Regression models using shapes of functions as predictors

Ahn, Kyungmin; Tucker, J. Derek; Wu, Wei; Srivastava, Anuj

doi:10.1016/j.csda.2020.107017

Regression models using shapes of functions as predictors

Journal Article · Sat May 30 00:00:00 EDT 2020 · Computational Statistics and Data Analysis (Print)

DOI:https://doi.org/10.1016/j.csda.2020.107017· OSTI ID:1634794

Ahn, Kyungmin ^[1]; ^[2]; Wu, Wei ^[3]; Srivastava, Anuj ^[3]

RIKEN Center for Biosystems Dynamics Research (BDR), Kobe (Japan)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Florida State Univ., Tallahassee, FL (United States)

Functional variables are often used as predictors in regression problems. A commonly used parametric approach, called scalar-on-function regression, uses the $$\mathbb L^2$$ inner product to map functional predictors into scalar responses. This method can perform poorly when predictor functions contain undesired phase variability, causing phases to have disproportionately large influence on the response variable. One past solution has been to perform phase–amplitude separation (as a pre-processing step) and then use only the amplitudes in the regression model. In this paper, we propose a more integrated approach, termed elastic functional regression model (EFRM), where phase-separation is performed inside the regression model, rather than as a pre-processing step. This approach generalizes the notion of phase in functional data, and is based on the norm-preserving time warping of predictors. Due to its invariance properties, this representation provides robustness to predictor phase variability and results in improved predictions of the response variable over traditional models. We demonstrate this framework using a number of datasets involving gait signals, NMR data, and stock market prices.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF)

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1634794

Alternate ID(s):: OSTI ID: 1776473

Report Number(s):: SAND--2020-5389J; 686289

Journal Information:: Computational Statistics and Data Analysis (Print), Journal Name: Computational Statistics and Data Analysis (Print) Journal Issue: C Vol. 151; ISSN 0167-9473

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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