Identifiable Signed Causal Learning via Latent Stochastic Differential Equations for Inferring Brain Dynamic Effective Connectivity

Yiding Wang, Chen Qiao

Understanding how brain regions interact to support cognitive tasks requires characterizing directed causal influences among them, known as effective connectivity (EC). As inter-regional coupling changes over time, a dynamic EC (dEC) estimate is required to track this temporal variation. Existing dEC learning methods typically lack a causal rationality guarantee or an identifiability analysis, and output unsigned connectivity that cannot distinguish excitatory from inhibitory influences, which limits further study of brain mechanisms. We propose ISCL, a latent stochastic differential equation framework that derives dEC from latent dynamics through a causal influence operator defined in observation space. As established by a rationality theorem, the operator captures a directed interventional response at each brain state, and under invariance assumptions the operator is identifiable from data, with its signed output separating excitatory from inhibitory influences. On synthetic benchmarks, \model recovers the causal structure on Lorenz96 and achieves the lowest mean structural Hamming distance among compared methods on NetSim, while preserving signed influence structures that…