PreprintarXiv licencearXiv
On Reduced Rank Regression
Abstract
We propose a decoupled solution to the Reduced Rank Regression (RRR) problem, i.e. a pair of matrices (A*, B*) whose product A*B* minimizes the least squares error under a rank constraint. Using our formalism, we rewrite two other solutions from the literature and compare them with ours. In particular, we prove that all these formulations are equivalent. We then analyze their time complexity, and compare their running time and numerical precision on synthetic data, from which we derive practical recommendations. An open-source implementation of the algorithms and experiments is available here: https://gitlab.inria.fr/trudkiew/reduced\_rank\_regression.
Related
- BARRR: Bidimensional Augmented Reduced Rank Regression for Multi-View Multi-Cohort Data
- A Bayesian Vertical Federated Learning Framework for Multivariate Reduced-Rank High-Dimensional Regression
- Sufficiently Reduced Distributional Regression
- Functional Regression with Reconstructed Curves: Local Rank Stability and Optimized Confidence Certificates
- Reduced-Rank Autoregressive Models for Matrix Time Series
BibTeX
@misc{rudkiewicz2026reduced,
title = {{On Reduced Rank Regression}},
author = {Théo Rudkiewicz and Manon Verbockhaven},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26051},
eprint = {2610.26051},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26051},
}
RIS
TY - UNPB
TI - On Reduced Rank Regression
AU - Th{é}o Rudkiewicz
AU - Manon Verbockhaven
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26051
UR - https://arxiv.org/abs/2610.26051
AB - We propose a decoupled solution to the Reduced Rank Regression (RRR) problem, i.e. a pair of matrices (A*, B*) whose product A*B* minimizes the least squares error under a rank constraint. Using our formalism, we rewrite two other solutions from the literature and compare them with ours. In particular, we prove that all these formulations are equivalent. We then analyze their time complexity, and compare their running time and numerical precision on synthetic data, from which we derive practical recommendations. An open-source implementation of the algorithms and experiments is available here: https://gitlab.inria.fr/trudkiew/reduced\_rank\_regression.
ER -