# Vertical Federated Learning without Revealing Intersection Membership

arXiv: https://arxiv.org/abs/2106.05508 · HTML: https://mlsanity.com/paper/2106.05508/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 39 references that are in the map.
- First posted on arXiv 10 Jun 2021.

## Builds on (most cited first, 18 of 18)

- [Communication-Efficient Learning of Deep Networks from Decentralized Data](https://mlsanity.com/paper/1602.05629/) (2016)
- [Wide & Deep Learning for Recommender Systems](https://mlsanity.com/paper/1606.07792/) (2016)
- [Inverting Gradients -- How easy is it to break privacy in federated learning?](https://mlsanity.com/paper/2003.14053/) (2020)
- [An Efficient Framework for Clustered Federated Learning](https://mlsanity.com/paper/2006.04088/) (2020)
- [Spectral Signatures in Backdoor Attacks](https://mlsanity.com/paper/1811.00636/) (2018)
- [Measuring Calibration in Deep Learning](https://mlsanity.com/paper/1904.01685/) (2019)
- [Split learning for health: Distributed deep learning without sharing raw patient data](https://mlsanity.com/paper/1812.00564/) (2018)
- [Distributed learning of deep neural network over multiple agents](https://mlsanity.com/paper/1810.06060/) (2018)
- [Lower Bounds and Optimal Algorithms for Personalized Federated Learning](https://mlsanity.com/paper/2010.02372/) (2020)
- [Acceleration for Compressed Gradient Descent in Distributed and Federated Optimization](https://mlsanity.com/paper/2002.11364/) (2020)
- [Label Leakage and Protection in Two-party Split Learning](https://mlsanity.com/paper/2102.08504/) (2021)
- [Privacy Preserving Vertical Federated Learning for Tree-based Models](https://mlsanity.com/paper/2008.06170/) (2020)
- [VAFL: a Method of Vertical Asynchronous Federated Learning](https://mlsanity.com/paper/2007.06081/) (2020)
- [Federated Accelerated Stochastic Gradient Descent](https://mlsanity.com/paper/2006.08950/) (2020)
- [Parallel Distributed Logistic Regression for Vertical Federated Learning without Third-Party Coordinator](https://mlsanity.com/paper/1911.09824/) (2019)
- [Can We Use Split Learning on 1D CNN Models for Privacy Preserving Training?](https://mlsanity.com/paper/2003.12365/) (2020)
- [SplitNN-driven Vertical Partitioning](https://mlsanity.com/paper/2008.04137/) (2020)
- [Asymmetrical Vertical Federated Learning](https://mlsanity.com/paper/2004.07427/) (2020)

## Built on by (most cited first, 19 of 19)

- [Vertical Federated Learning: Concepts, Advances and Challenges](https://mlsanity.com/paper/2211.12814/) (2022)
- [BlindFL: Vertical Federated Machine Learning without Peeking into Your Data](https://mlsanity.com/paper/2206.07975/) (2022)
- [Towards Personalized Federated Learning via Heterogeneous Model Reassembly](https://mlsanity.com/paper/2308.08643/) (2023)
- [A Survey on Vertical Federated Learning: From a Layered Perspective](https://mlsanity.com/paper/2304.01829/) (2023)
- [Differentially Private Label Protection in Split Learning](https://mlsanity.com/paper/2203.02073/) (2022)
- [Coresets for Vertical Federated Learning: Regularized Linear Regression and K-Means Clustering](https://mlsanity.com/paper/2210.14664/) (2022)
- [Vertical Federated Learning for Effectiveness, Security, Applicability: A Survey](https://mlsanity.com/paper/2405.17495/) (2024)
- [Vertical Semi-Federated Learning for Efficient Online Advertising](https://mlsanity.com/paper/2209.15635/) (2022)
- [Continual Horizontal Federated Learning for Heterogeneous Data](https://mlsanity.com/paper/2203.02108/) (2022)
- [Vertical Federated Learning: Taxonomies, Threats, and Prospects](https://mlsanity.com/paper/2302.01550/) (2023)
- [VFLAIR: A Research Library and Benchmark for Vertical Federated Learning](https://mlsanity.com/paper/2310.09827/) (2023)
- [Robust and IP-Protecting Vertical Federated Learning against Unexpected Quitting of Parties](https://mlsanity.com/paper/2303.18178/) (2023)
- [A Survey of Privacy Threats and Defense in Vertical Federated Learning: From Model Life Cycle Perspective](https://mlsanity.com/paper/2402.03688/) (2024)
- [VFed-SSD: Towards Practical Vertical Federated Advertising](https://mlsanity.com/paper/2205.15987/) (2022)
- [Starlit: Privacy-Preserving Federated Learning to Enhance Financial Fraud Detection](https://mlsanity.com/paper/2401.10765/) (2024)
- [Decoupled Vertical Federated Learning for Practical Training on Vertically Partitioned Data](https://mlsanity.com/paper/2403.03871/) (2024)
- [Survey of Privacy Threats and Countermeasures in Federated Learning](https://mlsanity.com/paper/2402.00342/) (2024)
- [Sherpa.ai Privacy-Preserving Multi-Party Entity Alignment without Intersection Disclosure for Noisy Identifiers](https://mlsanity.com/paper/2604.19219/) (2026)
- [Practical Anonymous Two-Party Gradient Boosting Decision Tree](https://mlsanity.com/paper/2605.26903/) (2026)

## Abstract (arXiv)

Vertical Federated Learning (vFL) allows multiple parties that own different attributes (e.g. features and labels) of the same data entity (e.g. a person) to jointly train a model. To prepare the training data, vFL needs to identify the common data entities shared by all parties. It is usually achieved by Private Set Intersection (PSI) which identifies the intersection of training samples from all parties by using personal identifiable information (e.g. email) as sample IDs to align data instances. As a result, PSI would make sample IDs of the intersection visible to all parties, and therefore each party can know that the data entities shown in the intersection also appear in the other parties, i.e. intersection membership. However, in many real-world privacy-sensitive organizations, e.g. banks and hospitals, revealing membership of their data entities is prohibited. In this paper, we propose a vFL framework based on Private Set Union (PSU) that allows each party to keep sensitive membership information to itself. Instead of identifying the intersection of all training samples, our PSU protocol generates the union of samples as training instances. In addition, we propose strategies to generate synthetic features and labels to handle samples that belong to the union but not the intersection. Through extensive experiments on two real-world datasets, we show our framework can protect the privacy of the intersection membership while maintaining the model utility.