# Dencentralized learning in the presence of low-rank noise

arXiv: https://arxiv.org/abs/2203.09810 · HTML: https://mlsanity.com/paper/2203.09810/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 22 references that are in the map.
- First posted on arXiv 18 Mar 2022.

## Builds on (most cited first, 5 of 5)

- [Multitask learning over graphs: An Approach for Distributed, Streaming Machine Learning](https://mlsanity.com/paper/2001.02112/) (2020)
- [Proximity Without Consensus in Online Multi-Agent Optimization](https://mlsanity.com/paper/1606.05578/) (2016)
- [Adaptation and learning over networks under subspace constraints -- Part I: Stability Analysis](https://mlsanity.com/paper/1905.08750/) (2019)
- [Distributed Optimization With Local Domains: Applications in MPC and Network Flows](https://mlsanity.com/paper/1305.1885/) (2013)
- [Adaptation and learning over networks under subspace constraints -- Part II: Performance Analysis](https://mlsanity.com/paper/1906.12250/) (2019)

## Abstract (arXiv)

Observations collected by agents in a network may be unreliable due to observation noise or interference. This paper proposes a distributed algorithm that allows each node to improve the reliability of its own observation by relying solely on local computations and interactions with immediate neighbors, assuming that the field (graph signal) monitored by the network lies in a low-dimensional subspace and that a low-rank noise is present in addition to the usual full-rank noise. While oblique projections can be used to project measurements onto a low-rank subspace along a direction that is oblique to the subspace, the resulting solution is not distributed. Starting from the centralized solution, we propose an algorithm that performs the oblique projection of the overall set of observations onto the signal subspace in an iterative and distributed manner. We then show how the oblique projection framework can be extended to handle distributed learning and adaptation problems over networks.