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arxiv: 2605.07549 · v1 · submitted 2026-05-08 · 💻 cs.CV · cs.LG

Probabilistic Object Detection with Conformal Prediction

Christopher Ries , Moussa Kassem Sbeyti , Nicolas Bianco , Nadja Klein This is my paper

Pith reviewed 2026-05-11 02:16 UTC · model grok-4.3

classification 💻 cs.CV cs.LG
keywords conformal predictionobject detectionuncertainty quantificationaleatoric uncertaintybounding box regressionautonomous drivingprobabilistic models
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The pith

Scaled conformal prediction adapts bounding box intervals to uncertainty estimates, improving sharpness while preserving coverage in object detection.

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

The paper applies conformal prediction to the structured outputs of object detectors to obtain reliable uncertainty sets for bounding boxes. It shows that scaling the conformal intervals using aleatoric uncertainty from a probabilistic detector makes those intervals narrower for easy predictions without losing the guaranteed coverage. This is tested on multiple autonomous driving datasets including cases with distribution shift. The result matters because fixed-width intervals waste sharpness on low-uncertainty cases, while adaptive ones give more precise localization uncertainty for downstream decisions.

Core claim

By applying conformal prediction coordinate-wise to the four corners of bounding boxes with a Bonferroni correction and then scaling the interval widths by per-prediction aleatoric uncertainty estimates from a loss-attenuated probabilistic object detector, the method produces prediction intervals that are sharper than unscaled conformal prediction while retaining marginal coverage guarantees. This holds across three datasets and in a cross-domain setting.

What carries the argument

Scaled conformal prediction, where interval widths are multiplied by input-dependent aleatoric uncertainty scores before conformal calibration, applied coordinate-wise with Bonferroni correction for box-level validity.

If this is right

  • Scaled CP achieves up to 19 percent higher intersection-over-union and 39 percent lower interval scores than unscaled CP at the same coverage level.
  • Adding class-wise calibration improves coverage rates for both scaled and unscaled versions with little change in sharpness.
  • The two-step pipeline first builds class prediction sets with RAPS and then conditions the conformalized boxes on those sets.
  • The improvements persist under distribution shift in cross-domain evaluation on autonomous driving data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • These sharper intervals could allow downstream planners to make tighter safety margins around detected objects.
  • The approach may extend to other multi-output regression tasks where outputs have natural structure like keypoints or segmentation masks.
  • Further gains might come from combining the aleatoric scaling with other forms of uncertainty calibration beyond the two variants tested.

Load-bearing premise

The aleatoric uncertainty estimates produced by the probabilistic detector are well enough calibrated that they can be used directly as scaling factors without breaking the coverage guarantee.

What would settle it

Observing that the empirical coverage of the scaled intervals falls below the target level on a new test set drawn from the same distribution as the calibration data, or that the sharpness gains disappear while coverage remains intact.

Figures

Figures reproduced from arXiv: 2605.07549 by Christopher Ries, Moussa Kassem Sbeyti, Nadja Klein, Nicolas Bianco.

Figure 1
Figure 1. Figure 1: Overview of the pipeline. The upper branch applies unscaled CP and the lower branch applies scaled CP, where the prediction intervals are scaled by aleatoric uncertainty estimates derived via loss attenuation. In both branches, the class￾wise path additionally computes prediction sets for the classification head using RAPS, followed by class-conditional quantile selection. In summary, we demonstrate that s… view at source ↗
Figure 2
Figure 2. Figure 2: Percentage of true bounding boxes falling below a given IoU threshold with the point prediction that are now fully contained within the conformalized bounding box, shown for KITTI (left), BDD (mid), and CODA (right) at different IoU thresholds. Colors represent unscaled, LA, Rel. IR, and Rel. IR PCo PC. Solid lines (-) correspond to α = 0.025 and dashed lines (--) to α = 0.1. 4.1.2. Class-wise Conformal Pr… view at source ↗
Figure 3
Figure 3. Figure 3: Distribution of empirical average coverage over 1000 runs using 1589 evaluation samples on KITTI. The top row shows RAPS without empty prediction sets and the bottom row shows RAPS with empty prediction sets, evaluated at α ∈ {0.01, 0.05, 0.1} [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
read the original abstract

Conformal Prediction (CP) is a distribution-free method for constructing prediction sets with marginal finite-sample coverage guarantees, making it a suitable framework for reliable uncertainty quantification in safety-critical object detection. However, object detection introduces structured multi-output predictions, complicating the application of classical CP theory developed for single outputs. In addition, standard, unscaled CP produces fixed-width prediction intervals across inputs, leading to unnecessary width for low-uncertainty predictions. While scaled CP addresses this by adapting the interval width to an input-dependent uncertainty estimate, prior work has neither systematically compared unscaled and scaled CP for multi-class object detection, nor integrated CP with a complementary uncertainty quantification method in this setting. We fill this gap by: (i) applying CP coordinate-wise to bounding box corners with a Bonferroni correction for box-level guarantees; (ii) scaling the resulting intervals using per-prediction aleatoric uncertainty estimates derived from a probabilistic object detector trained with loss attenuation, evaluated in uncalibrated and two calibrated variants; (iii) extending to a two-step pipeline that constructs prediction sets for the class using RAPS and conditions the conformalized bounding boxes on the predicted class set. Across three autonomous driving datasets (KITTI, BDD, CODA), including a cross-domain setting under distribution shift, scaled CP consistently improves interval sharpness over unscaled CP, achieving up to 19% higher IoU and 39% lower interval scores, without sacrificing coverage. Class-wise calibration further improves coverage for both variants with a negligible effect on sharpness. Together, these improvements yield more actionable uncertainty estimates for real-time, real-world object detection.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 3 minor

Summary. The paper applies conformal prediction (CP) to probabilistic object detection for bounding-box uncertainty quantification. It proposes coordinate-wise CP on box corners with Bonferroni correction for box-level coverage, scales the intervals using per-prediction aleatoric uncertainty from a loss-attenuated probabilistic detector (in uncalibrated and calibrated variants), and extends the pipeline with RAPS for class prediction sets. Experiments on KITTI, BDD, and CODA (including cross-domain shift) report that scaled CP yields up to 19% higher IoU and 39% lower interval scores than unscaled CP while maintaining coverage, with class-wise calibration further improving coverage at negligible sharpness cost.

Significance. If the empirical improvements hold under the stated conditions, the work provides a practical, adaptive method for tighter prediction intervals in multi-output detection tasks without apparent loss of coverage. The systematic comparison of scaled vs. unscaled CP, integration with loss-attenuated detectors, and inclusion of a cross-domain shift setting are strengths; the approach could inform real-time safety-critical applications if the coverage behavior is robustly characterized.

major comments (3)
  1. [Abstract, §4.3] Abstract and §4.3 (cross-domain experiments): The framing that CP supplies 'marginal finite-sample coverage guarantees' for safety-critical detection is undercut by the explicit inclusion of distribution-shift settings (e.g., KITTI-to-BDD or CODA). CP theory requires exchangeability between calibration and test points for the finite-sample guarantee; shift violates this, rendering reported coverage purely empirical. The claim of 'without sacrificing coverage' therefore needs qualification as an observed property rather than a guaranteed one.
  2. [§3.2] §3.2 (scaled CP construction): The scaling of conformal intervals by per-prediction aleatoric uncertainty estimates assumes these estimates are sufficiently calibrated to preserve validity after scaling. No explicit calibration diagnostics (e.g., reliability diagrams or ECE for the uncertainty outputs) are reported for the loss-attenuated detector variants; if the scaling factors are miscalibrated, the adaptive intervals may lose the marginal coverage property even under exchangeability.
  3. [§3.1] §3.1 (Bonferroni correction for box-level coverage): Coordinate-wise application with Bonferroni correction is used to obtain box-level guarantees. While conservative, the paper should quantify the resulting over-coverage or interval inflation relative to a joint conformal method; the reported sharpness gains (19% IoU, 39% interval score) may be partly offset by this conservatism, and an ablation comparing Bonferroni to other multiplicity corrections would strengthen the central comparison.
minor comments (3)
  1. [§3] Notation for the conformal quantile and scaling factor (e.g., Eq. (3) and (5)) is introduced without an explicit table of symbols; adding one would improve readability for readers unfamiliar with CP variants.
  2. [Figure 3] Figure 3 (interval score vs. IoU plots) lacks error bars or statistical significance markers for the reported improvements; including them would clarify whether the 19%/39% gains are consistent across seeds or splits.
  3. [§3.3] The two-step pipeline (RAPS class sets then conditional box CP) is described clearly, but the interaction between class-set size and box coverage is not tabulated; a small table showing coverage as a function of class-set cardinality would be helpful.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments. We respond to each major comment below, indicating where revisions will be made to clarify and strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract, §4.3] The framing that CP supplies 'marginal finite-sample coverage guarantees' for safety-critical detection is undercut by the explicit inclusion of distribution-shift settings (e.g., KITTI-to-BDD or CODA). CP theory requires exchangeability between calibration and test points for the finite-sample guarantee; shift violates this, rendering reported coverage purely empirical. The claim of 'without sacrificing coverage' therefore needs qualification as an observed property rather than a guaranteed one.

    Authors: We agree that the finite-sample marginal coverage guarantees of conformal prediction require exchangeability between calibration and test points. This assumption does not hold in the cross-domain shift experiments (e.g., KITTI-to-BDD or CODA), so coverage there is necessarily empirical. We will revise the abstract and §4.3 to qualify the phrase 'without sacrificing coverage' as an empirical observation under the evaluated conditions, while explicitly noting that the theoretical guarantees apply only under exchangeability. The reported empirical results and comparisons remain unchanged. revision: yes

  2. Referee: [§3.2] The scaling of conformal intervals by per-prediction aleatoric uncertainty estimates assumes these estimates are sufficiently calibrated to preserve validity after scaling. No explicit calibration diagnostics (e.g., reliability diagrams or ECE for the uncertainty outputs) are reported for the loss-attenuated detector variants; if the scaling factors are miscalibrated, the adaptive intervals may lose the marginal coverage property even under exchangeability.

    Authors: This point is valid. Although the manuscript evaluates uncalibrated and calibrated variants of the loss-attenuated detector, explicit calibration diagnostics for the aleatoric uncertainty estimates (such as reliability diagrams or ECE) were not included. In the revised manuscript we will add these diagnostics for all variants to substantiate that the scaling factors are sufficiently well-calibrated to preserve the marginal coverage property under exchangeability. revision: yes

  3. Referee: [§3.1] Coordinate-wise application with Bonferroni correction is used to obtain box-level guarantees. While conservative, the paper should quantify the resulting over-coverage or interval inflation relative to a joint conformal method; the reported sharpness gains (19% IoU, 39% interval score) may be partly offset by this conservatism, and an ablation comparing Bonferroni to other multiplicity corrections would strengthen the central comparison.

    Authors: We acknowledge that the Bonferroni correction is conservative and can induce over-coverage relative to a joint conformal procedure. We will add a quantification of the observed over-coverage and interval inflation in our experiments. In addition, we will include an ablation comparing Bonferroni to alternative multiplicity corrections (e.g., Holm-Bonferroni) to evaluate the impact on sharpness and to better contextualize the reported gains of 19% IoU and 39% lower interval scores. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical application of standard CP methods

full rationale

The paper applies existing conformal prediction techniques (coordinate-wise with Bonferroni, RAPS for classes, scaling by aleatoric uncertainty from a separately trained probabilistic detector) to object detection and reports empirical results on held-out test sets across datasets. All claims of improved sharpness (e.g., higher IoU, lower interval scores) without loss of coverage are measured outcomes on external data, not quantities derived by construction from fitted parameters inside the same pipeline. No equations reduce to self-definition, no predictions are statistically forced renamings of inputs, and no load-bearing steps rely on self-citations or imported uniqueness theorems. The work is self-contained as a methodological extension plus experimental validation against standard CP theory.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review performed on abstract only; full text unavailable, so ledger is minimal and reflects standard CP assumptions stated at high level.

axioms (1)
  • domain assumption Data points are exchangeable so that conformal prediction yields marginal coverage guarantees
    Standard assumption invoked for any CP method to deliver finite-sample validity.

pith-pipeline@v0.9.0 · 5591 in / 1236 out tokens · 40354 ms · 2026-05-11T02:16:04.551534+00:00 · methodology

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Works this paper leans on

47 extracted references · 47 canonical work pages

  1. [1]

    Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence , publisher =

    McAllister, Rowan and Gal, Yarin and Kendall, Alex and Van Der Wilk, Mark and Shah, Amar and Cipolla, Roberto and Weller, Adrian , title =. Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence , publisher =. 2017 , pages =

    work page 2017

  2. [2]

    Proceedings of the Twelfth Symposium on Conformal and Probabilistic Prediction with Applications , publisher =

    Andeol, Leo and Fel, Thomas and de Grancey, Florence and Mossina, Luca , title =. Proceedings of the Twelfth Symposium on Conformal and Probabilistic Prediction with Applications , publisher =. 2023 , pages =

    work page 2023

  3. [3]

    Object detection with probabilistic guarantees: a conformal prediction approach , booktitle =

    de Grancey, Florence and Adam, Jean-Luc and Alecu, Lucian and Gerchinovitz, S. Object detection with probabilistic guarantees: a conformal prediction approach , booktitle =. 2022 , pages =

    work page 2022

  4. [4]

    Proceedings of the 33rd International Conference on Machine Learning , publisher =

    Gal, Yarin and Ghahramani, Zoubin , title =. Proceedings of the 33rd International Conference on Machine Learning , publisher =. 2016 , pages =

    work page 2016

  5. [5]

    and Lenz, P

    Geiger, A. and Lenz, P. and Urtasun, R. , title =. 2012. 2012 , pages =

    work page 2012

  6. [6]

    Making deep learning models clinically useful --- improving diagnostic confidence in inherited retinal disease with conformal prediction , booktitle =

    Ghoshal, Biraja and Woof, William and Mendes, Bernardo and. Making deep learning models clinically useful --- improving diagnostic confidence in inherited retinal disease with conformal prediction , booktitle =. 2025 , pages =

    work page 2025

  7. [7]

    , title =

    Guo, Chuan and Pleiss, Geoff and Sun, Yu and Weinberger, Kilian Q. , title =. Proceedings of the 34th International Conference on Machine Learning , publisher =. 2017 , pages =

    work page 2017

  8. [8]

    Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence , publisher =

    Kassem Sbeyti, Moussa and Karg, Michelle and Wirth, Christian and Klein, Nadja and Albayrak, Sahin , title =. Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence , publisher =. 2024 , pages =

    work page 2024

  9. [9]

    , title =

    Lyu, Zongyao and Gutierrez, Nolan and Rajguru, Aditya and Beksi, William J. , title =. Computer Vision -- ECCV 2020 Workshops , publisher =. 2020 , pages =

    work page 2020

  10. [10]

    Advances in Neural Information Processing Systems , publisher =

    Kendall, Alex and Gal, Yarin , title =. Advances in Neural Information Processing Systems , publisher =. 2017 , volume =

    work page 2017

  11. [11]

    , title =

    Harakeh, Ali and Smart, Michael and Waslander, Steven L. , title =. Proceedings of the IEEE International Conference on Robotics and Automation (ICRA) , publisher =. 2020 , pages =

    work page 2020

  12. [12]

    Proceedings of the 35th International Conference on Machine Learning , publisher =

    Kuleshov, Volodymyr and Fenner, Nathan and Ermon, Stefano , title =. Proceedings of the 35th International Conference on Machine Learning , publisher =. 2018 , pages =

    work page 2018

  13. [13]

    Advances in Neural Information Processing Systems , publisher =

    Lakshminarayanan, Balaji and Pritzel, Alexander and Blundell, Charles , title =. Advances in Neural Information Processing Systems , publisher =. 2017 , volume =

    work page 2017

  14. [14]

    Copula-based conformal prediction for object detection: a more efficient approach , booktitle =

    Mukama, Bruce Cyusa and Messoudi, Soundouss and Rousseau, Sylvain and Destercke, S. Copula-based conformal prediction for object detection: a more efficient approach , booktitle =. 2024 , volume =

    work page 2024

  15. [15]

    Machine Learning:

    Papadopoulos, Harris and Proedrou, Kostas and Vovk, Volodya and Gammerman, Alex , title =. Machine Learning:. 2002 , pages =

    work page 2002

  16. [16]

    Aleatoric and epistemic uncertainty in conformal prediction , booktitle =

    Sale, Yusuf and Javanmardi, Alireza and H. Aleatoric and epistemic uncertainty in conformal prediction , booktitle =. 2025 , volume =

    work page 2025

  17. [17]

    , title =

    Tan, Mingxing and Pang, Ruoming and Le, Quoc V. , title =. 2020. 2020 , pages =

    work page 2020

  18. [18]

    Computer Vision --

    Timans, Alexander and Straehle, Christoph-Nikolas and Sakmann, Kaspar and Nalisnick, Eric , title =. Computer Vision --. 2025 , pages =

    work page 2025

  19. [19]

    Yu, Fisher and Chen, Haofeng and Wang, Xin and Xian, Wenqi and Chen, Yingying and Liu, Fangchen and Madhavan, Vashisht and Darrell, Trevor , title =. 2020. 2020 , pages =

    work page 2020

  20. [20]

    Proceedings of the

    Choi, Jiwoong and Chun, Dayoung and Kim, Hyun and Lee, Hyuk-Jae , title =. Proceedings of the. 2019 , pages =

    work page 2019

  21. [21]

    , title =

    Choi, Jiwoong and Elezi, Ismail and Lee, Hyuk-Jae and Farabet, Clement and Alvarez, Jose M. , title =. 2021. 2021 , pages =

    work page 2021

  22. [22]

    Advances in Neural Information Processing Systems , publisher =

    Romano, Yaniv and Sesia, Matteo and Candes, Emmanuel , title =. Advances in Neural Information Processing Systems , publisher =. 2020 , volume =

    work page 2020

  23. [23]

    Machine Learning and Knowledge Discovery in Databases: Research Track , publisher =

    Kassem Sbeyti, Moussa and Karg, Michelle and Wirth, Christian and Nowzad, Azarm and Albayrak, Sahin , title =. Machine Learning and Knowledge Discovery in Databases: Research Track , publisher =. 2023 , pages =

    work page 2023

  24. [24]

    Fair conformal predictors for applications in medical imaging , booktitle =

    Lu, Charles and Lemay, Andr. Fair conformal predictors for applications in medical imaging , booktitle =. 2022 , pages =

    work page 2022

  25. [25]

    and Brunk, Hugh D

    Barlow, Richard E. and Brunk, Hugh D. , title =. Journal of the American Statistical Association , year =

    work page

  26. [26]

    Annals of Mathematics and Artificial Intelligence , year =

    Vovk, Vladimir , title =. Annals of Mathematics and Artificial Intelligence , year =

    work page

  27. [27]

    Machine Learning , year =

    Vovk, Vladimir , title =. Machine Learning , year =

    work page

  28. [28]

    Analysis of explainers of black box deep neural networks for computer vision: a survey , journal =

    Buhrmester, Vanessa and M. Analysis of explainers of black box deep neural networks for computer vision: a survey , journal =. 2021 , volume =

    work page 2021

  29. [29]

    Meta-Radiology , year =

    Zou, Ke and Chen, Zhihao and Yuan, Xuedong and Shen, Xiaojing and Wang, Meng and Fu, Huazhu , title =. Meta-Radiology , year =

    work page

  30. [30]

    Proceedings of the

    Zou, Zhengxia and Chen, Keyan and Shi, Zhenwei and Guo, Yuhong and Ye, Jieping , title =. Proceedings of the. 2023 , volume =

    work page 2023

  31. [31]

    and Altman, Douglas G

    Bland, Martin J. and Altman, Douglas G. , title =. BMJ (Clinical Research Ed.) , year =

    work page

  32. [32]

    , title =

    Vazquez, Janette and Facelli, Julio C. , title =. Journal of Healthcare Informatics Research , year =

    work page

  33. [33]

    Artificial Intelligence Review , year =

    Gawlikowski, Jakob and Tassi, Cedrique Rovile Njieutcheu and Ali, Mohsin and Lee, Jongseok and Humt, Matthias and Feng, Jianxiang and Kruspe, Anna and Triebel, Rudolph and Jung, Peter and Roscher, Ribana and Shahzad, Muhammad and Yang, Wen and Bamler, Richard and Zhu, Xiao Xiang , title =. Artificial Intelligence Review , year =

    work page

  34. [34]

    and Dietmayer, Klaus , title =

    Feng, Di and Harakeh, Ali and Waslander, Steven L. and Dietmayer, Klaus , title =. IEEE Transactions on Intelligent Transportation Systems , year =

    work page

  35. [35]

    Reliable prediction errors for deep neural networks using test-time dropout , journal =

    Cort. Reliable prediction errors for deep neural networks using test-time dropout , journal =. 2019 , volume =

    work page 2019

  36. [36]

    Proceedings of the

    Karimi, Hamed and Samavi, Reza , title =. Proceedings of the. 2023 , volume =

    work page 2023

  37. [37]

    and Girshick, Ross B

    Felzenszwalb, Pedro F. and Girshick, Ross B. and McAllister, David and Ramanan, Deva , title =. IEEE Transactions on Pattern Analysis and Machine Intelligence , year =

    work page

  38. [38]

    and Wasserman, Larry , title =

    Lei, Jing and G'Sell, Max and Rinaldo, Alessandro and Tibshirani, Ryan J. and Wasserman, Larry , title =. Journal of the American Statistical Association , year =

    work page

  39. [39]

    Journal of the American Statistical Association , year =

    Sadinle, Mauricio and Lei, Jing and Wasserman, Larry , title =. Journal of the American Statistical Association , year =

    work page

  40. [40]

    , title =

    Gneiting, Tilmann and Raftery, Adrian E. , title =. Journal of the American Statistical Association , year =

    work page

  41. [41]

    Copula-based conformal prediction for multi-target regression , journal =

    Messoudi, Soundouss and Destercke, S. Copula-based conformal prediction for multi-target regression , journal =. 2021 , volume =

    work page 2021

  42. [42]

    and Foygel Barber, Rina and Candes, Emmanuel and Ramdas, Aaditya , title =

    Tibshirani, Ryan J. and Foygel Barber, Rina and Candes, Emmanuel and Ramdas, Aaditya , title =. Advances in Neural Information Processing Systems , year =

    work page

  43. [43]

    Vovk, Vladimir and Gammerman, Alexander and Shafer, Glenn , title =

    work page

  44. [44]

    2022 , booktitle =

    Li, Kaican and Chen, Kai and Wang, Haoyu and Hong, Lanqing and Ye, Chaoqiang and Han, Jianhua and Chen, Yukuai and Zhang, Wei and Xu, Chunjing and Yeung, Dit-Yan and Liang, Xiaodan and Li, Zhenguo and Xu, Hang , title =. 2022 , booktitle =

    work page 2022

  45. [45]

    and Bates, Stephen , title =

    Angelopoulos, Anastasios N. and Bates, Stephen , title =. arXiv preprint , note =

    work page

  46. [46]

    arXiv preprint , note =

    Shafer, Glenn and Vovk, Vladimir , title =. arXiv preprint , note =

    work page

  47. [47]

    and Bates, Stephen and Malik, Jitendra and Jordan, Michael I

    Angelopoulos, Anastasios N. and Bates, Stephen and Malik, Jitendra and Jordan, Michael I. , title =. International Conference on Learning Representations , year=

    work page