# Conformal Prediction for Hierarchical Data

arXiv: https://arxiv.org/abs/2411.13479 · HTML: https://mlsanity.com/paper/2411.13479/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 45 references that are in the map.
- First posted on arXiv 20 Nov 2024.

## Builds on (most cited first, 16 of 16)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [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)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal Inference for Online Prediction with Arbitrary Distribution Shifts](https://mlsanity.com/paper/2208.08401/) (2022)
- [Copula-based conformal prediction for Multi-Target Regression](https://mlsanity.com/paper/2101.12002/) (2021)
- [Calibrated Multiple-Output Quantile Regression with Representation Learning](https://mlsanity.com/paper/2110.00816/) (2021)
- [Conformal Uncertainty Sets for Robust Optimization](https://mlsanity.com/paper/2105.14957/) (2021)
- [Conformal prediction for multi-dimensional time series by ellipsoidal sets](https://mlsanity.com/paper/2403.03850/) (2024)
- [Distribution-Free Prediction Sets for Two-Layer Hierarchical Models](https://mlsanity.com/paper/1809.07441/) (2018)
- [Distribution-free inference with hierarchical data](https://mlsanity.com/paper/2306.06342/) (2023)
- [Efficiency of conformalized ridge regression](https://mlsanity.com/paper/1404.2083/) (2014)
- [Probabilistic forecast reconciliation under the Gaussian framework](https://mlsanity.com/paper/2103.11128/) (2021)
- [Online Hierarchical Forecasting for Power Consumption Data](https://mlsanity.com/paper/2003.00585/) (2020)
- [Predictive Inference in Multi-environment Scenarios](https://mlsanity.com/paper/2403.16336/) (2024)
- [Forecasting Electric Vehicle Charging Station Occupancy: Smarter Mobility Data Challenge](https://mlsanity.com/paper/2306.06142/) (2023)

## Built on by (most cited first, 5 of 5)

- [Conformal Calibration: Ensuring the Reliability of Black-Box AI in Wireless Systems](https://mlsanity.com/paper/2504.09310/) (2025)
- [Multivariate Standardized Residuals for Conformal Prediction](https://mlsanity.com/paper/2507.20941/) (2025)
- [Simulation-Augmented Multi-Step Split Conformal Prediction for Aggregated Forecasts](https://mlsanity.com/paper/2606.16356/) (2026)
- [Multivariate conformal uncertainty propagation in multitask atomistic simulation: Successes and pitfalls](https://mlsanity.com/paper/2609.31384/) (2026)
- [Probabilistic Forecasting of Electric Vehicle Charging in a Time-varying Hierarchical Infrastructure](https://mlsanity.com/paper/2610.13588/) (2026)

## Abstract (arXiv)

We consider conformal prediction for multivariate data and focus on hierarchical data, where some components are linear combinations of others. Intuitively, the hierarchical structure can be leveraged to reduce the size of prediction regions for the same coverage level. We implement this intuition by including a projection step (also called a reconciliation step) in the split conformal prediction [SCP] procedure, and prove that the resulting prediction regions are indeed globally smaller. We do so both under the classic objective of joint coverage and under a new and challenging task: component-wise coverage, for which efficiency results are more difficult to obtain. The associated strategies and their analyses are based both on the literature of SCP and of forecast reconciliation, which we connect. We also illustrate the theoretical findings, for different scales of hierarchies on simulated data.