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arxiv: 2604.13253 · v1 · submitted 2026-04-14 · 💻 cs.LG · stat.ME· stat.ML

Bias-Corrected Adaptive Conformal Inference for Multi-Horizon Time Series Forecasting

Ankit Lade , Sai Krishna J. , Indar Kumar This is my paper

Pith reviewed 2026-05-10 15:59 UTC · model grok-4.3

classification 💻 cs.LG stat.MEstat.ML
keywords adaptive conformal inferencebias correctiontime series forecastingprediction intervalsdistribution shiftexponentially weighted moving averageWinkler scorenonconformity scores
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The pith

Bias-Corrected Adaptive Conformal Inference recenters prediction intervals using an online bias estimate, avoiding the symmetric widening that standard ACI applies after persistent forecast errors.

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

Standard Adaptive Conformal Inference adapts only the quantile threshold to maintain coverage under distribution shift but leaves the interval center fixed, so persistent bias in the base forecaster forces wider intervals. BC-ACI augments ACI with an online exponentially weighted moving average estimate of that bias, corrects the nonconformity scores before quantile computation, and recenters the intervals around the adjusted center. An adaptive dead-zone suppresses corrections when the bias signal is indistinguishable from noise, preventing degradation on well-calibrated data. Controlled experiments across 688 runs on synthetic regimes and real datasets show 13-17% lower Winkler scores under mean and compound shifts while matching stationary performance. Finite-sample analysis establishes that coverage guarantees degrade gracefully as bias estimation error increases.

Core claim

BC-ACI augments ACI with an online EWM bias estimate that corrects nonconformity scores before quantile selection and re-centers prediction intervals, gated by an adaptive dead-zone threshold; this addresses bias-induced miscalibration at its source rather than by widening intervals, with coverage that degrades gracefully under bias estimation error.

What carries the argument

Online exponentially weighted moving average (EWM) estimate of forecast bias, used both to adjust nonconformity scores prior to quantile computation and to recenter intervals, combined with an adaptive dead-zone threshold that suppresses corrections below a noise level.

If this is right

  • Prediction intervals become tighter after persistent mean shifts because the center moves with the bias rather than widening symmetrically.
  • Coverage guarantees continue to hold, degrading only gradually as the bias estimate becomes less accurate.
  • Performance on stationary series remains statistically equivalent to standard ACI because the dead-zone blocks unnecessary corrections.
  • The method applies across multiple base forecasters and forecasting horizons without requiring changes to the underlying model.

Where Pith is reading between the lines

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

  • The same recentering idea could be layered onto other conformal methods that currently assume an unbiased base predictor.
  • Faster bias estimators than EWM might reduce lag after abrupt changes while preserving the dead-zone safeguard.
  • Multi-horizon forecasts may see larger gains because bias errors compound across steps and recentering corrects the entire trajectory at once.

Load-bearing premise

The online EWM bias estimate remains accurate enough and responsive enough after regime changes, and the dead-zone threshold correctly separates real bias from noise without adding miscalibration.

What would settle it

A test case in which bias shifts abruptly right after a regime change, causing the EWM estimate to lag and produce either undercoverage or Winkler scores no better than standard ACI.

Figures

Figures reproduced from arXiv: 2604.13253 by Ankit Lade, Indar Kumar, Sai Krishna J..

Figure 1
Figure 1. Figure 1: Prediction intervals around a mean shift at [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Winkler score ratios (BC-ACI / ACI) across all datasets. Values below 1 (red bars, left) [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Top: Online bias estimate ˆbt (solid red) tracking the true running mean (dashed blue) on mean-shift data (Ridge, h = 1). The grey band shows the dead-zone | ˆbt | ≤ k · MAD. Pre-shift, ˆbt stays inside the dead-zone; post-shift (t > 1000), it rapidly converges to b ≈ 3.99. Bottom: Raw residuals showing the shift in location. • Models with persistent bias (ridge regression, gradient boosting, neural networ… view at source ↗
read the original abstract

Adaptive Conformal Inference (ACI) provides distribution-free prediction intervals with asymptotic coverage guarantees for time series under distribution shift. However, ACI only adapts the quantile threshold -- it cannot shift the interval center. When a base forecaster develops persistent bias after a regime change, ACI compensates by widening intervals symmetrically, producing unnecessarily conservative bands. We propose Bias-Corrected ACI (BC-ACI), which augments standard ACI with an online exponentially weighted moving average (EWM) estimate of forecast bias. BC-ACI corrects nonconformity scores before quantile computation and re-centers prediction intervals, addressing the root cause of miscalibration rather than its symptom. An adaptive dead-zone threshold suppresses corrections when estimated bias is indistinguishable from noise, ensuring no degradation on well-calibrated data. In controlled experiments across 688 runs spanning two base models, four synthetic regimes, and three real datasets, BC-ACI reduces Winkler interval scores by 13--17% under mean and compound distribution shifts (Wilcoxon p < 0.001) while maintaining equivalent performance on stationary data (ratio 1.002x). We provide finite-sample analysis showing that coverage guarantees degrade gracefully with bias estimation error.

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

1 major / 2 minor

Summary. The paper proposes Bias-Corrected Adaptive Conformal Inference (BC-ACI) as an extension of Adaptive Conformal Inference (ACI) for multi-horizon time series forecasting under distribution shift. BC-ACI augments ACI with an online exponentially weighted moving average (EWM) bias estimator that corrects nonconformity scores before quantile computation and re-centers the prediction intervals; an adaptive dead-zone threshold suppresses corrections when estimated bias is indistinguishable from noise. The central claims are that this yields 13-17% lower Winkler scores under mean and compound shifts (Wilcoxon p<0.001) while preserving performance on stationary data (ratio 1.002x), supported by finite-sample analysis showing graceful degradation of coverage with bias estimation error. Experiments comprise 688 runs across two base models, four synthetic regimes, and three real datasets.

Significance. If the coverage guarantees remain valid, the approach provides a targeted improvement over standard ACI by correcting bias at the source rather than widening intervals symmetrically, which is practically relevant for efficient uncertainty quantification in non-stationary forecasting. The scale of the controlled empirical evaluation with statistical testing is a clear strength and supports the performance claims under the tested regimes.

major comments (1)
  1. [Finite-sample analysis] Finite-sample analysis (the section presenting the coverage bound): the graceful-degradation claim assumes bias estimation error is independent of the nonconformity scores and the adaptive quantile process. The online EWM bias estimate is computed from the same forecast residuals that enter the nonconformity scores; after a mean shift the EWM update and ACI quantile update become coupled through the shared data stream, and the dead-zone threshold adds a data-dependent selection effect. This dependence is not addressed in the analysis, so the stated bound may not degrade gracefully in the regime the method targets.
minor comments (2)
  1. [Experiments] Table 1 and §5.2: report the exact values chosen for the EWM smoothing factor and dead-zone threshold (or the procedure used to select them) and confirm they were fixed across all 688 runs.
  2. [Method] §3.2: the multi-horizon extension is described only at a high level; clarify how the bias correction and dead-zone are applied across horizons and whether the coverage argument extends directly.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. We address the single major comment below and will revise the paper accordingly.

read point-by-point responses

  1. Referee: [Finite-sample analysis] Finite-sample analysis (the section presenting the coverage bound): the graceful-degradation claim assumes bias estimation error is independent of the nonconformity scores and the adaptive quantile process. The online EWM bias estimate is computed from the same forecast residuals that enter the nonconformity scores; after a mean shift the EWM update and ACI quantile update become coupled through the shared data stream, and the dead-zone threshold adds a data-dependent selection effect. This dependence is not addressed in the analysis, so the stated bound may not degrade gracefully in the regime the method targets.

    Authors: We agree that the finite-sample analysis in the current manuscript derives the graceful-degradation bound under an independence assumption between bias-estimation error and the nonconformity scores/quantile process. This assumption does not strictly hold because the EWM bias estimator and the ACI updates share the same residual stream, and the dead-zone introduces an additional data-dependent selection. In the revised manuscript we will rewrite the finite-sample section to (i) explicitly state the independence assumption used in the original derivation, (ii) discuss the coupling induced by the shared data stream and the dead-zone, and (iii) provide an extended bound that controls the extra error term via the EWM forgetting factor and the dead-zone threshold. The revised bound will still establish graceful degradation (with a modestly larger constant), thereby preserving the central claim while making the analysis rigorous for the online regime the method targets. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical extension of ACI with independent bias correction

full rationale

The paper augments standard ACI with a conventional online EWM bias estimator and dead-zone rule, then reports empirical gains on Winkler scores under shifts. The finite-sample coverage claim is presented as an analysis of graceful degradation with bias error, without any reduction of the result to fitted parameters, self-defined quantities, or self-citation chains. No load-bearing step equates a prediction to its own inputs by construction; the central guarantees and performance statements remain externally falsifiable via the described experiments.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the asymptotic coverage properties of standard ACI under distribution shift plus the assumption that EWM bias estimation error remains small enough for the finite-sample bound to be useful.

free parameters (2)
  • EWM smoothing factor
    Controls responsiveness of the online bias estimate; value is not stated in abstract and must be chosen or tuned.
  • dead-zone threshold
    Suppresses correction when estimated bias is indistinguishable from noise; chosen to avoid degradation on stationary data.
axioms (1)
  • domain assumption Standard ACI provides asymptotic coverage guarantees under distribution shift when only the quantile threshold is adapted.
    The paper builds directly on ACI's established properties without re-deriving them.

pith-pipeline@v0.9.0 · 5513 in / 1376 out tokens · 61444 ms · 2026-05-10T15:59:04.798999+00:00 · methodology

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