A0674
Title: Conformal prediction for fragmented functional data
Authors: Fangyi Wang - The Ohio State University (United States) [presenting]
Sebastian Kurtek - The Ohio State University (United States)
Yuan Zhang - The Ohio State University (United States)
Abstract: Predicting missing segments in incomplete curves is a significant challenge in functional data analysis due to unknown nuisance transformations among different curves. Existing methods typically rely on correct (parametric) model specifications and often involve computationally intensive estimation procedures. A very different approach, using conformal prediction, is proposed to tackle this problem. Applying conformal prediction to fragmented functional data is highly non-trivial due to the lack of naturally defined predictor and response variables. These variables are constructed from given complete functions, and the downstream analysis is carefully designed such that exchangeability is preserved, even in the presence of unknown nuisance transformations. Based on a neighborhood smoothing algorithm, various types of pointwise prediction bands can be produced. The method is simple, easy to implement, and supported by finite sample theoretical guarantees under rather weak assumptions. It also computes much faster than existing methods and allows straightforward parallelization. Extensive numerical studies and real-world examples clearly demonstrate the effectiveness and practical utility of the approach.
