Uncertainty Quantification in Bayesian Reduced-Rank Sparse Regressions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917588387233792 |
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| author | Pintado, Maria F. Iacopini, Matteo Rossini, Luca Shestopaloff, Alexander Y. |
| author_facet | Pintado, Maria F. Iacopini, Matteo Rossini, Luca Shestopaloff, Alexander Y. |
| contents | Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows for uncertainty quantification. Our method employs a mixture prior on the regression coefficient matrix along with a global-local shrinkage prior on its low-rank decomposition. Then, we rely on the Signal Adaptive Variable Selector to perform sparsification and define two novel tools: the Posterior Inclusion Probability uncertainty index and the Relevance Index. The validity of the method is assessed in a simulation study, and then its advantages and usefulness are shown in real-data applications on the chemical composition of tobacco and on the photometry of galaxies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_01521 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Uncertainty Quantification in Bayesian Reduced-Rank Sparse Regressions Pintado, Maria F. Iacopini, Matteo Rossini, Luca Shestopaloff, Alexander Y. Methodology Applications Reduced-rank regression recognises the possibility of a rank-deficient matrix of coefficients. We propose a novel Bayesian model for estimating the rank of the coefficient matrix, which obviates the need for post-processing steps and allows for uncertainty quantification. Our method employs a mixture prior on the regression coefficient matrix along with a global-local shrinkage prior on its low-rank decomposition. Then, we rely on the Signal Adaptive Variable Selector to perform sparsification and define two novel tools: the Posterior Inclusion Probability uncertainty index and the Relevance Index. The validity of the method is assessed in a simulation study, and then its advantages and usefulness are shown in real-data applications on the chemical composition of tobacco and on the photometry of galaxies. |
| title | Uncertainty Quantification in Bayesian Reduced-Rank Sparse Regressions |
| topic | Methodology Applications |
| url | https://arxiv.org/abs/2306.01521 |