Subspace decompositions for association structure learning in multivariate categorical response regression
Autor: | Zhao, Hongru, Molstad, Aaron J., Rothman, Adam J. |
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Rok vydání: | 2024 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | 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. Comment: 31 pages, 2 figures, 8 sections, journal paper |
Databáze: | arXiv |
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