Hybrid Partial Least Squares Regression with Multiple Functional and Scalar Predictors

Fuente: arXiv
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Main Authors: Mun, Jongmin, Jang, Jeong Hoon
Format: Preprint
Published: 2026
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author Mun, Jongmin
Jang, Jeong Hoon
author_facet Mun, Jongmin
Jang, Jeong Hoon
contents Motivated by renal imaging studies that combine renogram curves with pharmacokinetic and demographic covariates, we propose Hybrid partial least squares (Hybrid PLS) for simultaneous supervised dimension reduction and regression in the presence of cross-modality correlations. The proposed approach embeds multiple functional and scalar predictors into a unified hybrid Hilbert space and rigorously extends the nonlinear iterative PLS (NIPALS) algorithm. This theoretical development is complemented by a sample-level algorithm that incorporates roughness penalties to control smoothness. By exploiting the rank-one structure of the resulting optimization problem, the algorithm admits a computationally efficient closed-form solution that requires solving only linear systems at each iteration. We establish fundamental geometric properties of the proposed framework, including orthogonality of the latent scores and PLS directions. Extensive numerical studies on synthetic data, together with an application to a renal imaging study, validate these theoretical results and demonstrate the method's ability to recover predictive structure under intermodal multicollinearity, yielding parsimonious low-dimensional representations.
format Preprint
id arxiv_https___arxiv_org_abs_2601_16364
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Hybrid Partial Least Squares Regression with Multiple Functional and Scalar Predictors
Mun, Jongmin
Jang, Jeong Hoon
Methodology
62R10, 62H25, 62P10
Motivated by renal imaging studies that combine renogram curves with pharmacokinetic and demographic covariates, we propose Hybrid partial least squares (Hybrid PLS) for simultaneous supervised dimension reduction and regression in the presence of cross-modality correlations. The proposed approach embeds multiple functional and scalar predictors into a unified hybrid Hilbert space and rigorously extends the nonlinear iterative PLS (NIPALS) algorithm. This theoretical development is complemented by a sample-level algorithm that incorporates roughness penalties to control smoothness. By exploiting the rank-one structure of the resulting optimization problem, the algorithm admits a computationally efficient closed-form solution that requires solving only linear systems at each iteration. We establish fundamental geometric properties of the proposed framework, including orthogonality of the latent scores and PLS directions. Extensive numerical studies on synthetic data, together with an application to a renal imaging study, validate these theoretical results and demonstrate the method's ability to recover predictive structure under intermodal multicollinearity, yielding parsimonious low-dimensional representations.
title Hybrid Partial Least Squares Regression with Multiple Functional and Scalar Predictors
topic Methodology
62R10, 62H25, 62P10
url https://arxiv.org/abs/2601.16364