# Spectral Adaptive Conformal Prediction for Structured Non-Exchangeable Data

arXiv: https://arxiv.org/abs/2606.15950 · HTML: https://mlsanity.com/paper/2606.15950/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 26 references that are in the map.
- First posted on arXiv 14 Jun 2026.

## Builds on (most cited first, 14 of 14)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformalized Quantile Regression](https://mlsanity.com/paper/1905.03222/) (2019)
- [Conformal Prediction Under Covariate Shift](https://mlsanity.com/paper/1904.06019/) (2019)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Improved Online Conformal Prediction via Strongly Adaptive Online Learning](https://mlsanity.com/paper/2302.07869/) (2023)
- [Copula Conformal Prediction for Multi-step Time Series Forecasting](https://mlsanity.com/paper/2212.03281/) (2022)
- [Open Power System Data - Frictionless data for electricity system modelling](https://mlsanity.com/paper/1812.10405/) (2018)
- [Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series](https://mlsanity.com/paper/2402.05203/) (2024)
- [Dual-Splitting Conformal Prediction for Multi-Step Time Series Forecasting](https://mlsanity.com/paper/2503.21251/) (2025)

## Built on by (most cited first, 1 of 1)

- [Signed Evidence Flow: Conflict-Aware and Stability-Calibrated Data Analysis](https://mlsanity.com/paper/2606.21875/) (2026)

## Abstract (arXiv)

Conformal prediction gives prediction intervals with finite-sample coverage when the data are exchangeable. Many time-indexed datasets are not exchangeable: they have seasons, recurring regimes, changing frequencies, or other forms of structured dependence. This paper studies a simple way to use that structure. We propose spectral adaptive conformal prediction, a method that forms weighted conformal quantiles using local spectral similarity and then updates the target miscoverage level online. The spectral weights choose calibration residuals that look relevant to the current test point. The adaptive update corrects the long-run miss rate when uncertainty changes over time. The theory makes both parts controllable. We give an approximate coverage bound that splits the error into a spectral mismatch term and an effective-sample-size term, prove that kernel spectral weighting never increases the mismatch term relative to uniform weighting, show that a bandwidth of order N^(-1/(d+2)) balances the two terms, and establish an unconditional long-run calibration bound for the adaptive update that holds for every sample path without independence or stationarity. Simulations with recurring regimes and slowly changing frequencies, together with four real-data examples spanning monthly, weekly, and daily U.S. and European series, show when the hybrid method improves on strong adaptive baselines and when it does not, and an effective-sample-size safeguard, computable at prediction time without outcomes, detects and repairs the one observed failure.