| Title: |
Bayesian Partial Reduced-Rank Regression |
| Authors: |
Pintado, Maria F., Iacopini, Matteo, Rossini, Luca, Shestopaloff, Alexander Y. |
| Publication Year: |
2024 |
| Collection: |
Statistics |
| Subject Terms: |
Statistics - Methodology, Statistics - Computation |
| More Details: |
Reduced-rank (RR) regression may be interpreted as a dimensionality reduction technique able to reveal complex relationships among the data parsimoniously. However, RR regression models typically overlook any potential group structure among the responses by assuming a low-rank structure on the coefficient matrix. To address this limitation, a Bayesian Partial RR (BPRR) regression is exploited, where the response vector and the coefficient matrix are partitioned into low- and full-rank sub-groups. As opposed to the literature, which assumes known group structure and rank, a novel strategy is introduced that treats them as unknown parameters to be estimated. The main contribution is two-fold: an approach to infer the low- and full-rank group memberships from the data is proposed, and then, conditionally on this allocation, the corresponding (reduced) rank is estimated. Both steps are carried out in a Bayesian approach, allowing for full uncertainty quantification and based on a partially collapsed Gibbs sampler. It relies on a Laplace approximation of the marginal likelihood and the Metropolized Shotgun Stochastic Search to estimate the group allocation efficiently. Applications to synthetic and real-world data reveal the potential of the proposed method to reveal hidden structures in the data. |
| Document Type: |
Working Paper |
| Access URL: |
http://arxiv.org/abs/2406.17444 |
| Accession Number: |
edsarx.2406.17444 |
| Database: |
arXiv |
