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 covariat...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/2/203 |
| _version_ | 1797480564148666368 |
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| author | Joseph Naiman Peter Xuekun Song |
| author_facet | Joseph Naiman Peter Xuekun Song |
| author_sort | Joseph Naiman |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-09T22:02:51Z |
| format | Article |
| id | doaj.art-bb876a28e0c14a508939dd299765ba57 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-09T22:02:51Z |
| publishDate | 2022-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-bb876a28e0c14a508939dd299765ba572023-11-23T19:47:38ZengMDPI AGEntropy1099-43002022-01-0124220310.3390/e24020203Multivariate Functional Kernel Machine Regression and Sparse Functional Feature SelectionJoseph Naiman0Peter Xuekun Song1Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USADepartment of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USAMotivated 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.https://www.mdpi.com/1099-4300/24/2/203functional principal component analysisfunctional predictorlinear mixed-effects modelmobile devicesparse group regularizationwearable device data |
| spellingShingle | Joseph Naiman Peter Xuekun Song Multivariate Functional Kernel Machine Regression and Sparse Functional Feature Selection Entropy functional principal component analysis functional predictor linear mixed-effects model mobile device sparse group regularization wearable device data |
| title | Multivariate Functional Kernel Machine Regression and Sparse Functional Feature Selection |
| title_full | Multivariate Functional Kernel Machine Regression and Sparse Functional Feature Selection |
| title_fullStr | Multivariate Functional Kernel Machine Regression and Sparse Functional Feature Selection |
| title_full_unstemmed | Multivariate Functional Kernel Machine Regression and Sparse Functional Feature Selection |
| title_short | Multivariate Functional Kernel Machine Regression and Sparse Functional Feature Selection |
| title_sort | multivariate functional kernel machine regression and sparse functional feature selection |
| topic | functional principal component analysis functional predictor linear mixed-effects model mobile device sparse group regularization wearable device data |
| url | https://www.mdpi.com/1099-4300/24/2/203 |
| work_keys_str_mv | AT josephnaiman multivariatefunctionalkernelmachineregressionandsparsefunctionalfeatureselection AT peterxuekunsong multivariatefunctionalkernelmachineregressionandsparsefunctionalfeatureselection |