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Retrieval-Corrected Conformal Prediction for Time Series

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Pith's one-line read RCCP retrieves similar past residuals to set an asymmetric interval shape and calibrates that interval with a scalar conformal correction.

arxiv 2608.10553 v1 pith:77WRZTSB submitted 2026-08-11 cs.LG cs.AI

Sangjin Jin , Kangmin Kim , Junhyeong Lee , Yongjae Lee This is my paper · ORCID
classification cs.LGcs.AI
keywords calibrationpredictiontimeconformalrccpretrievalserieslocal
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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The reading

Forecasting models usually output a single number, but decision makers also need a range of plausible outcomes. Conformal prediction builds such ranges from past prediction errors: it takes a quantile of past residuals and adds that margin to the forecast. For time series, this is tricky because errors change over time and under different conditions, so a global margin is too wide in calm periods and too narrow in volatile ones.

RCCP changes how the past errors are selected. For each new forecast, it finds the K past time steps whose contexts look most similar to the current context, using an embedding of the input window and the point forecast. It then forms an asymmetric interval from the upper residuals and lower residuals of those similar steps. Because this retrieved interval is not guaranteed to cover enough test points, RCCP adds a correction step: on a calibration period, it measures how far the realized error falls outside the retrieved interval, normalizing by the retrieved scale, takes the 1 minus alpha quantile of those normalized deviations, and uses that single number to scale the interval at test time.

On four benchmark datasets and two forecasters, RCCP keeps empirical coverage near the target level and produces the lowest or tied-lowest Winkler scores, a combined measure of interval width and coverage violations. The width adaptivity analysis shows that RCCP widens intervals most where realized errors are large, so the gains come from better allocation of interval width rather than from uniformly inflating intervals. The main caveat is that the formal coverage guarantee is conditional on a stability assumption about the normalized retrieval error distribution, and the paper does not directly verify that assumption in the experiments.

Extended reading notes

Core claim

The load-bearing claim is that separating residual retrieval from conformal correction yields calibrated, locally adaptive intervals: Theorem 1 states that under Assumptions 1-4, |P_test{Y_t in C_t(hat c)} - q| <= rho_n + (2L/m)(e_n + r_n), and the experiments claim RCCP attains target coverage and the lowest Winkler scores across four benchmarks. If correct, RCCP is a simple, scalable way to obtain locally sharp and coverage-calibrated intervals for fixed time series forecasters.

Load-bearing premise

Assumption 1 in Section 3.4: |F_test(c*) - F_cal(c*)| <= rho_n, where F_cal and F_test are the CDFs of the normalized retrieval error B at the oracle multiplier c*. The entire coverage guarantee collapses to this stability premise. It is especially fragile because during calibration each B_j is computed with a knowledge base containing only earlier calibration points, while at test time the retrieved scale is computed from the full calibration set plus earlier test points, so the B distributions can systematically differ even if the raw residuals are stationary.

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Assumptions & free parameters 3 free parameters · 7 assumptions · 0 invented entities

The method introduces no new physical or ontological entities. Its free parameters are the retrieval neighborhood size, the retrieval temperature, and the conformal correction factor, all chosen or estimated on calibration data. The theoretical guarantee rests on four explicitly stated stability assumptions and two implicit domain assumptions: positive retrieved scales and error-relevant keys.

free parameters (3)
  • Neighborhood size K = 64 (default; grid 32, 64, 128)
    Controls the number of retrieved residuals in Eq. (4); selected on a validation half of the calibration period, so the reported results are tuned on calibration data.
  • Retrieval temperature tau = not reported per dataset (grid 0.75, 1.0, 1.25)
    Weight concentration in Eq. (3); tuned on the validation half of the calibration split.
  • Conformal correction scalar hat c = quantile of {B_j} on calibration data
    The scalar multiplier in Eq. (7); estimated from normalized retrieval errors on the calibration period. This is a data-fitted quantity, though it is the intended conformal calibration step.
assumptions (7)
  • domain assumption Assumption 1 (Calibration-test score stability): |F_test(c*) - F_cal(c*)| <= rho_n.
    Invoked in Theorem 1 proof; this is the load-bearing premise that the normalized retrieval error distribution at the oracle multiplier is close between calibration and test. If the knowledge base density differs between calibration and test, this can fail.
  • domain assumption Assumption 2 (Local identifiability): F_cal has slope at least m near c*.
    Ensures the empirical quantile hat c stays close to c*; a flat CDF would make the correction factor poorly identified.
  • domain assumption Assumption 3 (Local Lipschitzness of F_test).
    Converts multiplier error into a coverage gap; requires smoothness of the test score distribution near c*.
  • domain assumption Assumption 4 (Empirical calibration accuracy): e_n + r_n <= m delta_0 / 2.
    Requires enough calibration data and a suitably small finite-sample quantile adjustment; not verified empirically.
  • domain assumption Retrieved quantiles are strictly positive (tilde R^+, tilde R^- > 0).
    Needed for the division in Eq. (6) and used in the proof of Lemma 1; zero residuals can produce zero quantiles, with no handling described.
  • standard math Forecaster f is fixed after the training period and calibration uses only held-out residuals.
    Standard split conformal setup; stated in Section 3.1 and used by all baselines.
  • domain assumption The retrieval key psi_f captures error-relevant similarity between contexts.
    Acknowledged in Limitations; if the key misses error-relevant structure, retrieved residuals are poor local evidence and interval efficiency degrades.

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Pith. "Pith review of Retrieval-Corrected Conformal Prediction for Time Series." pith.science (2026). https://pith.science/paper/77WRZTSB

@misc{pith2026260810553,
  author       = {Pith},
  title        = {Pith review of: Retrieval-Corrected Conformal Prediction for Time Series},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/77WRZTSB}},
  note         = {Machine review of arXiv:2608.10553}
}
read the original abstract

Conformal prediction (CP) provides distribution-free prediction intervals for fixed forecasters, but its standard calibration procedure is often inefficient for time series data, where forecast errors are temporally dependent and change across time and operating conditions. Recent time series CP methods improve local calibration using recent, weighted, or localized residuals. Yet local calibration can remain indirect, since broad residual weighting or additional adaptation procedures may dilute the evidence most relevant to the current prediction. This motivates a simple retrieval and correction strategy that selects similar past residuals as local evidence and then corrects the coverage error left by retrieval. In this paper, we propose Retrieval--Corrected Conformal Prediction (RCCP), a retrieval-augmented calibration method for time series prediction intervals. RCCP builds an asymmetric interval from retrieved one-sided residuals and calibrates its normalized retrieval error with a scalar conformal correction. Thus, retrieval provides local residual evidence, while conformal correction determines the final scale needed for coverage. We provide a coverage-gap bound based on the stability of the normalized retrieval error distribution. Across standard benchmarks and backbone forecasters, RCCP attains the target coverage in every setting and achieves the lowest Winkler scores, with fewer severe misses. RCCP also achieves low calibration and inference overhead, showing that retrieval-corrected calibration is an effective and scalable approach to uncertainty quantification in time series forecasting. Code is available at https://github.com/jinsaaang/rccp.

Figures

Figures reproduced from arXiv: 2608.10553 by the authors.

Figure 1
Figure 1. Overview of Retrieval–Corrected Conformal Prediction. RCCP builds a retrieval knowledge base from evaluated prediction contexts, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Winkler-score decomposition into interval width and miss [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Interval width and empirical coverage stratified by realized error decile. Higher deciles correspond to larger realized errors and test [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: CDF of miscoverage distance for uncovered test points. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Coverage, interval width, and Winkler score for direct retrieval and corrected intervals across target miscoverage levels. The dotted [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Sensitivity to retrieval size 𝐾. The figure reports interval width, coverage, and Winkler score across neighborhood sizes. changes smoothly, suggesting that the conformal correction ab￾sorbs much of the retrieval variability. The default 𝐾 = 64 provides a stable balanc…
Figure 7
Figure 7. Figure 7: Average tradeoff across four datasets at [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

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