Elastic kernel Ridge regression, with applications in phonetics
Abstract
Predicting the shapes of entire curves requires accounting for nonlinear geometry and unknown alignments between curves. We develop elastic kernel ridge regression, a nonparametric method for planar curve responses with scalar, multivariate, or functional covariates. Using square-root velocity representations, we formulate penalized conditional Fréchet mean estimation in a shape space invariant to translation, rotation, scaling, and reparametrization. A vector-valued reproducing kernel Hilbert space provides a flexible nonlinear link through the spherical exponential map. We use an alternating algorithm to align each observed curve to its current fitted value, and updates the regression function. To facilitate this, we provide a new Euclidean quasi-Newton solver that exploits scale invariance of the reparametrization objective; this accelerates alignment while retaining accuracy in a numerical comparison. Simulations demonstrate the benefits of estimating alignment within the regression and respecting spherical geometry. Applied to vocal tract contours from a real-time magnetic resonance imaging recording, the method recovers missing frames and reconstructs shape trajectories from downsampled data. A speech inversion proof of concept on the same recording predicts tongue shapes from acoustic features, illustrating the method's potential. The method is implemented in the \texttt{R} package \texttt{sphereg2}.
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BibTeX
@misc{matteo2026elastic,
title = {{Elastic kernel Ridge regression, with applications in phonetics}},
author = {Beatrice Matteo and Almond Stoecker and Davide Pigoli and Shahin Tavakoli},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08386},
eprint = {2610.08386},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08386},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Elastic kernel Ridge regression, with applications in phonetics
AU - Beatrice Matteo
AU - Almond Stoecker
AU - Davide Pigoli
AU - Shahin Tavakoli
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08386
UR - https://arxiv.org/abs/2610.08386
AB - Predicting the shapes of entire curves requires accounting for nonlinear geometry and unknown alignments between curves. We develop elastic kernel ridge regression, a nonparametric method for planar curve responses with scalar, multivariate, or functional covariates. Using square-root velocity representations, we formulate penalized conditional Fréchet mean estimation in a shape space invariant to translation, rotation, scaling, and reparametrization. A vector-valued reproducing kernel Hilbert space provides a flexible nonlinear link through the spherical exponential map. We use an alternating algorithm to align each observed curve to its current fitted value, and updates the regression function. To facilitate this, we provide a new Euclidean quasi-Newton solver that exploits scale invariance of the reparametrization objective; this accelerates alignment while retaining accuracy in a numerical comparison. Simulations demonstrate the benefits of estimating alignment within the regression and respecting spherical geometry. Applied to vocal tract contours from a real-time magnetic resonance imaging recording, the method recovers missing frames and reconstructs shape trajectories from downsampled data. A speech inversion proof of concept on the same recording predicts tongue shapes from acoustic features, illustrating the method's potential. The method is implemented in the \texttt{R} package \texttt{sphereg2}.
ER -