Bayesian Multivariate Sparse Functional Principal Components Analysis
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917470239981568 |
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| author | Sartini, Joseph Zeger, Scott Crainiceanu, Ciprian |
| author_facet | Sartini, Joseph Zeger, Scott Crainiceanu, Ciprian |
| contents | Functional Principal Components Analysis (FPCA) provides a parsimonious, semi-parametric model for multivariate, sparsely-observed functional data. Frequentist FPCA approaches estimate principal components (PCs) from the data, then condition on these estimates in subsequent analyses. As an alternative, we propose a fully-Bayesian inferential framework for multivariate, sparse functional data (MSFAST) which explicitly models the PCs and incorporates their uncertainty. MSFAST builds upon the FAST approach to FPCA for univariate, densely-observed functional data. Like FAST, MSFAST represents PCs using orthonormal splines and samples the orthonormal spline coefficients using parameter expansion. MSFAST extends FAST to multivariate, sparsely-observed data by (1) standardizing each functional covariate to mitigate poor posterior conditioning due to disparate scales; (2) using a better-suited orthogonal spline basis; (3) updating parameterizations for computational stability; (4) introducing routines that leverage multiple cores and threads to accelerate compute; (5) using a Procrustes-based posterior PC alignment procedure; and (6) providing efficient prediction routines. We evaluate MSFAST alongside existing implementations using simulations. MSFAST produces uniquely valid inferences and accurate estimates, particularly in smaller signal-to-noise regimes. MSFAST is motivated by and applied to a study of child growth, with an accompanying vignette illustrating the implementation step-by-step. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03512 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian Multivariate Sparse Functional Principal Components Analysis Sartini, Joseph Zeger, Scott Crainiceanu, Ciprian Methodology Functional Principal Components Analysis (FPCA) provides a parsimonious, semi-parametric model for multivariate, sparsely-observed functional data. Frequentist FPCA approaches estimate principal components (PCs) from the data, then condition on these estimates in subsequent analyses. As an alternative, we propose a fully-Bayesian inferential framework for multivariate, sparse functional data (MSFAST) which explicitly models the PCs and incorporates their uncertainty. MSFAST builds upon the FAST approach to FPCA for univariate, densely-observed functional data. Like FAST, MSFAST represents PCs using orthonormal splines and samples the orthonormal spline coefficients using parameter expansion. MSFAST extends FAST to multivariate, sparsely-observed data by (1) standardizing each functional covariate to mitigate poor posterior conditioning due to disparate scales; (2) using a better-suited orthogonal spline basis; (3) updating parameterizations for computational stability; (4) introducing routines that leverage multiple cores and threads to accelerate compute; (5) using a Procrustes-based posterior PC alignment procedure; and (6) providing efficient prediction routines. We evaluate MSFAST alongside existing implementations using simulations. MSFAST produces uniquely valid inferences and accurate estimates, particularly in smaller signal-to-noise regimes. MSFAST is motivated by and applied to a study of child growth, with an accompanying vignette illustrating the implementation step-by-step. |
| title | Bayesian Multivariate Sparse Functional Principal Components Analysis |
| topic | Methodology |
| url | https://arxiv.org/abs/2509.03512 |