# Conformal Predictions for Longitudinal Data

arXiv: https://arxiv.org/abs/2310.02863 · HTML: https://mlsanity.com/paper/2310.02863/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 25 references that are in the map.
- First posted on arXiv 4 Oct 2023.

## Builds on (most cited first, 13 of 13)

- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [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)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Nested conformal prediction and quantile out-of-bag ensemble methods](https://mlsanity.com/paper/1910.10562/) (2019)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Sequential Predictive Conformal Inference for Time Series](https://mlsanity.com/paper/2212.03463/) (2022)
- [Adaptive, Distribution-Free Prediction Intervals for Deep Networks](https://mlsanity.com/paper/1905.10634/) (2019)
- [Conformal prediction for time series](https://mlsanity.com/paper/2010.09107/) (2020)
- [Ensemble Conformalized Quantile Regression for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2202.08756/) (2022)
- [Conformal Prediction with Temporal Quantile Adjustments](https://mlsanity.com/paper/2205.09940/) (2022)

## Built on by (most cited first, 3 of 3)

- [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 introduce Longitudinal Predictive Conformal Inference (LPCI), a novel distribution-free conformal prediction algorithm for longitudinal data. Current conformal prediction approaches for time series data predominantly focus on the univariate setting, and thus lack cross-sectional coverage when applied individually to each time series in a longitudinal dataset. The current state-of-the-art for longitudinal data relies on creating infinitely-wide prediction intervals to guarantee both cross-sectional and asymptotic longitudinal coverage. The proposed LPCI method addresses this by ensuring that both longitudinal and cross-sectional coverages are guaranteed without resorting to infinitely wide intervals. In our approach, we model the residual data as a quantile fixed-effects regression problem, constructing prediction intervals with a trained quantile regressor. Our extensive experiments demonstrate that LPCI achieves valid cross-sectional coverage and outperforms existing benchmarks in terms of longitudinal coverage rates. Theoretically, we establish LPCI's asymptotic coverage guarantees for both dimensions, with finite-width intervals. The robust performance of LPCI in generating reliable prediction intervals for longitudinal data underscores its potential for broad applications, including in medicine, finance, and supply chain management.