Regression models using shapes of functions as predictors
Abstract
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.
- Authors:
-
[2];
- 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)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program; National Science Foundation (NSF)
- OSTI Identifier:
- 1634794
- Alternate Identifier(s):
- OSTI ID: 1776473
- Report Number(s):
- SAND-2020-5389J
Journal ID: ISSN 0167-9473; 686289
- Grant/Contract Number:
- AC04-94AL85000; NA0003525; 1621787; 1617397
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computational Statistics and Data Analysis (Print)
- Additional Journal Information:
- Journal Name: Computational Statistics and Data Analysis (Print); Journal Volume: 151; Journal Issue: C; Journal ID: ISSN 0167-9473
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; functional data analysis; scalar-on-function regression; functional single-index model; function alignment; SRVF
Citation Formats
Ahn, Kyungmin, Tucker, J. Derek, Wu, Wei, and Srivastava, Anuj. Regression models using shapes of functions as predictors. United States: N. p., 2020.
Web. doi:10.1016/j.csda.2020.107017.
Ahn, Kyungmin, Tucker, J. Derek, Wu, Wei, & Srivastava, Anuj. Regression models using shapes of functions as predictors. United States. https://doi.org/10.1016/j.csda.2020.107017
Ahn, Kyungmin, Tucker, J. Derek, Wu, Wei, and Srivastava, Anuj. Sat .
"Regression models using shapes of functions as predictors". United States. https://doi.org/10.1016/j.csda.2020.107017. https://www.osti.gov/servlets/purl/1634794.
@article{osti_1634794,
title = {Regression models using shapes of functions as predictors},
author = {Ahn, Kyungmin and Tucker, J. Derek and Wu, Wei and Srivastava, Anuj},
abstractNote = {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.},
doi = {10.1016/j.csda.2020.107017},
journal = {Computational Statistics and Data Analysis (Print)},
number = C,
volume = 151,
place = {United States},
year = {Sat May 30 00:00:00 EDT 2020},
month = {Sat May 30 00:00:00 EDT 2020}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
Cited by: 2 works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.
Works referenced in this record:
Cross-validated estimations in the single-functional index model
journal, December 2008
- Ait-Saïdi, Ahmed; Ferraty, Frédéric; Kassa, Rabah
- Statistics, Vol. 42, Issue 6
Prediction in functional linear regression
journal, October 2006
- Cai, T. Tony; Hall, Peter
- The Annals of Statistics, Vol. 34, Issue 5
Functional linear model
journal, October 1999
- Cardot, Hervé; Ferraty, Frédéric; Sarda, Pascal
- Statistics & Probability Letters, Vol. 45, Issue 1
Wavelet-based scalar-on-function finite mixture regression models
journal, January 2016
- Ciarleglio, Adam; Todd Ogden, R.
- Computational Statistics & Data Analysis, Vol. 93
Multivariate calibration with single-index signal regression
journal, April 2009
- Eilers, Paul H. C.; Li, Bin; Marx, Brian D.
- Chemometrics and Intelligent Laboratory Systems, Vol. 96, Issue 2
Statistical Computing in Functional Data Analysis: The R Package fda.usc
journal, January 2012
- Febrero-Bande, Manuel; Fuente, Manuel Oviedo de la
- Journal of Statistical Software, Vol. 51, Issue 4
Treadmill walking as an external pacemaker to improve gait rhythm and stability in Parkinson's disease
journal, January 2005
- Frenkel-Toledo, Silvi; Giladi, Nir; Peretz, Chava
- Movement Disorders, Vol. 20, Issue 9
Penalized scalar-on-functions regression with interaction term
journal, January 2015
- Fuchs, Karen; Scheipl, Fabian; Greven, Sonja
- Computational Statistics & Data Analysis, Vol. 81
A Goodness-of-Fit Test for the Functional Linear Model with Scalar Response
journal, June 2014
- García-Portugués, Eduardo; González-Manteiga, Wenceslao; Febrero-Bande, Manuel
- Journal of Computational and Graphical Statistics, Vol. 23, Issue 3
Longitudinal scalar-on-functions regression with application to tractography data
journal, January 2013
- Gertheiss, J.; Goldsmith, J.; Crainiceanu, C.
- Biostatistics, Vol. 14, Issue 3
PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals
journal, June 2000
- Goldberger, Ary L.; Amaral, Luis A. N.; Glass, Leon
- Circulation, Vol. 101, Issue 23
Estimator selection and combination in scalar-on-function regression
journal, February 2014
- Goldsmith, Jeff; Scheipl, Fabian
- Computational Statistics & Data Analysis, Vol. 70
Generalized linear models with functional predictors
journal, August 2002
- James, Gareth M.
- Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 64, Issue 3
Functional single index models for longitudinal data
journal, February 2011
- Jiang, Ci-Ren; Wang, Jane-Ling
- The Annals of Statistics, Vol. 39, Issue 1
Generalized Functional Linear Models With Semiparametric Single-Index Interactions
journal, June 2010
- Li, Yehua; Wang, Naisyin; Carroll, Raymond J.
- Journal of the American Statistical Association, Vol. 105, Issue 490
Functional Convex Averaging and Synchronization for Time-Warped Random Curves
journal, September 2004
- Liu, Xueli; Müller, Hans-Georg
- Journal of the American Statistical Association, Vol. 99, Issue 467
Statistics of time warpings and phase variations
journal, January 2014
- Marron, J. S.; Ramsay, James O.; Sangalli, Laura M.
- Electronic Journal of Statistics, Vol. 8, Issue 2
Functional Data Analysis of Amplitude and Phase Variation
journal, November 2015
- Marron, J. S.; Ramsay, James O.; Sangalli, Laura M.
- Statistical Science, Vol. 30, Issue 4
Functional Regression
journal, April 2015
- Morris, Jeffrey S.
- Annual Review of Statistics and Its Application, Vol. 2, Issue 1
On Estimating Regression
journal, January 1964
- Nadaraya, E. A.
- Theory of Probability & Its Applications, Vol. 9, Issue 1
Curve registration
journal, January 1998
- Ramsay, J. O.; Li, Xiaochun
- Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 60, Issue 2
Methods for Scalar-on-Function Regression: Scalar-on-Function Regression
journal, February 2016
- Reiss, Philip T.; Goldsmith, Jeff; Shang, Han Lin
- International Statistical Review, Vol. 85, Issue 2
Consistent Estimation of Scaled Coefficients
journal, November 1986
- Stoker, Thomas M.
- Econometrica, Vol. 54, Issue 6
Generative models for functional data using phase and amplitude separation
journal, May 2013
- Tucker, J. Derek; Wu, Wei; Srivastava, Anuj
- Computational Statistics & Data Analysis, Vol. 61
An exploratory NMR nutri-metabonomic investigation reveals dimethyl sulfone as a dietary biomarker for onion intake
journal, January 2009
- Winning, Hanne; Roldán-Marín, Eduvigis; Dragsted, Lars O.
- The Analyst, Vol. 134, Issue 11
Dual tasking, gait rhythmicity, and Parkinson's disease: Which aspects of gait are attention demanding?
journal, September 2005
- Yogev, Galit; Giladi, Nir; Peretz, Chava
- European Journal of Neuroscience, Vol. 22, Issue 5
Estimator selection and combination in scalar-on-function regression
journal, February 2014
- Goldsmith, Jeff; Scheipl, Fabian
- Computational Statistics & Data Analysis, Vol. 70
Wavelet-based scalar-on-function finite mixture regression models
journal, January 2016
- Ciarleglio, Adam; Todd Ogden, R.
- Computational Statistics & Data Analysis, Vol. 93
An exploratory NMR nutri-metabonomic investigation reveals dimethyl sulfone as a dietary biomarker for onion intake
journal, January 2009
- Winning, Hanne; Roldán-Marín, Eduvigis; Dragsted, Lars O.
- The Analyst, Vol. 134, Issue 11
Longitudinal scalar-on-functions regression with application to tractography data
journal, January 2013
- Gertheiss, J.; Goldsmith, J.; Crainiceanu, C.
- Biostatistics, Vol. 14, Issue 3
Dual tasking, gait rhythmicity, and Parkinson's disease: Which aspects of gait are attention demanding?
journal, September 2005
- Yogev, Galit; Giladi, Nir; Peretz, Chava
- European Journal of Neuroscience, Vol. 22, Issue 5
Functional Data Analysis of Amplitude and Phase Variation
text, January 2015
- Anuj, Srivastava,; O., Ramsay, James; M., Sangalli, Laura
- The University of North Carolina at Chapel Hill University Libraries
Statistical Computing in Functional Data Analysis: The R Package fda.usc
journal, January 2012
- Febrero-Bande, Manuel; Fuente, Manuel Oviedo de la
- Journal of Statistical Software, Vol. 51, Issue 4
Consistent Estimation of Scaled Coefficients
journal, November 1986
- Stoker, Thomas M.
- Econometrica, Vol. 54, Issue 6
Generalized functional linear models
text, January 2005
- Muller, Hans-Georg; Stadtmuller, Ulrich
- arXiv