Joint Registration and Conformal Prediction for Partially Observed Functional Data

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.