# Noisy Low Rank Column-wise Sensing

arXiv: https://arxiv.org/abs/2409.08384 · HTML: https://mlsanity.com/paper/2409.08384/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 10 references that are in the map.
- First posted on arXiv 12 Sep 2024.

## Builds on (most cited first, 1 of 1)

- [Exploiting Shared Representations for Personalized Federated Learning](https://mlsanity.com/paper/2102.07078/) (2021)

## Built on by (most cited first, 2 of 2)

- [RepUCB: Representation Learning-Based UCB for Heterogeneous Multi-Task Linear Bandits](https://mlsanity.com/paper/2604.00531/) (2026)
- [Multi-Task Representation Learning for Conservative Linear Bandits](https://mlsanity.com/paper/2605.12176/) (2026)

## Abstract (arXiv)

This letter studies the AltGDmin algorithm for solving the noisy low rank column-wise sensing (LRCS) problem. Our sample complexity guarantee improves upon the best existing one by a factor max(r, log(1/ε))/r where r is the rank of the unknown matrix and ε is the final desired accuracy. A second contribution of this work is a detailed comparison of guarantees from all work that studies the exact same mathematical problem as LRCS, but refers to it by different names.