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Abstract In this article, we introduce a functional structural equation model for estimating directional relations from multivariate functional data. We decouple the estimation into two major steps: directional order determination and selection through sparse functional regression. We first propose a score function at the linear operator level, and show that its minimization can recover the true directional order when the relation between each function and its parental functions is nonlinear. We then develop a sparse functional additive regression, where both the response and the multivariate predictors are functions and the regression relation is additive and nonlinear. We also propose strategies to speed up the computation and scale up our method. In theory, we establish the consistencies of order determination, sparse functional additive regression, and directed acyclic graph estimation, while allowing both the dimension of the Karhunen–Loéve expansion coefficients and the number of random functions to diverge with the sample size. We illustrate the efficacy of our method through simulations, and an application to brain effective connectivity analysis.
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Multivariate Functional Kernel Machine Regression and Sparse Functional Feature Selection
Motivated by mobile devices that record data at a high frequency, we propose a new methodological framework for analyzing a semi-parametric regression model that allow us to study a nonlinear relationship between a scalar response and multiple functional predictors in the presence of scalar covariates. Utilizing functional principal component analysis (FPCA) and the least-squares kernel machine method (LSKM), we are able to substantially extend the framework of semi-parametric regression models of scalar responses on scalar predictors by allowing multiple functional predictors to enter the nonlinear model. Regularization is established for feature selection in the setting of reproducing kernel Hilbert spaces. Our method performs simultaneously model fitting and variable selection on functional features. For the implementation, we propose an effective algorithm to solve related optimization problems in that iterations take place between both linear mixed-effects models and a variable selection method (e.g., sparse group lasso). We show algorithmic convergence results and theoretical guarantees for the proposed methodology. We illustrate its performance through simulation experiments and an analysis of accelerometer data.
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- Award ID(s):
- 2113564
- PAR ID:
- 10328749
- Date Published:
- Journal Name:
- Entropy
- Volume:
- 24
- Issue:
- 2
- ISSN:
- 1099-4300
- Page Range / eLocation ID:
- 203
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.3390/e24020203
