  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.
