# Conformal Prediction Intervals with Temporal Dependence

arXiv: https://arxiv.org/abs/2205.12940 · HTML: https://mlsanity.com/paper/2205.12940/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 47 references that are in the map.
- First posted on arXiv 25 May 2022.

## Builds on (most cited first, 22 of 22)

- [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)
- [Bayesian Deep Learning and a Probabilistic Perspective of Generalization](https://mlsanity.com/paper/2002.08791/) (2020)
- [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)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [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)
- [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)
- [Multiplicative Normalizing Flows for Variational Bayesian Neural Networks](https://mlsanity.com/paper/1703.01961/) (2017)
- [Localized Conformal Prediction: A Generalized Inference Framework for Conformal Prediction](https://mlsanity.com/paper/2106.08460/) (2021)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [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)
- [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)
- [Concepts and Applications of Conformal Prediction in Computational Drug Discovery](https://mlsanity.com/paper/1908.03569/) (2019)

## Built on by (most cited first, 9 of 9)

- [Non-Exchangeable Conformal Risk Control](https://mlsanity.com/paper/2310.01262/) (2023)
- [Conformal Prediction: A Data Perspective](https://mlsanity.com/paper/2410.06494/) (2024)
- [Multivariate Conformal Prediction using Optimal Transport](https://mlsanity.com/paper/2502.03609/) (2025)
- [Non-Exchangeable Conformal Language Generation with Nearest Neighbors](https://mlsanity.com/paper/2402.00707/) (2024)
- [Early Time Classification with Accumulated Accuracy Gap Control](https://mlsanity.com/paper/2402.00857/) (2024)
- [Conformalization of Sparse Generalized Linear Models](https://mlsanity.com/paper/2307.05109/) (2023)
- [From Conformal Predictions to Confidence Regions](https://mlsanity.com/paper/2405.18601/) (2024)
- [On the Need to Align Intent and Implementation in Uncertainty Quantification for Machine Learning](https://mlsanity.com/paper/2506.03037/) (2025)
- [Prediction Intervals for Individual Treatment Effects in a Multiple Decision Point Framework using Conformal Inference](https://mlsanity.com/paper/2512.08828/) (2025)

## Abstract (arXiv)

Cross-sectional prediction is common in many domains such as healthcare, including forecasting tasks using electronic health records, where different patients form a cross-section. We focus on the task of constructing valid prediction intervals (PIs) in time series regression with a cross-section. A prediction interval is considered valid if it covers the true response with (a pre-specified) high probability. We first distinguish between two notions of validity in such a setting: cross-sectional and longitudinal. Cross-sectional validity is concerned with validity across the cross-section of the time series data, while longitudinal validity accounts for the temporal dimension. Coverage guarantees along both these dimensions are ideally desirable; however, we show that distribution-free longitudinal validity is theoretically impossible. Despite this limitation, we propose Conformal Prediction with Temporal Dependence (CPTD), a procedure that is able to maintain strict cross-sectional validity while improving longitudinal coverage. CPTD is post-hoc and light-weight, and can easily be used in conjunction with any prediction model as long as a calibration set is available. We focus on neural networks due to their ability to model complicated data such as diagnosis codes for time series regression, and perform extensive experimental validation to verify the efficacy of our approach. We find that CPTD outperforms baselines on a variety of datasets by improving longitudinal coverage and often providing more efficient (narrower) PIs.