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  3. Joint Registration And Conformal Prediction For Partially Observed Functional Data.
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Related Experiment Video

Multimodal Cross-Device and Marker-Free Co-Registration of Preclinical Imaging Modalities
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Multimodal Cross-Device and Marker-Free Co-Registration of Preclinical Imaging Modalities

Published on: October 27, 2023

Joint Registration and Conformal Prediction for Partially Observed Functional Data.

Fangyi Wang1, Sebastian Kurtek1, Yuan Zhang1

  • 1Department of Statistics, The Ohio State University, Columbus, OH.

Journal of Computational and Graphical Statistics : a Joint Publication of American Statistical Association, Institute of Mathematical Statistics, Interface Foundation of North America
|May 13, 2026

View abstract on PubMed

Summary
This summary is machine-generated.

This study introduces a novel method for predicting missing data in functional observations. The approach combines registration and prediction, offering efficient and reliable prediction bands for complex functional data.

Keywords:
Conformal predictionElastic functional data analysisNeighborhood smoothingPhase variation

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Area of Science:

  • Statistics
  • Functional Data Analysis

Background:

  • Predicting missing segments in partially observed functional data is complex due to infinite dimensions, observation dependencies, and noise.
  • Amplitude and phase variations in functional data complicate prediction, especially with partial observations, leading existing methods to often ignore phase variation.
  • Current prediction methods require specific models and computationally intensive tools for prediction intervals.

Purpose of the Study:

  • To propose a unified approach for registration and prediction of partially observed functional data.
  • To develop a computationally efficient method that provides reliable prediction bands.
  • To address the challenges posed by amplitude and phase variations in functional data prediction.

Main Methods:

  • A unified registration and prediction framework using conformal prediction is proposed.
  • The method ensures exchangeability via predictor-response pairs and employs neighborhood smoothing.
  • Pointwise prediction bands with finite-sample marginal coverage guarantees are generated under weak assumptions.

    • Main Results:

    • The proposed method effectively integrates registration and prediction for partially observed functions.
    • It produces prediction bands with guaranteed coverage under weak assumptions.
    • The approach is computationally efficient, easy to implement, and parallelizable.

    Conclusions:

    • The novel conformal prediction framework offers an effective solution for predicting missing segments in partially observed functional data.
    • This method overcomes limitations of existing approaches by handling both amplitude and phase variations efficiently.
    • The approach demonstrates practical utility and effectiveness through numerical studies and real-world examples.