# Scalable Interpretable Multi-Response Regression via SEED

arXiv: https://arxiv.org/abs/1608.03686 · HTML: https://mlsanity.com/paper/1608.03686/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Aug 2016.

## Built on by (most cited first, 4 of 4)

- [SOFARI: High-Dimensional Manifold-Based Inference](https://mlsanity.com/paper/2309.15032/) (2023)
- [Parallel integrative learning for large-scale multi-response regression with incomplete outcomes](https://mlsanity.com/paper/2104.05076/) (2021)
- [Regression for matrix-valued data via Kronecker products factorization](https://mlsanity.com/paper/2404.19220/) (2024)
- [Simultaneous Best Subset Selection and Dimension Reduction via Primal-Dual Iterations](https://mlsanity.com/paper/2211.15889/) (2022)

## Abstract (arXiv)

Sparse reduced-rank regression is an important tool to uncover meaningful dependence structure between large numbers of predictors and responses in many big data applications such as genome-wide association studies and social media analysis. Despite the recent theoretical and algorithmic advances, scalable estimation of sparse reduced-rank regression remains largely unexplored. In this paper, we suggest a scalable procedure called sequential estimation with eigen-decomposition (SEED) which needs only a single top-r singular value decomposition to find the optimal low-rank and sparse matrix by solving a sparse generalized eigenvalue problem. Our suggested method is not only scalable but also performs simultaneous dimensionality reduction and variable selection. Under some mild regularity conditions, we show that SEED enjoys nice sampling properties including consistency in estimation, rank selection, prediction, and model selection. Numerical studies on synthetic and real data sets show that SEED outperforms the state-of-the-art approaches for large-scale matrix estimation problem.