Subspace decompositions for association structure learning in multivariate categorical response regression
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909337210847232 |
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| author | Zhao, Hongru Molstad, Aaron J. Rothman, Adam J. |
| author_facet | Zhao, Hongru Molstad, Aaron J. Rothman, Adam J. |
| contents | Modeling the complex relationships between multiple categorical response variables as a function of predictors is a fundamental task in the analysis of categorical data. However, existing methods can be difficult to interpret and may lack flexibility. To address these challenges, we introduce a penalized likelihood method for multivariate categorical response regression that relies on a novel subspace decomposition to parameterize interpretable association structures. Our approach models the relationships between categorical responses by identifying mutual, joint, and conditionally independent associations, which yields a linear problem within a tensor product space. We establish theoretical guarantees for our estimator, including error bounds in high-dimensional settings, and demonstrate the method's interpretability and prediction accuracy through comprehensive simulation studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04356 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Subspace decompositions for association structure learning in multivariate categorical response regression Zhao, Hongru Molstad, Aaron J. Rothman, Adam J. Methodology Statistics Theory 62H20, 62J12(Primary) 62F10, 62H12 (Secondary) Modeling the complex relationships between multiple categorical response variables as a function of predictors is a fundamental task in the analysis of categorical data. However, existing methods can be difficult to interpret and may lack flexibility. To address these challenges, we introduce a penalized likelihood method for multivariate categorical response regression that relies on a novel subspace decomposition to parameterize interpretable association structures. Our approach models the relationships between categorical responses by identifying mutual, joint, and conditionally independent associations, which yields a linear problem within a tensor product space. We establish theoretical guarantees for our estimator, including error bounds in high-dimensional settings, and demonstrate the method's interpretability and prediction accuracy through comprehensive simulation studies. |
| title | Subspace decompositions for association structure learning in multivariate categorical response regression |
| topic | Methodology Statistics Theory 62H20, 62J12(Primary) 62F10, 62H12 (Secondary) |
| url | https://arxiv.org/abs/2410.04356 |