Federated Binary Matrix Factorization using Proximal Optimization
This work addresses the need for privacy-preserving binary data analysis in fields like life sciences and recommendation systems, offering an incremental improvement by adapting existing BMF methods to a federated setting.
The paper tackles the problem of performing Boolean matrix factorization on distributed binary data while preserving privacy, by proposing a federated learning approach with a proximal optimization method that shares only relaxed component matrices. The result is a federated algorithm that outperforms existing federation schemes in quality and efficacy on real-world and synthetic datasets, with demonstrated convergence and differential privacy guarantees.
Identifying informative components in binary data is an essential task in many research areas, including life sciences, social sciences, and recommendation systems. Boolean matrix factorization (BMF) is a family of methods that performs this task by efficiently factorizing the data. In real-world settings, the data is often distributed across stakeholders and required to stay private, prohibiting the straightforward application of BMF. To adapt BMF to this context, we approach the problem from a federated-learning perspective, while building on a state-of-the-art continuous binary matrix factorization relaxation to BMF that enables efficient gradient-based optimization. We propose to only share the relaxed component matrices, which are aggregated centrally using a proximal operator that regularizes for binary outcomes. We show the convergence of our federated proximal gradient descent algorithm and provide differential privacy guarantees. Our extensive empirical evaluation demonstrates that our algorithm outperforms, in terms of quality and efficacy, federation schemes of state-of-the-art BMF methods on a diverse set of real-world and synthetic data.