On Evolution-Based Models for Experimentation Under Interference
Sadegh Shirani, Mohsen Bayati
TL;DR
This paper develops an evolution-based paradigm for causal effect estimation under network interference, arguing that identifying population-level effects can be achieved by modeling how outcomes evolve across observation rounds rather than reconstructing the full interference network. Central to the approach is the experimental state evolution (ESE) framework, which uses exposure mappings to relate treatments to outcome dynamics via low-dimensional, recursive mappings $f_t$. The authors connect ESE to a distributional analogue of difference‑in‑difference, showing how randomized treatment induces implicit sampling of hidden interference channels and enables learning about heterogeneous spillovers; they also instantiate the method with causal message passing (CMP) in dense networks and extend to structured interference such as influencer networks. They provide an extended treatment of partially known interference via stable decompositions and discuss limitations, including cases with strong temporal trends or endogenous interference that threaten identification. Overall, the framework offers principled tools for learning population-level causal effects from evolving outcome data without full network reconstruction, with practical implications for experiments in socially and technologically interconnected systems.
Abstract
Causal effect estimation in networked systems is central to data-driven decision making. In such settings, interventions on one unit can spill over to others, and in complex physical or social systems, the interaction pathways driving these interference structures remain largely unobserved. We argue that for identifying population-level causal effects, it is not necessary to recover the exact network structure; instead, it suffices to characterize how those interactions contribute to the evolution of outcomes. Building on this principle, we study an evolution-based approach that investigates how outcomes change across observation rounds in response to interventions, hence compensating for missing network information. Using an exposure-mapping perspective, we give an axiomatic characterization of when the empirical distribution of outcomes follows a low-dimensional recursive equation, and identify minimal structural conditions under which such evolution mappings exist. We frame this as a distributional counterpart to difference-in-differences. Rather than assuming parallel paths for individual units, it exploits parallel evolution patterns across treatment scenarios to estimate counterfactual trajectories. A key insight is that treatment randomization plays a role beyond eliminating latent confounding; it induces an implicit sampling from hidden interference channels, enabling consistent learning about heterogeneous spillover effects. We highlight causal message passing as an instantiation of this method in dense networks while extending to more general interference structures, including influencer networks where a small set of units drives most spillovers. Finally, we discuss the limits of this approach, showing that strong temporal trends or endogenous interference can undermine identification.