# Conformal Prediction with Temporal Quantile Adjustments

arXiv: https://arxiv.org/abs/2205.09940 · HTML: https://mlsanity.com/paper/2205.09940/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 62 references that are in the map.
- First posted on arXiv 20 May 2022.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [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)
- [Uncertainty Sets for Image Classifiers using Conformal Prediction](https://mlsanity.com/paper/2009.14193/) (2020)
- [Stochastic Gradient Hamiltonian Monte Carlo](https://mlsanity.com/paper/1402.4102/) (2014)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [A Multi-Horizon Quantile Recurrent Forecaster](https://mlsanity.com/paper/1711.11053/) (2017)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Multiplicative Normalizing Flows for Variational Bayesian Neural Networks](https://mlsanity.com/paper/1703.01961/) (2017)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Distribution-free uncertainty quantification for classification under label shift](https://mlsanity.com/paper/2103.03323/) (2021)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Few-shot Conformal Prediction with Auxiliary Tasks](https://mlsanity.com/paper/2102.08898/) (2021)
- [PAC Prediction Sets Under Covariate Shift](https://mlsanity.com/paper/2106.09848/) (2021)
- [Doubly Robust Calibration of Prediction Sets under Covariate Shift](https://mlsanity.com/paper/2203.01761/) (2022)
- [Bayesian Recurrent Neural Networks](https://mlsanity.com/paper/1704.02798/) (2017)
- [Locally Valid and Discriminative Prediction Intervals for Deep Learning Models](https://mlsanity.com/paper/2106.00225/) (2021)
- [Frequentist Uncertainty in Recurrent Neural Networks via Blockwise Influence Functions](https://mlsanity.com/paper/2006.13707/) (2020)
- [Concepts and Applications of Conformal Prediction in Computational Drug Discovery](https://mlsanity.com/paper/1908.03569/) (2019)

## Built on by (most cited first, 25 of 25)

- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Online conformal prediction with decaying step sizes](https://mlsanity.com/paper/2402.01139/) (2024)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Split Localized Conformal Prediction](https://mlsanity.com/paper/2206.13092/) (2022)
- [Knowing When to Stop: Delay-Adaptive Spiking Neural Network Classifiers with Reliability Guarantees](https://mlsanity.com/paper/2305.11322/) (2023)
- [RDIT: Residual-based Diffusion Implicit Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2509.02341/) (2025)
- [Online Conformal Prediction with Adversarial Semi-bandit Feedback via Regret Minimization](https://mlsanity.com/paper/2604.17984/) (2026)
- [Conformal Predictions for Longitudinal Data](https://mlsanity.com/paper/2310.02863/) (2023)
- [Sparse Deep Learning for Time Series Data: Theory and Applications](https://mlsanity.com/paper/2310.03243/) (2023)
- [Conformal time series decomposition with component-wise exchangeability](https://mlsanity.com/paper/2406.16766/) (2024)
- [On the Need to Align Intent and Implementation in Uncertainty Quantification for Machine Learning](https://mlsanity.com/paper/2506.03037/) (2025)
- [Retrieval-Corrected Conformal Prediction for Time Series](https://mlsanity.com/paper/2608.10553/) (2026)
- [Causally-Aware Spatio-Temporal Multi-Graph Convolution Network for Accurate and Reliable Traffic Prediction](https://mlsanity.com/paper/2408.13293/) (2024)
- [Dual-Splitting Conformal Prediction for Multi-Step Time Series Forecasting](https://mlsanity.com/paper/2503.21251/) (2025)
- [Uncertainty-Calibrated Prediction of Randomly-Timed Biomarker Trajectories with Conformal Bands](https://mlsanity.com/paper/2511.13911/) (2025)
- [Conformal Path Reasoning: Trustworthy Knowledge Graph Question Answering via Path-Level Calibration](https://mlsanity.com/paper/2605.08077/) (2026)
- [Calibrating AI Models for Wireless Communications via Conformal Prediction](https://mlsanity.com/paper/2212.07775/) (2022)
- [Distribution-Free Predictive Inference under Unknown Temporal Drift](https://mlsanity.com/paper/2406.06516/) (2024)
- [CONTINA: Confidence Interval for Traffic Demand Prediction with Coverage Guarantee](https://mlsanity.com/paper/2504.13961/) (2025)
- [Statistical Guarantees in Synthetic Data through Conformal Adversarial Generation](https://mlsanity.com/paper/2504.17058/) (2025)
- [Feature Fitted Online Conformal Prediction for Deep Time Series Forecasting Model](https://mlsanity.com/paper/2505.08158/) (2025)
- [Prediction Intervals for Individual Treatment Effects in a Multiple Decision Point Framework using Conformal Inference](https://mlsanity.com/paper/2512.08828/) (2025)
- [Online Conformal Prediction for Non-Exchangeable Panel Data](https://mlsanity.com/paper/2605.17705/) (2026)

## Abstract (arXiv)

We develop Temporal Quantile Adjustment (TQA), a general method to construct efficient and valid prediction intervals (PIs) for regression on cross-sectional time series data. Such data is common in many domains, including econometrics and healthcare. A canonical example in healthcare is predicting patient outcomes using physiological time-series data, where a population of patients composes a cross-section. Reliable PI estimators in this setting must address two distinct notions of coverage: cross-sectional coverage across a cross-sectional slice, and longitudinal coverage along the temporal dimension for each time series. Recent works have explored adapting Conformal Prediction (CP) to obtain PIs in the time series context. However, none handles both notions of coverage simultaneously. CP methods typically query a pre-specified quantile from the distribution of nonconformity scores on a calibration set. TQA adjusts the quantile to query in CP at each time t, accounting for both cross-sectional and longitudinal coverage in a theoretically-grounded manner. The post-hoc nature of TQA facilitates its use as a general wrapper around any time series regression model. We validate TQA's performance through extensive experimentation: TQA generally obtains efficient PIs and improves longitudinal coverage while preserving cross-sectional coverage.