Differentially Private and Federated Structure Learning in Bayesian Networks

TL;DR

This paper introduces Fed-Sparse-BNSL, a federated method for learning Bayesian network structures that balances privacy, communication efficiency, and accurate structure estimation.

Contribution

It combines differential privacy with greedy edge updates to efficiently learn Bayesian networks in a decentralized setting.

Findings

Achieves utility close to non-private methods.

Offers stronger privacy guarantees.

Reduces communication costs significantly.

Abstract

Learning the structure of a Bayesian network from decentralized data poses two major challenges: (i) ensuring rigorous privacy guarantees for participants, and (ii) avoiding communication costs that scale poorly with dimensionality. In this work, we introduce Fed-Sparse-BNSL, a novel federated method for learning linear Gaussian Bayesian network structures that addresses both challenges. By combining differential privacy with greedy updates that target only a few relevant edges per participant, Fed-Sparse-BNSL efficiently uses the privacy budget while keeping communication costs low. Our careful algorithmic design preserves model identifiability and enables accurate structure estimation. Experiments on synthetic and real datasets demonstrate that Fed-Sparse-BNSL achieves utility close to non-private baselines while offering substantially stronger privacy and communication efficiency.