# Coresets for Vertical Federated Learning: Regularized Linear Regression and K-Means Clustering

arXiv: https://arxiv.org/abs/2210.14664 · HTML: https://mlsanity.com/paper/2210.14664/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 85 references that are in the map.
- First posted on arXiv 26 Oct 2022.

## Builds on (most cited first, 30 of 48)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Advances and Open Problems in Federated Learning](https://mlsanity.com/paper/1912.04977/) (2019)
- [Federated Learning: Challenges, Methods, and Future Directions](https://mlsanity.com/paper/1908.07873/) (2019)
- [Federated Learning: Strategies for Improving Communication Efficiency](https://mlsanity.com/paper/1610.05492/) (2016)
- [Federated Learning with Differential Privacy: Algorithms and Performance Analysis](https://mlsanity.com/paper/1911.00222/) (2019)
- [SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives](https://mlsanity.com/paper/1407.0202/) (2014)
- [A Field Guide to Federated Optimization](https://mlsanity.com/paper/2107.06917/) (2021)
- [Error Feedback Fixes SignSGD and other Gradient Compression Schemes](https://mlsanity.com/paper/1901.09847/) (2019)
- [Private federated learning on vertically partitioned data via entity resolution and additively homomorphic encryption](https://mlsanity.com/paper/1711.10677/) (2017)
- [SecureBoost: A Lossless Federated Learning Framework](https://mlsanity.com/paper/1901.08755/) (2019)
- [EF21: A New, Simpler, Theoretically Better, and Practically Faster Error Feedback](https://mlsanity.com/paper/2106.05203/) (2021)
- [LDP-Fed: Federated Learning with Local Differential Privacy](https://mlsanity.com/paper/2006.03637/) (2020)
- [Linear Convergence in Federated Learning: Tackling Client Heterogeneity and Sparse Gradients](https://mlsanity.com/paper/2102.07053/) (2021)
- [Feature Inference Attack on Model Predictions in Vertical Federated Learning](https://mlsanity.com/paper/2010.10152/) (2020)
- [Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering](https://mlsanity.com/paper/1807.04518/) (2018)
- [Acceleration for Compressed Gradient Descent in Distributed and Federated Optimization](https://mlsanity.com/paper/2002.11364/) (2020)
- [Local SGD: Unified Theory and New Efficient Methods](https://mlsanity.com/paper/2011.02828/) (2020)
- [VAFL: a Method of Vertical Asynchronous Federated Learning](https://mlsanity.com/paper/2007.06081/) (2020)
- [MARINA: Faster Non-Convex Distributed Learning with Compression](https://mlsanity.com/paper/2102.07845/) (2021)
- [Local Differential Privacy based Federated Learning for Internet of Things](https://mlsanity.com/paper/2004.08856/) (2020)
- [Coresets and Sketches](https://mlsanity.com/paper/1601.00617/) (2016)
- [Vertical Federated Learning: Challenges, Methodologies and Experiments](https://mlsanity.com/paper/2202.04309/) (2022)
- [Parallel Distributed Logistic Regression for Vertical Federated Learning without Third-Party Coordinator](https://mlsanity.com/paper/1911.09824/) (2019)
- [Input Sparsity Time Low-Rank Approximation via Ridge Leverage Score Sampling](https://mlsanity.com/paper/1511.07263/) (2015)
- [BEER: Fast O(1/T) Rate for Decentralized Nonconvex Optimization with Communication Compression](https://mlsanity.com/paper/2201.13320/) (2022)
- [New Frameworks for Offline and Streaming Coreset Constructions](https://mlsanity.com/paper/1612.00889/) (2016)
- [Training Gaussian Mixture Models at Scale via Coresets](https://mlsanity.com/paper/1703.08110/) (2017)
- [A Quasi-Newton Method Based Vertical Federated Learning Framework for Logistic Regression](https://mlsanity.com/paper/1912.00513/) (2019)
- [A New Coreset Framework for Clustering](https://mlsanity.com/paper/2104.06133/) (2021)
- [SoteriaFL: A Unified Framework for Private Federated Learning with Communication Compression](https://mlsanity.com/paper/2206.09888/) (2022)

## Built on by (most cited first, 14 of 14)

- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [Accelerating Heterogeneous Federated Learning with Closed-form Classifiers](https://mlsanity.com/paper/2406.01116/) (2024)
- [VertiBench: Advancing Feature Distribution Diversity in Vertical Federated Learning Benchmarks](https://mlsanity.com/paper/2307.02040/) (2023)
- [From Risk to Resilience: Towards Assessing and Mitigating the Risk of Data Reconstruction Attacks in Federated Learning](https://mlsanity.com/paper/2512.15460/) (2025)
- [A new type of federated clustering: A non-model-sharing approach](https://mlsanity.com/paper/2506.10244/) (2025)
- [Bayesian Coreset Optimization for Personalized Federated Learning](https://mlsanity.com/paper/2511.01800/) (2025)
- [Training-Free Dynamic Upcycling of Expert Language Models](https://mlsanity.com/paper/2603.29765/) (2026)
- [X-VFL: A New Vertical Federated Learning Framework with Cross Completion and Decision Subspace Alignment](https://mlsanity.com/paper/2508.05568/) (2025)
- [Coresets for Clustering Under Stochastic Noise](https://mlsanity.com/paper/2510.23438/) (2025)
- [VertCoHiRF: Decentralized Vertical Clustering Beyond k-means](https://mlsanity.com/paper/2602.07279/) (2026)
- [Learning Unknown Interdependencies for Decentralized Root Cause Analysis in Nonlinear Dynamical Systems](https://mlsanity.com/paper/2602.21928/) (2026)
- [COREKG: Coreset-Guided Personalized Summarization of Knowledge Graphs](https://mlsanity.com/paper/2605.14900/) (2026)
- [IR3DE: A Linear Router for Large Language Models](https://mlsanity.com/paper/2606.06098/) (2026)
- [Beyond Worst-Case Coreset Bounds for k-Clustering via Determinantal Sampling](https://mlsanity.com/paper/2609.06394/) (2026)

## Abstract (arXiv)

Vertical federated learning (VFL), where data features are stored in multiple parties distributively, is an important area in machine learning. However, the communication complexity for VFL is typically very high. In this paper, we propose a unified framework by constructing coresets in a distributed fashion for communication-efficient VFL. We study two important learning tasks in the VFL setting: regularized linear regression and k-means clustering, and apply our coreset framework to both problems. We theoretically show that using coresets can drastically alleviate the communication complexity, while nearly maintain the solution quality. Numerical experiments are conducted to corroborate our theoretical findings.