Title: VFedCD: Causal Discovery under Vertical Federated Scenario
Primary area: causal reasoning
Keywords: Causal Discovery; Vertical Federated Learning; Homomorphic Encryption; Secure Multi-party Computation

Abstract: Causal discovery seeks to identify causal relationships among attributes, typically represented as directed acyclic graphs (DAGs) where vertices denote attributes and edges denote direct causal effects. Existing methods struggle in vertically federated scenarios. In these settings, data is partitioned across parties that hold disjoint attributes, and strict privacy constraints prevent centralized aggregation, leaving vertical federated causal discovery underexplored.
We propose VFedCD, the first framework for causal discovery in vertical federated settings. VFedCD models causal mechanisms with a shallow-encoder, deep-decoder design. Each party uses a shallow encoder to transform its local attributes into privacy-preserving features for all parties, and then a deep decoder to aggregate received features and predict local attributes, implicitly capturing causal dependencies. To avoid cycles or overly dense graph structures, a Centralized Topology Validator (CTV) extracts partial causal structures from party encoders, aggregates them into a global graph and enforces structural constraints. In addition, a Secure Dispatch Protocol (SDP) is designed to enhance the security of feature exchange and gradient propagation by redesigning encoding and aggregation with semi-homomorphic encryption and secret sharing.
Experiments on synthetic and real-world datasets with artificial vertical partitioning show that VFedCD matches the accuracy of centralized methods while guaranteeing privacy.