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Randomized experiments are a powerful methodology for data-driven evaluationof decisions or interventions. Yet, their validity may be undermined by networkinterference. This occurs when the treatment of one unit impacts not only itsoutcome but also that of connected units, biasing traditional treatment effectestimations. Our study introduces a new framework to accommodate complex andunknown network interference, moving beyond specialized models in the existingliterature. Our framework, which we term causal message-passing, is grounded ina high-dimensional approximate message passing methodology and is specificallytailored to experimental design settings with prevalent network interference.Utilizing causal message-passing, we present a practical algorithm forestimating the total treatment effect and demonstrate its efficacy in fournumerical scenarios, each with its unique interference structure.

Causal Message Passing: A Method for Experiments with Unknown and General Network Interference