# Conformal Prediction Bands for Multivariate Functional Data

arXiv: https://arxiv.org/abs/2106.01792 · HTML: https://mlsanity.com/paper/2106.01792/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2021.

## Built on by (most cited first, 29 of 29)

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- [Uncertainty Quantification of Surrogate Models using Conformal Prediction](https://mlsanity.com/paper/2408.09881/) (2024)
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- [Flow-based Conformal Prediction for Multi-dimensional Time Series](https://mlsanity.com/paper/2502.05709/) (2025)
- [Uncertainty quantification in metric spaces](https://mlsanity.com/paper/2405.05110/) (2024)
- [Conformal Loss-Controlling Prediction](https://mlsanity.com/paper/2301.02424/) (2023)
- [Reliable uncertainty quantification for 2D/3D anatomical landmark localization using multi-output conformal prediction](https://mlsanity.com/paper/2503.14106/) (2025)
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- [Locally Adaptive Conformal Inference for Operator Models](https://mlsanity.com/paper/2507.20975/) (2025)
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- [Minimax Multi-Target Conformal Prediction with Applications to Imaging Inverse Problems](https://mlsanity.com/paper/2511.13533/) (2025)
- [Joint Registration and Conformal Prediction for Partially Observed Functional Data](https://mlsanity.com/paper/2502.15000/) (2025)
- [Multi-fidelity aerodynamic data fusion by autoencoder transfer learning](https://mlsanity.com/paper/2512.13069/) (2025)
- [Contrastive Conformal Sets](https://mlsanity.com/paper/2603.26261/) (2026)
- [Conformal Robust Set Estimation](https://mlsanity.com/paper/2604.18441/) (2026)
- [Manifold Constrained Conformal Prediction for Spatial Events](https://mlsanity.com/paper/2607.10008/) (2026)
- [SPARC: Single-Pass Scaling for Motion Forecasting with Conformal Bayesian Last Layers](https://mlsanity.com/paper/2608.20802/) (2026)
- [OGAM: Connecting Systematic Testing to Runtime Assurance through Object-Grounded Attention Monitoring for VLA Policies](https://mlsanity.com/paper/2610.05878/) (2026)

## Abstract (arXiv)

Motivated by the pressing request of methods able to create prediction sets in a general regression framework for a multivariate functional response and pushed by new methodological advancements in non-parametric prediction for functional data, we propose a set of conformal predictors that produce finite-sample either valid or exact multivariate simultaneous prediction bands under the mild assumption of exchangeable regression pairs. The fact that the prediction bands can be built around any regression estimator and that can be easily found in closed form yields a very widely usable method, which is fairly straightforward to implement. In addition, we first introduce and then describe a specific conformal predictor that guarantees an asymptotic result in terms of efficiency and inducing prediction bands able to modulate their width based on the local behavior and magnitude of the functional data. The method is investigated and analyzed through a simulation study and a real-world application in the field of urban mobility.