# Joint Registration and Conformal Prediction for Partially Observed Functional Data

arXiv: https://arxiv.org/abs/2502.15000 · HTML: https://mlsanity.com/paper/2502.15000/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 51 references that are in the map.
- First posted on arXiv 20 Feb 2025.

## Builds on (most cited first, 21 of 21)

- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Adaptive Conformal Predictions for Time Series](https://mlsanity.com/paper/2202.07282/) (2022)
- [Conformal PID Control for Time Series Prediction](https://mlsanity.com/paper/2307.16895/) (2023)
- [A Conformal Prediction Approach to Explore Functional Data](https://mlsanity.com/paper/1302.6452/) (2013)
- [Conformalized Survival Analysis](https://mlsanity.com/paper/2103.09763/) (2021)
- [Conformal Prediction Bands for Multivariate Functional Data](https://mlsanity.com/paper/2106.01792/) (2021)
- [Estimating network edge probabilities by neighborhood smoothing](https://mlsanity.com/paper/1509.08588/) (2015)
- [Conformalized survival analysis with adaptive cutoffs](https://mlsanity.com/paper/2211.01227/) (2022)
- [Functional Data Analysis of Amplitude and Phase Variation](https://mlsanity.com/paper/1512.03216/) (2015)
- [The Importance of Being a Band: Finite-Sample Exact Distribution-Free Prediction Sets for Functional Data](https://mlsanity.com/paper/2102.06746/) (2021)
- [Conformal prediction after data-dependent model selection](https://mlsanity.com/paper/2408.07066/) (2024)
- [Conformalized matrix completion](https://mlsanity.com/paper/2305.10637/) (2023)
- [Conformal Prediction Bands for Two-Dimensional Functional Time Series](https://mlsanity.com/paper/2207.13656/) (2022)
- [Functional time series prediction under partial observation of the future curve](https://mlsanity.com/paper/1906.00281/) (2019)
- [Distribution-Free Matrix Prediction Under Arbitrary Missing Pattern](https://mlsanity.com/paper/2305.11640/) (2023)
- [Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse and Fragmented Functional Data](https://mlsanity.com/paper/1912.05125/) (2019)
- [Shape Analysis of Functional Data with Elastic Partial Matching](https://mlsanity.com/paper/2105.08604/) (2021)
- [Adapted Variational Bayes for Functional Data Registration, Smoothing, and Prediction](https://mlsanity.com/paper/1502.00552/) (2015)
- [Registration for Incomplete Non-Gaussian Functional Data](https://mlsanity.com/paper/2108.05634/) (2021)
- [Conformal prediction for functional Ordinary kriging](https://mlsanity.com/paper/2409.20084/) (2024)

## Abstract (arXiv)

Predicting missing segments in partially observed functions is challenging due to infinite-dimensionality, complex dependence within and across observations, and irregular noise. These challenges are further exacerbated by the existence of two distinct sources of variation in functional data, termed amplitude (variation along the y-axis) and phase (variation along the x-axis). While registration can disentangle them from complete functional data, the process is more difficult for partial observations. Thus, existing methods for functional data prediction often ignore phase variation. Furthermore, they rely on strong parametric assumptions, and require either precise model specifications or computationally intensive techniques, such as bootstrapping, to construct prediction intervals. To tackle this problem, we propose a unified registration and prediction approach for partially observed functions under the conformal prediction framework, which separately focuses on the amplitude and phase components. By leveraging split conformal methods, our approach integrates registration and prediction while ensuring exchangeability through carefully constructed predictor-response pairs. Using a neighborhood smoothing algorithm, the framework produces pointwise prediction bands with finite-sample marginal coverage guarantees under weak assumptions. The method is easy to implement, computationally efficient, and suitable for parallelization. Numerical studies and real-world data examples clearly demonstrate the effectiveness and practical utility of the proposed approach.