# Robustness of Iteratively Pre-Conditioned Gradient-Descent Method: The Case of Distributed Linear Regression Problem

arXiv: https://arxiv.org/abs/2101.10967 · HTML: https://mlsanity.com/paper/2101.10967/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 17 references that are in the map.
- First posted on arXiv 26 Jan 2021.

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

- [Federated Machine Learning: Concept and Applications](https://mlsanity.com/paper/1902.04885/) (2019)
- [Linear Hypothesis Testing in Dense High-Dimensional Linear Models](https://mlsanity.com/paper/1610.02987/) (2016)
- [Distributed Solution of Large-Scale Linear Systems via Accelerated Projection-Based Consensus](https://mlsanity.com/paper/1708.01413/) (2017)
- [Iterative Pre-Conditioning to Expedite the Gradient-Descent Method](https://mlsanity.com/paper/2003.07180/) (2020)
- [Iterative Pre-Conditioning for Expediting the Gradient-Descent Method: The Distributed Linear Least-Squares Problem](https://mlsanity.com/paper/2008.02856/) (2020)

## Built on by (most cited first, 1 of 1)

- [Distributed Linear Solvers and Data Heterogeneity](https://mlsanity.com/paper/2304.10640/) (2023)

## Abstract (arXiv)

This paper considers the problem of multi-agent distributed linear regression in the presence of system noises. In this problem, the system comprises multiple agents wherein each agent locally observes a set of data points, and the agents' goal is to compute a linear model that best fits the collective data points observed by all the agents. We consider a server-based distributed architecture where the agents interact with a common server to solve the problem; however, the server cannot access the agents' data points. We consider a practical scenario wherein the system either has observation noise, i.e., the data points observed by the agents are corrupted, or has process noise, i.e., the computations performed by the server and the agents are corrupted. In noise-free systems, the recently proposed distributed linear regression algorithm, named the Iteratively Pre-conditioned Gradient-descent (IPG) method, has been claimed to converge faster than related methods. In this paper, we study the robustness of the IPG method, against both the observation noise and the process noise. We empirically show that the robustness of the IPG method compares favorably to the state-of-the-art algorithms.