AdaptNC: Adaptive Nonconformity Scores for Conformal Prediction under Distribution Shift

Aditya Singh; Rahul Mangharam; Renukanandan Tumu

arxiv: 2602.01629 · v2 · pith:DHTKYIC4new · submitted 2026-02-02 · 💻 cs.LG · cs.RO· cs.SY· eess.SY

AdaptNC: Adaptive Nonconformity Scores for Conformal Prediction under Distribution Shift

Renukanandan Tumu , Aditya Singh , Rahul Mangharam This is my paper

Pith reviewed 2026-05-16 08:04 UTC · model grok-4.3

classification 💻 cs.LG cs.ROcs.SYeess.SY

keywords conformal predictiondistribution shiftnonconformity scoresonline adaptationrobotic benchmarksprediction regionsuncertainty quantificationadaptive methods

0 comments

The pith

AdaptNC adapts both nonconformity scores and thresholds online to shrink prediction regions under distribution shifts while preserving coverage.

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

Conformal prediction gives distribution-free uncertainty bounds but requires exchangeable data, an assumption broken by the shifts that occur in real robotics tasks. Existing online methods adjust only the threshold while keeping the nonconformity score fixed, which produces oversized prediction sets once the environment changes structure. AdaptNC instead updates the score function parameters through adaptive reweighting and adjusts the threshold together, using a replay buffer to avoid coverage drops during the transition. On benchmarks involving policy changes, environmental shifts, and sensor degradation, the method yields smaller volume regions than threshold-only baselines at the same coverage level. This makes rigorous uncertainty quantification more practical for autonomous systems that must operate as conditions evolve.

Core claim

AdaptNC performs joint online adaptation of both the nonconformity score parameters, via an adaptive reweighting scheme, and the conformal threshold, supported by a replay buffer that stabilizes coverage during score transitions. When evaluated on robotic tasks with multi-agent policy changes, environmental alterations, and sensor degradation, the resulting prediction regions have significantly smaller volume than those produced by state-of-the-art threshold-only methods while still meeting target coverage.

What carries the argument

The AdaptNC framework, which jointly adapts nonconformity score parameters through reweighting and maintains coverage with a replay buffer during online transitions.

If this is right

Prediction regions become smaller in volume on tasks with policy, environmental, or sensor changes while target coverage is retained.
The replay buffer prevents temporary coverage violations when the nonconformity score is updated online.
Conformal methods can be deployed in autonomous systems without requiring static score functions.
Volume reduction holds across diverse robotic benchmarks that include multi-agent interactions and degradation.

Where Pith is reading between the lines

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

The same joint-adaptation pattern could be tested in non-robotic domains such as online image classification under concept drift to check whether volume savings generalize.
The replay buffer mechanism might be added to other adaptive conformal algorithms to reduce coverage instability during score updates.
If the reweighting scheme can be made fully parameter-free, the method would require even fewer design choices when deployed in new environments.

Load-bearing premise

The adaptive reweighting of nonconformity scores together with the replay buffer preserves marginal coverage guarantees even while the score function itself is changing under distribution shift.

What would settle it

An experiment that records empirical coverage falling below the target level during an active score-reweighting period under a controlled, repeatable distribution shift would falsify the coverage claim.

Figures

Figures reproduced from arXiv: 2602.01629 by Aditya Singh, Rahul Mangharam, Renukanandan Tumu.

**Figure 2.** Figure 2: This figure shows the change in the optimal threshold α ∗ t based on scores from the initial and final distributions, N1 and N2. The bottom pane shows the rate of distribution change, while the top shows the difference between optimal quantiles. Remark 5.2. Then, for any window W = [r, s] ∈ [T] and any sequence α ∗ r , . . . , α∗ q s ∈ [0, 1], and η = P log(2k|W|)+1 s t=r E[ℓ(βt,αt) 2] and σ = 1/(2|W|), 1 … view at source ↗

**Figure 3.** Figure 3: This figure illustrates the evolution of local coverage over a sliding window of 100 timesteps. For readability, an exponential moving average is shown, with the raw data in a lighter color. AdaptNC exhibits the lowest variability in local coverage among all methods, indicating stable recovery of tight uncertainty regions under distribution shift. In contrast, AdaptNC without Replay shows substantially hig… view at source ↗

**Figure 4.** Figure 4: This figure illustrates the evolution of empirical coverage over the evaluation horizon relative to the target coverage level (shown in red). The proposed method consistently remains close to the desired coverage across time, whereas baseline methods exhibit pronounced periods of over- or under-coverage and, when recovery occurs, do so only after substantial deviation. This behavior highlights the flexibil… view at source ↗

**Figure 5.** Figure 5: This figure visualizes the uncertainty regions produced by AdaptNC and DtACI at three representative timesteps (t ∈ [720, 1560, 3120]) in the multirotor tracking task, paired with the realized residual at each timestep. The results show that AdaptNC recovers markedly tighter uncertainty regions while maintaining coverage. In contrast, DtACI adapts the score threshold, constraining the region geometry and l… view at source ↗

**Figure 6.** Figure 6: The 7000 points sampled from the Gaussian Mixture Model (GMM) data stream. 0 10 20 30 40 50 60 ¡lo g p(ztjN1) Likelihoods and mixture weight over time EMA 5 10 15 20 25 ¡lo g p(ztjN2) EMA 0 1000 2000 3000 4000 5000 6000 7000 timestep 0.0 0.2 0.4 0.6 0.8 1.0 wt [PITH_FULL_IMAGE:figures/full_fig_p020_6.png] view at source ↗

**Figure 8.** Figure 8: This figure shows the impact of changing nonconformity scores under a shifting GMM. Top: We compute the induced theoretical (1 − α) quantiles for each score function, which shift in opposite directions as the dominant mixture component changes. Middle: The corresponding optimal miscoverage rates α ⋆ t implied by each score function, illustrating that distribution shift can make the ideal miscoverage rat… view at source ↗

**Figure 10.** Figure 10: This figure shows the evolution of expert weights in the Indoor Localization setting over the course of the experiment. The pronounced, piecewise variation observed for AdaptNC arises from its adaptive reweighting mechanism, which enables rapid adjustment of expert weights in response to changes in the score function and contributes to maintaining valid coverage. In contrast, DtACI and AdaptNC without rep… view at source ↗

**Figure 11.** Figure 11: This figure contains the expert weights for the social navigation setting. The plots show the evolution of the weights over the course of the scenario. The stacatto pattern of the AdaptNC setting is a consequence of the adaptive reweighting scheme, which enables rapid adaptation of the expert weights in response to score function changes, which helps AdaptNC maintain coverage. We can see that the DtACI an… view at source ↗

**Figure 12.** Figure 12: This figure shows the evolution of expert weights in the multirotor navigation setting. The plots illustrate how weights change over time across the different methods. The pronounced oscillatory pattern observed for AdaptNC arises from its adaptive reweighting mechanism, which enables rapid adjustment of expert weights in response to changes in the nonconformity score and contributes to maintaining covera… view at source ↗

read the original abstract

Rigorous uncertainty quantification is essential for the safe deployment of autonomous systems in unconstrained environments. Conformal Prediction (CP) provides a distribution-free framework for this task, yet its standard formulations rely on exchangeability assumptions that are violated by the distribution shifts inherent in real-world robotics. Existing online CP methods maintain target coverage by adaptively scaling the conformal threshold, but typically employ a static nonconformity score function. We show that this fixed geometry leads to highly conservative, volume-inefficient prediction regions when environments undergo structural shifts. To address this, we propose $\textbf{AdaptNC}$, a framework for the joint online adaptation of both the nonconformity score parameters and the conformal threshold. AdaptNC leverages an adaptive reweighting scheme to optimize score functions, and introduces a replay buffer mechanism to mitigate the coverage instability that occurs during score transitions. We evaluate AdaptNC on diverse robotic benchmarks involving multi-agent policy changes, environmental changes and sensor degradation. Our results demonstrate that AdaptNC significantly reduces prediction region volume compared to state-of-the-art threshold-only baselines while maintaining target coverage levels.

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.

Desk Editor's Note private letter to a colleague

AdaptNC jointly adapts nonconformity scores and threshold via reweighting plus replay buffer, but the coverage argument for the joint change rests only on experiments.

read the letter

AdaptNC's main move is adapting the nonconformity score parameters online at the same time as the threshold, instead of freezing the score function and only moving the threshold like earlier online CP work. The reweighting scheme and replay buffer are the concrete mechanisms for that joint update. On the robotic benchmarks with policy switches, environment changes, and sensor degradation, the method produces smaller prediction regions than the threshold-only baselines while the reported coverage stays near the target. That empirical pattern is the clearest positive result in the abstract. The soft spot is the missing link between the adaptation and the coverage guarantee. Classical CP coverage needs exchangeability between the calibration scores and the test score. Changing the score function itself during operation breaks that exchangeability, and the replay buffer is presented as the fix for the resulting instability. The abstract gives no derivation, no explicit quantile argument, and no theorem showing that the buffered mixture restores uniform p-values under ongoing shift. Without that step, the coverage claim is carried entirely by the experiments. The paper is aimed at people who need tighter uncertainty sets for robotics and autonomous systems under realistic distribution shift. Readers working on practical conformal methods will find the empirical comparison useful even if they want more theory. It deserves a serious referee because the problem is well-motivated, the experiments cover relevant cases, and the joint-adaptation idea is a clear extension of prior online CP work, though the theoretical gap will need attention in revision.

Referee Report

2 major / 1 minor

Summary. The paper proposes AdaptNC, a framework for joint online adaptation of nonconformity score parameters and the conformal threshold under distribution shift. It uses an adaptive reweighting scheme for score optimization together with a replay buffer to stabilize coverage during transitions, and reports empirical results on robotic benchmarks (multi-agent policy changes, environmental shifts, sensor degradation) showing reduced prediction-region volume relative to threshold-only baselines while preserving target coverage.

Significance. If the coverage guarantees can be established, the approach would improve the efficiency of conformal prediction in non-stationary settings such as robotics, where static score functions produce overly conservative regions. The empirical volume reductions on diverse benchmarks would constitute a practical advance over existing online CP methods that adapt only the threshold.

major comments (2)

[Abstract / Method] Abstract and Method section: The central claim that AdaptNC maintains target coverage relies on the replay buffer restoring the exchangeability needed for valid (1-α) quantiles when nonconformity scores are adapted online. No theorem, derivation, or explicit argument is supplied showing that concatenating buffered scores with current scores (without additional reweighting or forgetting that accounts for the parameter change) yields uniform p-values under persistent distribution shift. This is load-bearing for the validity assertion.
[Experiments] Experiments section: The reported coverage maintenance is presented only as an empirical outcome. Without a supporting coverage proof or at least a clear statement of the precise conditions under which the joint adaptation preserves marginal coverage, the volume-reduction results cannot be interpreted as guaranteed improvements over threshold-only baselines.

minor comments (1)

[Abstract] The abstract refers to 'adaptive reweighting scheme' and 'replay buffer mechanism' without defining the precise update rules or hyperparameters; a short algorithmic box or pseudocode would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for their insightful comments and the opportunity to clarify the coverage aspects of AdaptNC. We address each major comment below.

read point-by-point responses

Referee: [Abstract / Method] Abstract and Method section: The central claim that AdaptNC maintains target coverage relies on the replay buffer restoring the exchangeability needed for valid (1-α) quantiles when nonconformity scores are adapted online. No theorem, derivation, or explicit argument is supplied showing that concatenating buffered scores with current scores (without additional reweighting or forgetting that accounts for the parameter change) yields uniform p-values under persistent distribution shift. This is load-bearing for the validity assertion.

Authors: We acknowledge that no formal theorem is provided in the manuscript to prove that the replay buffer restores the necessary exchangeability for exact coverage guarantees under persistent distribution shifts. The design of the replay buffer aims to retain a representative set of past nonconformity scores to compute stable quantiles while the score parameters adapt. However, we agree that a detailed argument or derivation would be beneficial. In the revised manuscript, we will include a new subsection discussing the role of the replay buffer in approximating exchangeability and explicitly note the empirical nature of the coverage validation. We will also add a statement clarifying that the method does not claim strict theoretical coverage for all possible shift scenarios. revision: partial
Referee: [Experiments] Experiments section: The reported coverage maintenance is presented only as an empirical outcome. Without a supporting coverage proof or at least a clear statement of the precise conditions under which the joint adaptation preserves marginal coverage, the volume-reduction results cannot be interpreted as guaranteed improvements over threshold-only baselines.

Authors: We agree with the observation that coverage is shown empirically. The experiments demonstrate that AdaptNC maintains the target coverage levels across the robotic benchmarks while achieving smaller prediction regions. To address this, we will revise the Experiments section to include a more explicit discussion of the conditions (e.g., buffer size relative to shift severity and adaptation speed) under which coverage is preserved in practice. We will also emphasize in the text that the volume reductions are practical improvements observed empirically, without claiming theoretical superiority in all settings. revision: yes

standing simulated objections not resolved

Providing a formal theorem establishing coverage guarantees for AdaptNC under arbitrary persistent distribution shifts

Circularity Check

0 steps flagged

No significant circularity; AdaptNC is an empirical framework without derivations that reduce to inputs by construction.

full rationale

The paper introduces AdaptNC as a practical method combining adaptive reweighting of nonconformity scores with a replay buffer for online conformal prediction under shift. No mathematical derivations, equations, or theorems are presented that equate the claimed volume reduction or coverage preservation to fitted parameters or prior results by construction. The approach is motivated empirically on robotic benchmarks rather than a closed logical chain. No self-citations are shown as load-bearing for uniqueness or ansatz, and the replay buffer is described as a mitigation heuristic without reducing the coverage claim to a tautology. This is a standard empirical proposal whose validity rests on experiments, not self-referential definitions.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard conformal prediction coverage guarantee holding after online score adaptation, plus the effectiveness of the reweighting scheme and replay buffer in practice.

free parameters (1)

reweighting scheme parameters
Parameters controlling the adaptive reweighting of nonconformity scores are introduced and presumably tuned to data.

axioms (1)

domain assumption Standard conformal prediction coverage relies on exchangeability, which is violated by distribution shifts in robotics.
Abstract explicitly notes that real-world robotics violates exchangeability assumptions of standard CP.

pith-pipeline@v0.9.0 · 5498 in / 1110 out tokens · 33164 ms · 2026-05-16T08:04:01.606656+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

AdaptNC leverages an adaptive reweighting scheme to optimize score functions, and introduces a replay buffer mechanism to mitigate the coverage instability that occurs during score transitions.

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages

[1]

doi: 10.1016/j.jmva.2005

ISSN 0047259X. doi: 10.1016/j.jmva.2005. 05.004. URL https://linkinghub.elsevier. com/retrieve/pii/S0047259X05000825. Clarke, R. H. A statistical theory of mobile-radio reception. Bell system technical journal, 47(6):957–1000, 1968. Cleaveland, M., Lee, I., Pappas, G. J., and Lindemann, L. Conformal Prediction Regions for Time Series Using Linear Compleme...

work page doi:10.1016/j.jmva.2005 2005
[2]

Gao, C., Shan, L., Srinivas, V ., and Vijayaragha- van, A

URL https://proceedings.mlr.press/ v211/dixit23a.html. Gao, C., Shan, L., Srinivas, V ., and Vijayaragha- van, A. V olume Optimality in Conformal Pre- diction with Structured Prediction Sets. June

work page
[3]

Gibbs, I

URL https://openreview.net/forum? id=oNDhnGrD51&noteId=7kR09SC5BY. Gibbs, I. and Candes, E. Adaptive Conformal In- ference Under Distribution Shift. InAdvances in Neural Information Processing Systems, vol- ume 34, pp. 1660–1672. Curran Associates, Inc., 2021. URL https://proceedings. neurips.cc/paper/2021/hash/ 0d441de75945e5acbc865406fc9a2559-Abstract. ...

work page 2021
[4]

URL http://jmlr.org/ papers/v25/22-1218.html

ISSN 1533-7928. URL http://jmlr.org/ papers/v25/22-1218.html. Gudmundson, M. Correlation model for shadow fading in mobile radio systems.Electronics letters, 27(23):2145– 2146, 1991. Helbing, D. and Moln ´ar, P. Social force model for pedestrian dynamics.Physical Review E, 51(5): 4282–4286, May 1995. doi: 10.1103/PhysRevE.51

work page doi:10.1103/physreve.51 1991
[5]

1103/PhysRevE.51.4282

URL https://link.aps.org/doi/10. 1103/PhysRevE.51.4282. Jakes, W. C. and Cox, D. C.Microwave mobile communica- tions. Wiley-IEEE press, 1994. Kiyani, S., Pappas, G., and Hassani, H. Length Opti- mization in Conformal Prediction.Advances in Neu- ral Information Processing Systems, 37:99519–99563, December 2024. doi: 10.52202/079017-3158. URL https://doi.or...

work page doi:10.52202/079017-3158 1994
[6]

Lindemann, M

ISSN 2377-3766. doi: 10.1109/LRA.2023. 3292071. URL https://ieeexplore.ieee. org/abstract/document/10172259. Lindemann, L., Zhao, Y ., Yu, X., Pappas, G. J., and Desh- mukh, J. V . Formal verification and control with con- formal prediction: Practical safety guarantees for au- tonomous systems.IEEE Control Systems, 45(6):72–122,

work page doi:10.1109/lra.2023 2023
[7]

Formal Verification and Control with Conformal Prediction: Practical Safety Guarantees for Autonomous Systems,

doi: 10.1109/MCS.2025.3611545. Lindqvist, B., Mansouri, S. S., Agha-mohammadi, A.-a., and Nikolakopoulos, G. Nonlinear MPC for Collision Avoidance and Control of UA Vs With Dynamic Obstacles. IEEE Robotics and Automation Letters, 5(4):6001–6008, October 2020. ISSN 2377-3766. doi: 10.1109/LRA. 2020.3010730. URL https://ieeexplore.ieee. org/abstract/documen...

work page doi:10.1109/mcs.2025.3611545 2025
[8]

Silverman, B

URL https://www.jstor.org/stable/ 2958700. Silverman, B. W.Density Estimation for Statistics and Data Analysis. CRC Press, April 1986. ISBN 978-0-412- 24620-3. Tayal, M., Singh, A., Kolathaya, S., and Bansal, S. A physics-informed machine learning framework for safe and optimal control of autonomous systems. InForty- second International Conference on Mac...

work page 1986
[9]

Tibshirani, R

URL https://openreview.net/forum? id=SrfwiloGQF. Tibshirani, R. J., Foygel Barber, R., Candes, E., and Ramdas, A. Conformal Prediction Under Covariate Shift. InAdvances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019. URL https: //papers.nips.cc/paper/2019/hash/ 8fb21ee7a2207526da55a679f0332de2-Abstract. html. Tumu, R., ...

work page doi:10.1109/iv55152 2019
[10]

Estimation of parameters and large quantiles based on the k largest observations

URL https://proceedings.mlr.press/ v242/tumu24a.html. Vaart, A. W. V . D.Asymptotic Statistics. Cambridge University Press, 1 edition, October 1998. ISBN 978- 0-511-80225-6 978-0-521-49603-2 978-0-521-78450-4. doi: 10.1017/CBO9780511802256. URL https: //www.cambridge.org/core/product/ identifier/9780511802256/type/book. V ovk, V ., Gammerman, A., and Shaf...

work page doi:10.1017/cbo9780511802256 1998
[11]

11 AdaptNC: Adaptive Nonconformity Scores for Dynamic Environments Appendix Contents A Limitations 13 B Method 14 B.1 Score Optimization Algorithm

URL https://proceedings.mlr.press/ v162/zaffran22a.html. 11 AdaptNC: Adaptive Nonconformity Scores for Dynamic Environments Appendix Contents A Limitations 13 B Method 14 B.1 Score Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 B.2 AdaptNC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . ...

work page 2024
[12]

The densityfis bounded and twice continuously differentiable

work page
[13]

The gradient of the density has strictly positive magnitude,inf f −1({t}) ∥∇f∥>0for almost everyt≥0

work page
[14]

The measureλ(f −1([tα −ϵ, t α +ϵ]))→0asϵ→0, andλ(f −1(0, ϵ])→0asϵ→0

work page
[15]

The kernel functionKis the gaussian kernel

work page
[16]

Scott”then 5:h←N −1 d+4 6:else ifbandwidth method is “Silverman

The bandwidth of the KDE is selected according to the rules of Scott (1979) or Silverman (1986). Then, asN→ ∞andM→ ∞, the estimated region ˆRN,M converges to the true regionR α in probability: λ( ˆRN,M ∆Rα) P − →0(9) Proof. We note that the procedure described in Algorithm 4 can be viewed as a two-step estimation process. First, we estimate the density fu...

work page 1979

[1] [1]

doi: 10.1016/j.jmva.2005

ISSN 0047259X. doi: 10.1016/j.jmva.2005. 05.004. URL https://linkinghub.elsevier. com/retrieve/pii/S0047259X05000825. Clarke, R. H. A statistical theory of mobile-radio reception. Bell system technical journal, 47(6):957–1000, 1968. Cleaveland, M., Lee, I., Pappas, G. J., and Lindemann, L. Conformal Prediction Regions for Time Series Using Linear Compleme...

work page doi:10.1016/j.jmva.2005 2005

[2] [2]

Gao, C., Shan, L., Srinivas, V ., and Vijayaragha- van, A

URL https://proceedings.mlr.press/ v211/dixit23a.html. Gao, C., Shan, L., Srinivas, V ., and Vijayaragha- van, A. V olume Optimality in Conformal Pre- diction with Structured Prediction Sets. June

work page

[3] [3]

Gibbs, I

URL https://openreview.net/forum? id=oNDhnGrD51&noteId=7kR09SC5BY. Gibbs, I. and Candes, E. Adaptive Conformal In- ference Under Distribution Shift. InAdvances in Neural Information Processing Systems, vol- ume 34, pp. 1660–1672. Curran Associates, Inc., 2021. URL https://proceedings. neurips.cc/paper/2021/hash/ 0d441de75945e5acbc865406fc9a2559-Abstract. ...

work page 2021

[4] [4]

URL http://jmlr.org/ papers/v25/22-1218.html

ISSN 1533-7928. URL http://jmlr.org/ papers/v25/22-1218.html. Gudmundson, M. Correlation model for shadow fading in mobile radio systems.Electronics letters, 27(23):2145– 2146, 1991. Helbing, D. and Moln ´ar, P. Social force model for pedestrian dynamics.Physical Review E, 51(5): 4282–4286, May 1995. doi: 10.1103/PhysRevE.51

work page doi:10.1103/physreve.51 1991

[5] [5]

1103/PhysRevE.51.4282

URL https://link.aps.org/doi/10. 1103/PhysRevE.51.4282. Jakes, W. C. and Cox, D. C.Microwave mobile communica- tions. Wiley-IEEE press, 1994. Kiyani, S., Pappas, G., and Hassani, H. Length Opti- mization in Conformal Prediction.Advances in Neu- ral Information Processing Systems, 37:99519–99563, December 2024. doi: 10.52202/079017-3158. URL https://doi.or...

work page doi:10.52202/079017-3158 1994

[6] [6]

Lindemann, M

ISSN 2377-3766. doi: 10.1109/LRA.2023. 3292071. URL https://ieeexplore.ieee. org/abstract/document/10172259. Lindemann, L., Zhao, Y ., Yu, X., Pappas, G. J., and Desh- mukh, J. V . Formal verification and control with con- formal prediction: Practical safety guarantees for au- tonomous systems.IEEE Control Systems, 45(6):72–122,

work page doi:10.1109/lra.2023 2023

[7] [7]

Formal Verification and Control with Conformal Prediction: Practical Safety Guarantees for Autonomous Systems,

doi: 10.1109/MCS.2025.3611545. Lindqvist, B., Mansouri, S. S., Agha-mohammadi, A.-a., and Nikolakopoulos, G. Nonlinear MPC for Collision Avoidance and Control of UA Vs With Dynamic Obstacles. IEEE Robotics and Automation Letters, 5(4):6001–6008, October 2020. ISSN 2377-3766. doi: 10.1109/LRA. 2020.3010730. URL https://ieeexplore.ieee. org/abstract/documen...

work page doi:10.1109/mcs.2025.3611545 2025

[8] [8]

Silverman, B

URL https://www.jstor.org/stable/ 2958700. Silverman, B. W.Density Estimation for Statistics and Data Analysis. CRC Press, April 1986. ISBN 978-0-412- 24620-3. Tayal, M., Singh, A., Kolathaya, S., and Bansal, S. A physics-informed machine learning framework for safe and optimal control of autonomous systems. InForty- second International Conference on Mac...

work page 1986

[9] [9]

Tibshirani, R

URL https://openreview.net/forum? id=SrfwiloGQF. Tibshirani, R. J., Foygel Barber, R., Candes, E., and Ramdas, A. Conformal Prediction Under Covariate Shift. InAdvances in Neural Information Processing Systems, volume 32. Curran Associates, Inc., 2019. URL https: //papers.nips.cc/paper/2019/hash/ 8fb21ee7a2207526da55a679f0332de2-Abstract. html. Tumu, R., ...

work page doi:10.1109/iv55152 2019

[10] [10]

Estimation of parameters and large quantiles based on the k largest observations

URL https://proceedings.mlr.press/ v242/tumu24a.html. Vaart, A. W. V . D.Asymptotic Statistics. Cambridge University Press, 1 edition, October 1998. ISBN 978- 0-511-80225-6 978-0-521-49603-2 978-0-521-78450-4. doi: 10.1017/CBO9780511802256. URL https: //www.cambridge.org/core/product/ identifier/9780511802256/type/book. V ovk, V ., Gammerman, A., and Shaf...

work page doi:10.1017/cbo9780511802256 1998

[11] [11]

11 AdaptNC: Adaptive Nonconformity Scores for Dynamic Environments Appendix Contents A Limitations 13 B Method 14 B.1 Score Optimization Algorithm

URL https://proceedings.mlr.press/ v162/zaffran22a.html. 11 AdaptNC: Adaptive Nonconformity Scores for Dynamic Environments Appendix Contents A Limitations 13 B Method 14 B.1 Score Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 B.2 AdaptNC Algorithm . . . . . . . . . . . . . . . . . . . . . . . . ...

work page 2024

[12] [12]

The densityfis bounded and twice continuously differentiable

work page

[13] [13]

The gradient of the density has strictly positive magnitude,inf f −1({t}) ∥∇f∥>0for almost everyt≥0

work page

[14] [14]

The measureλ(f −1([tα −ϵ, t α +ϵ]))→0asϵ→0, andλ(f −1(0, ϵ])→0asϵ→0

work page

[15] [15]

The kernel functionKis the gaussian kernel

work page

[16] [16]

Scott”then 5:h←N −1 d+4 6:else ifbandwidth method is “Silverman

The bandwidth of the KDE is selected according to the rules of Scott (1979) or Silverman (1986). Then, asN→ ∞andM→ ∞, the estimated region ˆRN,M converges to the true regionR α in probability: λ( ˆRN,M ∆Rα) P − →0(9) Proof. We note that the procedure described in Algorithm 4 can be viewed as a two-step estimation process. First, we estimate the density fu...

work page 1979