Continuous-domain signals, curves, and trajectories sampled over time or space—arise routinely in modern sensing, health, and human–computer interaction applications. Such a type of data is also called Functional data in the statistical literature. Despite their prevalence, providing reliable uncertainty quantification for predictions such as continuous-domain data remains challenging, especially when observations are irregular or sparsely sampled. We introduce a general conformal prediction framework that produces finite-sample valid prediction sets for functional data under any sampling regime, including dense and sparse designs.
Our approach uses a Karhunen–Loève (KL) representation to model non-stationary domain variability and introduces an efficient inversion procedure that converts conformal prediction sets into interpretable prediction bands with lower and upper envelopes. We establish theoretical guarantees for validity and coverage, and show that the prediction band achieves provably correct coverage under mild conditions for densely observed signals, and approximate coverage for sparsely observed data. Extensive simulations demonstrate strong empirical coverage and competitive predictive accuracy across both sparse and dense settings. Applications to three widely used datasets—fractional anisotropy profiles from multiple sclerosis patients and longitudinal measurements from Alzheimer’s disease cohorts—highlight the method’s robustness and ease of interpretation.
Salil Koner is an Assistant Professor of Statistics at the University of California, Riverside. His research develops principled statistical and machine learning methods for complex structured data, with a focus on continuous-domain signals, high-dimensional longitudinal data, and uncertainty quantification with application to biomedical data. Dr. Koner graduated with a Ph.D. in Statistics from North Carolina State University. Before joining UCR, he was a Postdoctoral Associate in the Department of Biostatistics at Duke University. His statistical research has been supported by fellowships and has been published at major venues in statistics, biomedicine, and data science.