining any models.

What would settle it

On a small dataset where exact computation is feasible, compute the proportional Shapley values for the lower- and upper-bound value functions and compare them with the paper's Algorithm 3 estimates at large $m$: if any singleton value is negative and the estimates deviate from the exact allocation, the claimed unbiasedness for the boundary games fails; a match would confirm that the missing sampling adjustment is immaterial.

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Extended reading notes

Core claim

The central claim is that uncertainty attribution can be built directly on conformal prediction intervals without changing the underlying regression model. For any of the three CP flavors the paper treats—standard mean regression, locally adaptive conformal prediction, and conformalized quantile regression—it defines a game with value function $v^{\omega}_{\mathrm{CP}}(A,x)$ that returns the width, lower bound, or upper bound of the interval produced when the model is retrained on feature subset $A$. Because Shapley and proportional Shapley values are efficient allocations, Proposition 3.1 guarantees the attributions sum exactly to $v^{\omega}_{\mathrm{CP}}(D,x)-v^{\omega}_{\mathrm{CP}}(\varnothing)$, so the interval property itself is decomposed across features. The paper further claims that the proportional Shapley value—which shares dividends in proportion to feature contributions rather than equally—is computable here, and that the permutation-based Monte Carlo estimators are unbiased, strongly consistent, and asymptotically normal for both allocations.

Load-bearing premise

The proportional-Shapley sampling step is a valid probability distribution only when every feature's singleton contribution to the value function is positive; for the lower- and upper-bound games used in the experiments singleton values can be negative, and the paper does not state how the sampling is adjusted, so the Monte Carlo guarantees for those boundary decompositions rest on an unstated condition.

Editorial extensions

If this is right

  • For any regression model that admits a conformal prediction interval, users get a per-instance additive decomposition of interval width or a chosen boundary into feature contributions; the total equals the interval property itself.
  • The method covers three CP variants (standard mean regression, locally adaptive conformal prediction, and conformalized quantile regression) with the same estimation code, so switching the interval construction does not require a new derivation.
  • The Monte Carlo scheme cuts the number of trained models from $2^d$ to roughly $m\times d$ or fewer, and the importance-sampling reweighting produces both Shapley and proportional Shapley estimates from one permutation sample; the experiments show about a tenfold speed-up at $m=1{,}000$.
  • Comparing Shapley and proportional Shapley rankings on the same value function acts as a sensitivity check: agreement signals stable importance, while disagreement flags features whose attributed uncertainty depends on the allocation rule.
  • After normalizing by the empty-coalition baseline, attributions sum to 1, so the decomposition has a clear accounting interpretation even though individual attributions may fall outside $[0,1]$.

Reading between the lines

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

  • Editorial inference: the decompositions measure how the interval's geometry depends on which features are available, not whether the interval is actually reliable; replacing the value function with conditional coverage or a sharpness gap would test whether the two views of uncertainty agree, and that comparison is not run in the paper.
  • Editorial inference: the proportional-Shapley sampling step as written requires positive singleton values; re-running the boundary-value experiments with an absolute-value or shifted sampling distribution, and checking whether the top-ranked features change, would show how much of the reported proportional-Shapley conclusions rests on that unstated choice.
  • Editorial inference: since every coalition retrains the model, an attribution conflates the effect of removing a feature on the fitted predictor with its effect on the calibration conformity scores; freezing the conformity scores while perturbing only the model input would separate those two channels.
  • Editorial inference: the same game construction extends to classification, where the value function could be the size or coverage of a conformal prediction set; only the interval property needs to be redefined.
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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 / 4 minor

Summary. The paper proposes an uncertainty attribution (UA) framework that combines split conformal prediction with cooperative game theory. CP-interval quantities (width, lower bound, upper bound) are used as coalition value functions, and the resulting cooperative games are allocated to features via Shapley values and proportional Shapley values. The authors provide an exact algorithm, a Monte Carlo permutation-sampling algorithm with claimed unbiasedness, consistency, and asymptotic normality, and an importance-sampling reweighting scheme. The experimental sections compare the resulting importance rankings with conditional-mean and conditional-variance rankings on synthetic and real-world datasets, showing that CP-based uncertainty attributions differ from moment-based rankings.

Significance. The framework addresses a genuine gap in XAI: most feature-attribution methods explain point predictions, whereas predictive uncertainty is increasingly important in high-stakes applications. Defining value functions directly from conformal intervals is a natural and model-agnostic idea, and the use of the broader Harsanyi allocation family, in particular proportional Shapley values, is a useful extension beyond classical Shapley. The paper ships reproducible code and the exact computation for small d is clearly described. The efficiency result in Proposition 3.1 is correct, and the Monte Carlo estimators are standard conditional on a fixed value function. However, the proportional-Shapley sampling and importance-sampling machinery, which supports the 'beyond Shapley' contribution and the experiments in Sections 4.2, 4.3 and Appendix C, is not correctly specified as printed. If the sampling distribution and the handling of negative singleton values are corrected, the framework is a solid and publishable contribution.

major comments (2)
  1. [Appendix A.3, Eq. (A.8); Theorems 1 and 2] The distribution PS(π) defined in Eq. (A.8) is not a probability mass function over permutations. For d=3 with |v({1})|=|v({2})|=|v({3})|=1, the formula gives PS(π)=exp[-(log(1+1+1)+log(1+1+1))]=1/9 for each of the 6 permutations, whose total mass is 2/3. The correct random-order distribution for the weighted Shapley value with weights |v({j})| is p(π)=∏_{j=1}^d |v({π_j})|/∑_{k=1}^j |v({π_k})|, which in this example is uniform 1/6. Because Theorem 1 and the importance-sampling weights in Appendix A.4 (PS(π)×d!) rely on the printed PS(π) being a valid distribution, the stated statistical guarantees for P-Shapley do not follow from the written formulas. This is load-bearing, since the P-Shapley approximations are used in the experiments of Sections 4.2, 4.3, and Appendix C.
  2. [Appendix A.3, Algorithm 3] Algorithm 3 samples permutations with probabilities proportional to v({k}) (no absolute values), which is a valid probability distribution only when every singleton value v({k}) is positive. For the lower- and upper-bound value functions used in Sections 4.2, 4.3, and Appendix C, v({k}) can be negative, and the paper does not specify any adjustment for negative values; the text only discusses zero individual values. Consequently, the P-Shapley Monte Carlo estimates for the boundary games are not well-defined as printed. This directly affects the validity of the P-Shapley results in Figure 4 and Appendix C. The definition of the weight system immediately before Eq. (3) also omits the absolute values that Eq. (3) uses, so the notation should be aligned.
minor comments (4)
  1. [Section 3.2, Theorems 1 and 2] The theorems are stated for a fixed value function v, but in the UA pipeline the value functions themselves depend on the random training/calibration split and on the fitted models; the additional variability from these sources is not quantified. The paper should explicitly acknowledge this limitation rather than describing the guarantees as covering the full uncertainty-attribution procedure.
  2. [Appendix C.1] The section header reads 'Sobol'-Ativan' while Section 4.1 calls the benchmark 'Sobol'–Levitan'; the typo should be fixed.
  3. [Algorithm 1] The algorithm's input includes a 'weight assignment λ' but the body never uses λ; the exact procedure always uses either the Shapley or proportional Shapley weight system. The role of λ should be clarified or removed.
  4. [Equation (3)] The proportional Shapley value as written in Eq. (3) uses absolute values of singleton contributions, which is a reasonable choice, but the text introducing λ_PS_j(A) uses v({j}) without absolute values; please make the convention explicit and consistent.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the CP-based value functions and standard allocation rules make the derivation self-contained; self-citations are related work and not load-bearing.

full rationale

The paper's central construction defines value functions directly from conformal prediction intervals: width, lower bound, and upper bound (Section 3.1, 'CP interval width' and 'Boundary points'). These definitions depend only on the split conformal prediction machinery and the chosen predictive model, not on the attribution output. The allocations applied to these games are the standard Shapley value and the proportional Shapley value, cited to external sources (Shapley [59], Béal et al. [8]) or to a random-order expression from Dehez [15], and the paper does not redefine these allocations to encode the desired uncertainty attributions. Proposition 3.1 is a direct consequence of the standard efficiency of Harsanyi allocations, so it adds no circularity. The Monte Carlo and importance-sampling estimators in Algorithm 2 and Appendix A.4 are classical sample-mean and importance-sampling estimators; Theorems 1 and 2 state standard LLN/CLT guarantees for any fixed probability mass function on permutations. These estimators target the same allocation defined by the exact formulas, rather than a fitted parameter that is later reported as a prediction. Experiments use synthetic benchmarks and external real-world datasets, and no model or parameter is fitted to the attribution values and then validated on the same attribution values. The self-citations [23] and [25] appear in related-work and background contexts, not as the justification for the paper's load-bearing definitions or guarantees. The main derivation chain -- conformal interval properties, cooperative-game allocations, and Monte Carlo approximation -- is therefore self-contained. The apparent issue in Algorithm 3 regarding unsigned sampling probabilities is a correctness or mathematical-consistency concern, not a circularity concern, and does not affect this verdict.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard game theory and CP coverage assumptions. The main ad hoc premise is the positivity of singleton values for the P-Shapley sampling, which is not guaranteed for boundary games. No new entities are introduced.

free parameters (1)
  • number of sampled permutations m = m=50 for blog; m=200 for facebook, UScrime, star; m=1000 for convenience; up to 5000 in convergence study
    User-chosen runtime/accuracy trade-off; the paper provides no rule for selecting m, and the MC guarantees are asymptotic so finite-m error is uncontrolled.
assumptions (4)
  • domain assumption Data exchangeability: (X_i,Y_i) are exchangeable, needed for conformal coverage guarantees.
    Invoked in Section 2.1 to establish that the CP interval (1) has finite-sample marginal coverage.
  • standard math Harsanyi dividends and Mobius inversion: every value function has a unique dividend decomposition.
    Used to define the Harsanyi set in Section 2.2 and Proposition 3.1; standard result attributed to Rota [57].
  • standard math Efficiency of Harsanyi set: any weight system yields an efficient allocation.
    Proposition Appendix A.2, used in Prop. 3.1.
  • ad hoc to paper For P-Shapley sampling, singleton values v({k}) are positive.
    Algorithm 3 and Eq. (A.8) require positive singleton values to define the permutation distribution; not guaranteed for lower/upper-bound value functions, and the paper does not handle negative values.

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Pith. "Pith review of Unveil Sources of Uncertainty: Feature Contribution to Conformal Prediction Intervals." pith.science (2026). https://pith.science/paper/GFLOF46F

@misc{pith2026250513118,
  author       = {Pith},
  title        = {Pith review of: Unveil Sources of Uncertainty: Feature Contribution to Conformal Prediction Intervals},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GFLOF46F}},
  note         = {Machine review of arXiv:2505.13118}
}
read the original abstract

Cooperative game theory methods, notably Shapley values, have significantly enhanced machine learning (ML) interpretability. However, existing explainable AI (XAI) frameworks mainly attribute average model predictions, overlooking predictive uncertainty. This work addresses that gap by proposing a novel, model-agnostic uncertainty attribution (UA) method grounded in conformal prediction (CP). By defining cooperative games where CP interval properties-such as width and bounds-serve as value functions, we systematically attribute predictive uncertainty to input features. Extending beyond the traditional Shapley values, we use the richer class of Harsanyi allocations, and in particular the proportional Shapley values, which distribute attribution proportionally to feature importance. We propose a Monte Carlo approximation method with robust statistical guarantees to address computational feasibility, significantly improving runtime efficiency. Our comprehensive experiments on synthetic benchmarks and real-world datasets demonstrate the practical utility and interpretative depth of our approach. By combining cooperative game theory and conformal prediction, we offer a rigorous, flexible toolkit for understanding and communicating predictive uncertainty in high-stakes ML applications.

Figures

Figures reproduced from arXiv: 2505.13118 by the authors.

Figure 1
Figure 1. Empirical convergence for the four most important features ( [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗
Figure 2
Figure 2. Feature attribution for the modified Friedman example. The bars mark the 90% intervals. [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. LACP width-based vs. conditional mean-based importance rankings for RF and LGB models on the [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Rank frequency of all the features (A) and top 5 most important feature (B) over the test data. CQR upper bound-based importance rankings for Q-LR and Q-RF models on the facebook dataset are used. 5. Conclusion We proposed a regression-model-agnostic uncertainty attrib…

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Reference graph

Works this paper leans on

86 extracted references · 56 canonical work pages

  1. [1]

    C. M. Achilles, B. A. Nye, J. B. Zaharias, and B. D. Fulton. The Lasting Benefits Study (LBS) in Grades 4 and 5 (1990-1991): A Legacy from Tennessee’s Four-Year (K-3) Class-Size Study (1985-1989), Project STAR. Technical report, Tennessee State University, Nashville. Center of Excellence for Research in Basic Skills., January 1993. URLhttps://eric.ed.gov/...

    1990

  2. [2]

    Approximating score-based explanation techniques using conformal regression

    Amr Alkhatib, Henrik Bostrom, Sofiane Ennadir, and Ulf Johansson. Approximating score-based explanation techniques using conformal regression. In Harris Papadopoulos, Khuong An Nguyen, Henrik Boström, and Lars Carlsson, editors,Proceedings of the Twelfth Symposium on Conformal and Probabilistic Prediction with Applications, volume 204 ofProceedings of Mac...

    2023

  3. [3]

    Estimating quality of approximated shapley values using conformal prediction

    Amr Alkhatib, Henrik Boström, and Ulf Johansson. Estimating quality of approximated shapley values using conformal prediction. In Simone Vantini, Matteo Fontana, Aldo Solari, Henrik Boström, and Lars Carlsson, editors,Proceedings of the Thirteenth Symposium on Conformal and Probabilistic Prediction with Applications, volume 230 ofProceedings of Machine Le...

  4. [4]

    Getting a {clue}: A method for explaining uncertainty estimates

    Javier Antoran, Umang Bhatt, Tameem Adel, Adrian Weller, and José Miguel Hernández-Lobato. Getting a {clue}: A method for explaining uncertainty estimates. InInternational Conference on Learning Representations, 2021. URL https://openreview.net/forum?id=XSLF1XFq5h

    2021

  5. [5]

    Explainable Artificial Intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI.Information Fusion, 58:82–115, June 2020

    Alejandro Barredo Arrieta, Natalia Díaz-Rodríguez, Javier Del Ser, Adrien Bennetot, Siham Tabik, Alberto Barbado, Salvador Garcia, Sergio Gil-Lopez, Daniel Molina, Richard Benjamins, Raja Chatila, and Francisco Herrera. Explainable Artificial Intelligence (XAI): Concepts, taxonomies, opportunities and challenges toward responsible AI.Information Fusion, 5...

    doi:10.1016/j.inffus.2019.12.012 2020

  6. [6]

    Explainingpredictive uncertainty by exposing second-order effects.Pattern Recognition, 160:111171, 2025

    FlorianBley, SebastianLapuschkin, WojciechSamek, andGrégoireMontavon. Explainingpredictive uncertainty by exposing second-order effects.Pattern Recognition, 160:111171, 2025. ISSN 0031-

    2025

  7. [7]

    Blogfeedback

    Krisztian Buza. Blogfeedback. UCI Machine Learning Repository, 2014. DOI: https://doi.org/10.24432/C58S3F

    doi:10.24432/c58s3f 2014

  8. [8]

    The proportional Shapley value and applications

    Sylvain Béal, Sylvain Ferrières, Eric Rémila, and Phillipe Solal. The proportional Shapley value and applications. Games and Economic Behavior, 108:93–112, March 2018. ISSN 0899-8256. doi: 10.1016/j.geb.2017.08.010. URL https://www.sciencedirect.com/science/article/pii/ S0899825617301446

    work page doi:10.1016/j.geb.2017.08.010 2018

Show all 86 references
  1. [9]

    RKHS-SHAP: Shapley Values for Kernel Methods

    Siu Lun Chau, Robert Hu, Javier González, and Dino Sejdinovic. RKHS-SHAP: Shapley Values for Kernel Methods. In S. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, and A. Oh, editors, Advances in Neural Information Processing Systems, volume 35, pages 13050–13063. Curran A...

    2022

  2. [10]

    Learning to explain: An information-theoretic perspective on model interpretation

    Jianbo Chen, Le Song, Martin Wainwright, and Michael Jordan. Learning to explain: An information-theoretic perspective on model interpretation. In Jennifer Dy and Andreas Krause, editors, Proceedings of the 35th International Conference on Machine Learning, volume 80 of Procee...

    2018

  3. [11]

    Fair prediction with disparate impact: A study of bias in recidivism prediction instruments.Big Data, 5(2):153–163, 2017

    Alexandra Chouldechova. Fair prediction with disparate impact: A study of bias in recidivism prediction instruments.Big Data, 5(2):153–163, 2017. doi: 10.1089/big.2016.0047. URLhttps: //doi.org/10.1089/big.2016.0047. PMID: 28632438

    2017

  4. [12]

    Understanding global feature contributions with additive importance measures

    Ian Covert, Scott M Lundberg, and Su-In Lee. Understanding global feature contributions with additive importance measures. In H. Larochelle, M. Ranzato, R. Hadsell, M.F. Balcan, and H. Lin, editors, Advances in Neural Information Processing Systems, volume 33, pages 17212–1722...

    2020

  5. [13]

    Explaining by removing: A unified framework for model explanation

    Ian Covert, Scott Lundberg, and Su-In Lee. Explaining by removing: A unified framework for model explanation. Journal of Machine Learning Research, 22(209):1–90, 2021. URL http: //jmlr.org/papers/v22/20-1316.html

    2021

  6. [14]

    Kernel-based anova decomposition and shapley effects – application to global sensitivity analysis, 2021

    Sébastien da Veiga. Kernel-based anova decomposition and shapley effects – application to global sensitivity analysis, 2021. URLhttps://arxiv.org/abs/2101.05487

    2021 arXiv

  7. [15]

    On Harsanyi Dividends and Asymmetric Values.International Game Theory Review, 19(03):1750012, September 2017

    Pierre Dehez. On Harsanyi Dividends and Asymmetric Values.International Game Theory Review, 19(03):1750012, September 2017. ISSN 0219-1989, 1793-6675. doi: 10.1142/S0219198917500128. URL https://www.worldscientific.com/doi/abs/10.1142/S0219198917500128. 11

    2017 doi

  8. [16]

    A new proof for Weber’s characterization of the random order values.Mathematical Social Sciences, 49(3):327–334, May 2005

    Jean Derks. A new proof for Weber’s characterization of the random order values.Mathematical Social Sciences, 49(3):327–334, May 2005. ISSN 0165-4896. doi: 10.1016/j.mathsocsci.2004.10.001. URL https://www.sciencedirect.com/science/article/pii/S0165489604000885

    2005 doi

  9. [17]

    On harsanyi payoff vectors and the weber set

    Jean Derks, Gerard van der Laan, and Valeri Vasil’ev. On harsanyi payoff vectors and the weber set. Tinbergen Institute Discussion Papers 02-105/1, Tinbergen Institute, Oct 2002. URL https://ideas.repec.org/p/tin/wpaper/20020105.html

    2002

  10. [18]

    Bike sharing

    Hadi Fanaee-T. Bike sharing. UCI Machine Learning Repository, 2013. DOI: https://doi.org/10.24432/C5W894

    2013 doi

  11. [19]

    Look at the Variance! Efficient Black-box Explanations with Sobol-based Sensitivity Analysis

    Thomas Fel, Remi Cadene, Mathieu Chalvidal, Matthieu Cord, David Vigouroux, and Thomas Serre. Look at the Variance! Efficient Black-box Explanations with Sobol-based Sensitivity Analysis. In Advances in Neural Information Processing Systems, volume 34, pages 26005– 26014. Curr...

    2021

  12. [20]

    Friedman

    Jerome H. Friedman. Multivariate Adaptive Regression Splines. The Annals of Statis- tics, 19(1):1–67, March 1991. ISSN 0090-5364, 2168-8966. doi: 10.1214/aos/1176347963. URL https://projecteuclid.org/journals/annals-of-statistics/volume-19/issue-1/ Multivariate-Adaptive-Regres...

    1991

  13. [21]

    Identifying homogeneous and interpretable groups for conformai prediction

    Natalia Martinez Gil, Dhaval Patel, Chandra Reddy, Giridhar Ganapavarapu, Roman Vaculin, and Jayant Kalagnanam. Identifying homogeneous and interpretable groups for conformai prediction. In Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence, UAI ’...

    2024

  14. [22]

    Harsanyi

    John C. Harsanyi. A simplified bargaining model for the n-person cooperative game.International Economic Review, 4(2):194–220, 1963. ISSN 00206598, 14682354. URLhttp://www.jstor.org/ stable/2525487

    1963

  15. [23]

    Proportional marginal effects for global sensitivity analysis.SIAM/ASA Journal on Uncertainty Quantification, 12(2): 667–692, 2024

    Margot Herin, Marouane Il Idrissi, Vincent Chabridon, and Bertrand Iooss. Proportional marginal effects for global sensitivity analysis.SIAM/ASA Journal on Uncertainty Quantification, 12(2): 667–692, 2024. doi: 10.1137/22M153032X. URLhttps://doi.org/10.1137/22M153032X

    2024 doi

  16. [24]

    Causal shapley values: exploiting causal knowledge to explain individual predictions of complex models

    Tom Heskes, Ioan Gabriel Bucur, Evi Sijben, and Tom Claassen. Causal shapley values: exploiting causal knowledge to explain individual predictions of complex models. InProceedings of the 34th International Conference on Neural Information Processing Systems, NIPS ’20, Red Hook...

    2020

  17. [25]

    Quantile-constrained wasserstein projections for robust interpretability of numerical and machine learning models.Electronic Journal of Statistics, 18(2):2721 – 2770, 2024

    Marouane Il Idrissi, Nicolas Bousquet, Fabrice Gamboa, Bertrand Iooss, and Jean-Michel Loubes. Quantile-constrained wasserstein projections for robust interpretability of numerical and machine learning models.Electronic Journal of Statistics, 18(2):2721 – 2770, 2024. doi: 10.1...

    2024 doi

  18. [26]

    A Review on Global Sensitivity Analysis Methods

    Bertrand Iooss and Paul Lemaître. A Review on Global Sensitivity Analysis Methods. In Uncertainty Management in Simulation-Optimization of Complex Systems, volume 59, pages 101–

  19. [27]

    Different Views of Interpretability

    Bertrand Iooss, Ron Kenett, and Piercesare Secchi. Different Views of Interpretability. In Interpretability for Industry 4.0 : Statistical and Machine Learning Approaches, pages1–20.Springer International Publishing, Cham, 2022. ISBN 978-3-031-12402-0. doi: 10.1007/978-3-031-1...

    2022 doi

  20. [28]

    Pascal Iversen, Simon Witzke, Katharina Baum, and Bernhard Y. Renard. Identifying drivers of predictive aleatoric uncertainty, 2024. URLhttps://arxiv.org/abs/2312.07252

    2024 arXiv

  21. [29]

    Shapley-value based inductive conformal prediction

    William Lopez Jaramillo and Evgueni Smirnov. Shapley-value based inductive conformal prediction. In Lars Carlsson, Zhiyuan Luo, Giovanni Cherubin, and Khuong An Nguyen, editors,Proceedings of the Tenth Symposium on Conformal and Probabilistic Prediction and Applications, volum...

    2021

  22. [30]

    Fast- SHAP: Real-time shapley value estimation

    Neil Jethani, Mukund Sudarshan, Ian Connick Covert, Su-In Lee, and Rajesh Ranganath. Fast- SHAP: Real-time shapley value estimation. InInternational Conference on Learning Representa- tions, 2022. URL https://openreview.net/forum?id=Zq2G_VTV53T

    2022

  23. [31]

    Don’t be fooled: label leakage in explanation methods and the importance of their quantitative evaluation

    Neil Jethani, Adriel Saporta, and Rajesh Ranganath. Don’t be fooled: label leakage in explanation methods and the importance of their quantitative evaluation. In Francisco Ruiz, Jennifer Dy, and Jan-Willem van de Meent, editors,Proceedings of The 26th International Conference ...

  24. [32]

    Interpretable and specialized conformal predictors

    Ulf Johansson, Tuwe Löfström, Henrik Boström, and Cecilia Sönströd. Interpretable and specialized conformal predictors. In Alex Gammerman, Vladimir Vovk, Zhiyuan Luo, and Evgueni Smirnov, editors, Proceedings of the Eighth Symposium on Conformal and Probabilistic Prediction an...

    2019

  25. [33]

    Customized interpretable conformal regressors

    Ulf Johansson, Cecilia Sönströd, Tuwe Löfström, and Henrik Boström. Customized interpretable conformal regressors. In 2019 IEEE International Conference on Data Science and Advanced Analytics (DSAA), pages 221–230, 2019. doi: 10.1109/DSAA.2019.00037

    2019

  26. [34]

    Navigating the maze of explainable ai: A systematic approach to evaluating methods and metrics

    Lukas Klein, Carsten Lüth, Udo Schlegel, Till Bungert, Mennatallah El-Assady, and Paul Jäger. Navigating the maze of explainable ai: A systematic approach to evaluating methods and metrics. In A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, e...

    2024

  27. [35]

    Tibshirani, and Larry Wasserman

    Jing Lei, Max G’Sell, Alessandro Rinaldo, Ryan J. Tibshirani, and Larry Wasserman. Distribution-Free Predictive Inference for Regression.Journal of the American Statistical Asso- ciation, 113(523):1094–1111, July 2018. ISSN 0162-1459. doi: 10.1080/01621459.2017.1307116. URL ht...

    2018

  28. [36]

    Diverse, global and amortised counterfactual explana- tions for uncertainty estimates.Proceedings of the AAAI Conference on Artificial Intelligence, 36: 7390–7398, 06 2022

    Dan Ley, Umang Bhatt, and Adrian Weller. Diverse, global and amortised counterfactual explana- tions for uncertainty estimates.Proceedings of the AAAI Conference on Artificial Intelligence, 36: 7390–7398, 06 2022. doi: 10.1609/aaai.v36i7.20702

    2022 doi

  29. [37]

    High Dimensional Model Representations

    Genyuan Li, Carey Rosenthal, and Herschel Rabitz. High Dimensional Model Representations. The Journal of Physical Chemistry A, 105(33):7765–7777, August 2001. ISSN 1089-5639, 1520-5215. doi: 10.1021/jp010450t. URL https://pubs.acs.org/doi/10.1021/jp010450t

    2001 doi

  30. [38]

    Calibrated explanations: With uncertainty information and counterfactuals.Expert Syst

    Helena Löfström, Tuwe Löfström, Ulf Johansson, and Cecilia Sönströd. Calibrated explanations: With uncertainty information and counterfactuals.Expert Syst. Appl., 246(C), July 2024. ISSN 0957-

    2024

  31. [39]

    Calibrated explanations for multi-class

    Tuwe Löfström, Helena Löfström, and Ulf Johansson. Calibrated explanations for multi-class. In Simone Vantini, Matteo Fontana, Aldo Solari, Henrik Boström, and Lars Carlsson, editors,Pro- ceedings of the Thirteenth Symposium on Conformal and Probabilistic Prediction with Appli...

    2024

  32. [40]

    A unified approach to interpreting model predictions

    Scott M Lundberg and Su-In Lee. A unified approach to interpreting model predictions. In I. Guyon, U. Von Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Gar- nett, editors, Advances in Neural Information Processing Systems, volume 30. Curran Asso- ciates, I...

    2017

  33. [41]

    Lundberg, Gabriel Erion, Hugh Chen, Alex DeGrave, Jordan M

    Scott M. Lundberg, Gabriel Erion, Hugh Chen, Alex DeGrave, Jordan M. Prutkin, Bala Nair, Ronit Katz, Jonathan Himmelfarb, Nisha Bansal, and Su-In Lee. From local explanations to global understanding with explainable ai for trees.Nature Machine Intelligence, 2(1):56–67, 2020. d...

    2020 doi

  34. [42]

    Quantifying and explaining machine learning uncertainty in predictive process monitoring: an operations research perspective

    Nijat Mehdiyev, Maxim Majlatow, and Peter Fettke. Quantifying and explaining machine learning uncertainty in predictive process monitoring: an operations research perspective. Annals of Operations Research, April 2024. ISSN 1572-9338. doi: 10.1007/s10479-024-05943-4. URL https...

    2024 doi

  35. [43]

    Integrating permutation feature importance with conformal prediction for robust explainable artificial intelligence in predictive process mon- itoring

    Nijat Mehdiyev, Maxim Majlatow, and Peter Fettke. Integrating permutation feature importance with conformal prediction for robust explainable artificial intelligence in predictive process mon- itoring. Engineering Applications of Artificial Intelligence, 149:110363, 2025. ISSN...

    2025

  36. [44]

    Dean, and Thomas J

    Hyejung Moon, Angela M. Dean, and Thomas J. Santner and. Two-stage sensitivity-based group screening in computer experiments.Technometrics, 54(4):376–387, 2012. doi: 10.1080/00401706. 2012.725994. URL https://doi.org/10.1080/00401706.2012.725994

    2012

  37. [45]

    shapiq: Shapley interactions for machine learning

    Maximilian Muschalik, Hubert Baniecki, Fabian Fumagalli, Patrick Kolpaczki, Barbara Hammer, and Eyke Hüllermeier. shapiq: Shapley interactions for machine learning. In A. Globerson, L. Mackey, D. Belgrave, A. Fan, U. Paquet, J. Tomczak, and C. Zhang, editors,Advances in Neural...

    2024

  38. [46]

    Confiderai: Conformal interpretable-by-design score function for explainable and reliable artificial intelligence

    Sara Narteni, Alberto Carlevaro, Fabrizio Dabbene, Marco Muselli, and Maurizio Mongelli. Confiderai: Conformal interpretable-by-design score function for explainable and reliable artificial intelligence. In Harris Papadopoulos, Khuong An Nguyen, Henrik Boström, and Lars Carlss...

    2023

  39. [47]

    Osborne and Ariel Rubinstein.A course in game theory

    Martin J. Osborne and Ariel Rubinstein.A course in game theory. MIT Press, Cambridge, Mass,

  40. [48]

    Art B. Owen. Sobol’ Indices and Shapley Value.SIAM/ASA Journal on Uncertainty Quantification, 2(1):245–251, January 2014. ISSN 2166-2525. doi: 10.1137/130936233. URLhttp://epubs.siam. org/doi/10.1137/130936233

    2014 doi

  41. [49]

    Ensuring medical ai safety: Explainable ai-driven detection and mitigation of spurious model behavior and associated data, 2025

    Frederik Pahde, Thomas Wiegand, Sebastian Lapuschkin, and Wojciech Samek. Ensuring medical ai safety: Explainable ai-driven detection and mitigation of spurious model behavior and associated data, 2025. URL https://arxiv.org/abs/2501.13818. 14

    2025 arXiv

  42. [50]

    Attribution of predictive uncertainties in classification models

    Iker Perez, Piotr Skalski, Alec Barns-Graham, Jason Wong, and David Sutton. Attribution of predictive uncertainties in classification models. In James Cussens and Kun Zhang, editors, Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, volume ...

    2022

  43. [51]

    Aliş, Jeffrey Shorter, and Kyurhee Shim

    Herschel Rabitz, Ömer F. Aliş, Jeffrey Shorter, and Kyurhee Shim. Efficient input—output model representations. Computer Physics Communications, 117(1-2):11–20, March 1999. ISSN 00104655. doi: 10.1016/S0010-4655(98)00152-0. URL https://linkinghub.elsevier.com/retrieve/pii/ S00...

    1999 doi

  44. [52]

    Physicochemical properties of protein tertiary structure

    Prashant Rana. Physicochemical properties of protein tertiary structure. UCI Machine Learning Repository, 2013. DOI: https://doi.org/10.24432/C5QW3H

    2013 doi

  45. [53]

    Saman Razavi, Anthony Jakeman, Andrea Saltelli, Clémentine Prieur, Bertrand Iooss, Emanuele Borgonovo, Elmar Plischke, Samuele Lo Piano, Takuya Iwanaga, William Becker, Stefano Tarantola, Joseph H.A. Guillaume, John Jakeman, Hoshin Gupta, Nicola Melillo, Giovanni Rabitti, Vinc...

    2021

  46. [54]

    Communities and crime

    Michael Redmond. Communities and crime. UCI Machine Learning Repository, 2002. DOI: https://doi.org/10.24432/C53W3X

    2002 doi

  47. [55]

    Robert and George Casella.Monte Carlo Statistical Methods (Springer Texts in Statistics)

    Christian P. Robert and George Casella.Monte Carlo Statistical Methods (Springer Texts in Statistics). Springer-Verlag, Berlin, Heidelberg, 2005. ISBN 0387212396

    2005

  48. [56]

    Conformalized Quantile Regres- sion

    Yaniv Romano, Evan Patterson, and Emmanuel Candes. Conformalized Quantile Regres- sion. In Advances in Neural Information Processing Systems , volume 32. Curran Asso- ciates, Inc., 2019. URL https://proceedings.neurips.cc/paper_files/paper/2019/hash/ 5103c3584b063c431bd1268e9b...

    2019

  49. [57]

    On the foundations of combinatorial theory I

    Gian Carlo Rota. On the foundations of combinatorial theory I. Theory of Möbius Functions. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 2(4):340–368, 1964. ISSN 0044-3719, 1432-2064. doi: 10.1007/BF00531932. URL http://link.springer.com/10.1007/ BF00531932

    1964 doi

  50. [58]

    A tutorial on conformal prediction.J

    Glenn Shafer and Vladimir Vovk. A tutorial on conformal prediction.J. Mach. Learn. Res., 9: 371–421, June 2008. ISSN 1532-4435

    2008

  51. [59]

    Lloyd S. Shapley. Notes on the n-Person Game – II: The Value of an n-Person Game. Researach Memorandum ATI 210720, RAND Corporation, Santa Monica, California, August 1951. URL https://www.rand.org/content/dam/rand/pubs/research_memoranda/2008/RM670.pdf

    1951

  52. [60]

    Shapley.17

    Lloyd S. Shapley.17. A Value for n-Person Games, pages 307–318. Princeton University Press, Princeton, 1953. ISBN 9781400881970. doi: doi:10.1515/9781400881970-018. URL https: //doi.org/10.1515/9781400881970-018

    1953 doi

  53. [61]

    Robinson

    Geethen Singh, Glenn Moncrieff, Zander Venter, Kerry Cawse-Nicholson, Jasper Slingsby, and Tamara B. Robinson. Uncertainty quantification for probabilistic machine learning in earth observation using conformal prediction.Scientific Reports, 14(1):16166, 2024. ISSN 2045-2322. d...

    2024 doi

  54. [62]

    Facebook comment volume

    Kamaljot Singh. Facebook comment volume. UCI Machine Learning Repository, 2015. DOI: https://doi.org/10.24432/C5Q886. 15

    2015 doi

  55. [63]

    Sobol’ and Yu.L

    I.M. Sobol’ and Yu.L. Levitan. On the use of variance reducing multipliers in monte carlo computations of a global sensitivity index.Computer Physics Communications, 117(1):52–61,

  56. [64]

    Nelson, and Jeremy Staum

    Eunhye Song, Barry L. Nelson, and Jeremy Staum. Shapley Effects for Global Sensitivity Analysis: Theory and Computation.SIAM/ASA Journal on Uncertainty Quantification, 4(1):1060–1083, January 2016. ISSN 2166-2525. doi: 10.1137/15M1048070. URLhttp://epubs.siam.org/doi/ 10.1137/...

    2016 doi

  57. [65]

    An efficient explanation of individual classifications using game theory.Journal of Machine Learning Research, 11(1):1–18, 2010

    Erik Štrumbelj and Igor Kononenko. An efficient explanation of individual classifications using game theory.Journal of Machine Learning Research, 11(1):1–18, 2010. URLhttp://jmlr.org/ papers/v11/strumbelj10a.html

    2010

  58. [66]

    The Many Shapley Values for Model Explanation

    Mukund Sundararajan and Amir Najmi. The Many Shapley Values for Model Explanation. In Proceedings of the 37th International Conference on Machine Learning, pages 9269–9278. PMLR, November 2020. URL https://proceedings.mlr.press/v119/sundararajan20b.html. ISSN: 2640-3498

    2020

  59. [67]

    Virtual library of simulation experiments: Test functions and datasets

    Sonja Surjanovic and Derek Bingham. Virtual library of simulation experiments: Test functions and datasets. Retrieved April 16, 2025, fromhttp://www.sfu.ca/~ssurjano, 2025

    2025

  60. [68]

    The Harsanyi Set for Cooperative TU-Games

    Valeri Vasil’ev and Gerard van der Laan. The Harsanyi Set for Cooperative TU-Games. Working Paper 01-004/1, Tinbergen Institute Discussion Paper, 2001. URLhttps://www.econstor.eu/ handle/10419/85790

    2001

  61. [69]

    Algorithmic Learning in a Ran- dom World

    Vladimir Vovk, Alexander Gammerman, and Glenn Shafer. Algorithmic Learning in a Ran- dom World. Springer International Publishing, Cham, 2022. ISBN 978-3-031-06648-1 978-3- 031-06649-8. doi: 10.1007/978-3-031-06649-8. URL https://link.springer.com/10.1007/ 978-3-031-06649-8

    2022 doi

  62. [70]

    Optimization-based uncertainty attribution via learning informative perturbations

    Hanjing Wang, Bashirul Azam Biswas, and Qiang Ji. Optimization-based uncertainty attribution via learning informative perturbations. In ECCV (78), pages 237–253, 2024. URL https: //doi.org/10.1007/978-3-031-73229-4_14

    2024 doi

  63. [71]

    Explaining predictive uncertainty with information theoretic shapley values

    David Watson, Joshua O’Hara, Niek Tax, Richard Mudd, and Ido Guy. Explaining predictive uncertainty with information theoretic shapley values. InThirty-seventh Conference on Neural Information Processing Systems, 2023. URL https://openreview.net/forum?id=6rabAZhCRS

    2023

  64. [72]

    Cambridge University Press, 1988

    Robert James Weber.Probabilistic values for games, page 101–120. Cambridge University Press, 1988

    1988

  65. [73]

    Boosted conformal prediction intervals

    Ran Xie, Rina Foygel Barber, and Emmanuel Candes. Boosted conformal prediction intervals. In The Thirty-eighth Annual Conference on Neural Information Processing Systems, 2024. URL https://openreview.net/forum?id=Tw032H2onS

    2024

  66. [74]

    Why you should not trust interpretations in machine learning: Adversarial attacks on partial dependence plots, 2024

    Xi Xin, Giles Hooker, and Fei Huang. Why you should not trust interpretations in machine learning: Adversarial attacks on partial dependence plots, 2024. URLhttps://arxiv.org/abs/2404.18702

    2024 arXiv

  67. [75]

    ConformaSight: Conformal prediction-based global and model-agnostic explainability framework

    Fatima Rabia Yapicioglu, Alessandra Stramiglio, and Fabio Vitali. ConformaSight: Conformal prediction-based global and model-agnostic explainability framework. In Luca Longo, Sebastian Lapuschkin, and Christin Seifert, editors,Explainable Artificial Intelligence, pages 270–293, Cham,

  68. [76]

    Concrete compressive strength

    I-Cheng Yeh. Concrete compressive strength. UCI Machine Learning Repository, 1998. DOI: https://doi.org/10.24432/C5PK67. 16

    1998 doi

  69. [77]

    Post-hoc predictive uncertainty quantification: methods with applications to electricity price forecasting

    Margaux Zaffran. Post-hoc predictive uncertainty quantification: methods with applications to electricity price forecasting. phdthesis, Institut Polytechnique de Paris, June 2024. URLhttps: //theses.hal.science/tel-04720002

    2024

  70. [78]

    model explanations

    Erik Štrumbelj and Igor Kononenko. Explaining prediction models and individual predictions with feature contributions.Knowledge and Information Systems, 41(3):647–665, December 2014. ISSN 0219-3116. doi: 10.1007/s10115-013-0679-x. URL https://link.springer.com/article/ 10.1007...

    2014 doi

  71. [122]

    ISBN 978-1-4899-7546-1 978-1-4899-7547-8

    Springer US, Boston, MA, 2015. ISBN 978-1-4899-7546-1 978-1-4899-7547-8. doi: 10.1007/ 978-1-4899-7547-8_5. URL http://link.springer.com/10.1007/978-1-4899-7547-8_5

    2015 doi

  72. [174]

    URLhttps://proceedings.mlr.press/v230/alkhatib24a.html

    PMLR, 09–11 Sep 2024. URLhttps://proceedings.mlr.press/v230/alkhatib24a.html. 10

    2024

  73. [1994]

    ISBN 978-0-262-15041-5 978-0-262-65040-3

  74. [1999]

    doi: https://doi.org/10.1016/S0010-4655(98)00156-8

    ISSN 0010-4655. doi: https://doi.org/10.1016/S0010-4655(98)00156-8. URLhttps://www. sciencedirect.com/science/article/pii/S0010465598001568

    doi

  75. [2024]

    ISBN 978-3-031-63800-8

    Springer Nature Switzerland. ISBN 978-3-031-63800-8. doi: 10.1007/978-3-031-63800-8_14

    doi

  76. [3203]

    URL https://www.sciencedirect

    doi: https://doi.org/10.1016/j.patcog.2024.111171. URL https://www.sciencedirect. com/science/article/pii/S0031320324009221

    2024

  77. [4174]

    URL https://doi.org/10.1016/j.eswa.2024.123154

    doi: 10.1016/j.eswa.2024.123154. URL https://doi.org/10.1016/j.eswa.2024.123154. 13

    2024

  78. [8953]

    URLhttps://proceedings.mlr.press/v206/jethani23a.html

    PMLR, 25–27 Apr 2023. URLhttps://proceedings.mlr.press/v206/jethani23a.html

    2023

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.