# Adaptive Reduced Rank Regression

arXiv: https://arxiv.org/abs/1905.11566 · HTML: https://mlsanity.com/paper/1905.11566/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2019.

## Built on by (most cited first, 3 of 3)

- [AI Ethics Statements -- Analysis and lessons learnt from NeurIPS Broader Impact Statements](https://mlsanity.com/paper/2111.01705/) (2021)
- [Symphony in the Latent Space: Provably Integrating High-dimensional Techniques with Non-linear Machine Learning Models](https://mlsanity.com/paper/2212.00852/) (2022)
- [Near-optimal Rank Adaptive Inference of High Dimensional Matrices](https://mlsanity.com/paper/2510.08117/) (2025)

## Abstract (arXiv)

We study the low rank regression problem my = Mmx + ε, where mx and my are d1 and d2 dimensional vectors respectively. We consider the extreme high-dimensional setting where the number of observations n is less than d1 + d2. Existing algorithms are designed for settings where n is typically as large as Rank(M)(d1+d2). This work provides an efficient algorithm which only involves two SVD, and establishes statistical guarantees on its performance. The algorithm decouples the problem by first estimating the precision matrix of the features, and then solving the matrix denoising problem. To complement the upper bound, we introduce new techniques for establishing lower bounds on the performance of any algorithm for this problem. Our preliminary experiments confirm that our algorithm often out-performs existing baselines, and is always at least competitive.