# Fast and Robust Sparsity Learning over Networks: A Decentralized Surrogate Median Regression Approach

arXiv: https://arxiv.org/abs/2202.05498 · HTML: https://mlsanity.com/paper/2202.05498/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 53 references that are in the map.
- First posted on arXiv 11 Feb 2022.

## Builds on (most cited first, 13 of 13)

- [Can Decentralized Algorithms Outperform Centralized Algorithms? A Case Study for Decentralized Parallel Stochastic Gradient Descent](https://mlsanity.com/paper/1705.09056/) (2017)
- [On the Convergence of Decentralized Gradient Descent](https://mlsanity.com/paper/1310.7063/) (2013)
- [On the Linear Convergence of the ADMM in Decentralized Consensus Optimization](https://mlsanity.com/paper/1307.5561/) (2013)
- [A decentralized proximal-gradient method with network independent step-sizes and separated convergence rates](https://mlsanity.com/paper/1704.07807/) (2017)
- [Efficient Distributed Learning with Sparsity](https://mlsanity.com/paper/1605.07991/) (2016)
- [Quantile Regression Under Memory Constraint](https://mlsanity.com/paper/1810.08264/) (2018)
- [Distributed High-dimensional Regression Under a Quantile Loss Function](https://mlsanity.com/paper/1906.05741/) (2019)
- [Distributed inference for quantile regression processes](https://mlsanity.com/paper/1701.06088/) (2017)
- [Distributed Proximal Gradient Algorithm for Partially Asynchronous Computer Clusters](https://mlsanity.com/paper/1704.03540/) (2017)
- [Monitoring and Optimization for Power Grids: A Signal Processing Perspective](https://mlsanity.com/paper/1302.0885/) (2013)
- [Local Linear Convergence of ISTA and FISTA on the LASSO Problem](https://mlsanity.com/paper/1501.02888/) (2015)
- [Distributed Discrete-time Optimization in Multi-agent Networks Using only Sign of Relative State](https://mlsanity.com/paper/1709.08360/) (2017)
- [Distributed Linear Model Clustering over Networks: A Tree-Based Fused-Lasso ADMM Approach](https://mlsanity.com/paper/1905.11549/) (2019)

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

- [Serverless Federated AUPRC Optimization for Multi-Party Collaborative Imbalanced Data Mining](https://mlsanity.com/paper/2308.03035/) (2023)
- [A Selective Review on Statistical Methods for Massive Data Computation: Distributed Computing, Subsampling, and Minibatch Techniques](https://mlsanity.com/paper/2403.11163/) (2024)
- [Efficient Distributed Learning over Decentralized Networks with Convoluted Support Vector Machine](https://mlsanity.com/paper/2503.07563/) (2025)
- [Adaptive Decentralized Federated Learning for Robust Optimization](https://mlsanity.com/paper/2512.02852/) (2025)

## Abstract (arXiv)

Decentralized sparsity learning has attracted a significant amount of attention recently due to its rapidly growing applications. To obtain the robust and sparse estimators, a natural idea is to adopt the non-smooth median loss combined with a ℓ1 sparsity regularizer. However, most of the existing methods suffer from slow convergence performance caused by the em double non-smooth objective. To accelerate the computation, in this paper, we proposed a decentralized surrogate median regression (deSMR) method for efficiently solving the decentralized sparsity learning problem. We show that our proposed algorithm enjoys a linear convergence rate with a simple implementation. We also investigate the statistical guarantee, and it shows that our proposed estimator achieves a near-oracle convergence rate without any restriction on the number of network nodes. Moreover, we establish the theoretical results for sparse support recovery. Thorough numerical experiments and real data study are provided to demonstrate the effectiveness of our method.