Elastic functional principal component regression

Tucker, James Derek; Lewis, John R.; Srivastava, Anuj

doi:10.1002/sam.11399

Elastic functional principal component regression

Journal Article · Thu Dec 13 23:00:00 EST 2018 · Statistical Analysis and Data Mining

DOI:https://doi.org/10.1002/sam.11399· OSTI ID:1492372

^[1]; Lewis, John R. ^[1]; Srivastava, Anuj ^[2]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Florida State Univ., Tallahassee, FL (United States)

We study regression using functional predictors in situations where these functions contains both phase and amplitude variability. In other words, the functions are misaligned due to errors in time measurements, and these errors can significantly degrade both model estimation and prediction performance. The current techniques either ignore the phase variability, or handle it via preprocessing, that is, use an off–the–shelf technique for functional alignment and phase removal. We develop a functional principal component regression model which has a comprehensive approach in handling phase and amplitude variability. The model utilizes a mathematical representation of the data known as the square–root slope function. These functions preserve the L² norm under warping and are ideally suited for simultaneous estimation of regression and warping parameters. Furthermore, using both simulated and real–world data sets, we demonstrate our approach and evaluate its prediction performance relative to current models. In addition, we propose an extension to functional logistic and multinomial logistic regression.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: DHS NTNFC; USDOE

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1492372

Report Number(s):: SAND--2018-12984J; 669889

Journal Information:: Statistical Analysis and Data Mining, Journal Name: Statistical Analysis and Data Mining Journal Issue: 2 Vol. 12; ISSN 1932-1864

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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