We will discuss causal effect estimation from observational data under interference. We adopt the chain-graph formalism of Tchetgen-Tchetgen et. al. (2021). Under “mean-field” assumptions on the interaction networks, we will introduce novel algorithms for causal effect estimation using Naive Mean Field approximations and Approximate Message Passing. Our algorithms are provablyconsistent under a “high-temperature” assumption on the underlying model.Finally, we will discuss parameter estimation in these models using maximum pseudo-likelihood, and establish the consistency of the downstream plug-in estimator. Based on joint work with Sohom Bhattacharya (U Florida).