Sadegh Shirani

Mohamad Kazem Shirani Faradonbeh, Sadegh Shirani, Mohsen Bayati

Linear diffusion processes serve as canonical continuous-time models for dynamic decision-making under uncertainty. These systems evolve according to drift matrices that specify the instantaneous rates of change in the expected system state, while also experiencing continuous random disturbances modeled by Brownian noise. For instance, in medical applications such as artificial pancreas systems, the drift matrices represent the internal dynamics of glucose concentrations. Classical results in stochastic control provide optimal policies under perfect knowledge of the drift matrices. However, practical decision-making scenarios typically feature uncertainty about the drift; in medical contexts, such parameters are patient-specific and unknown, requiring adaptive policies for efficiently learning the drift matrices while ensuring system stability and optimal performance. We study the Thompson sampling (TS) algorithm for decision-making in linear diffusion processes with unknown drift matrices. For this algorithm that designs control policies as if samples from a posterior belief about the parameters fully coincide with the unknown truth, we establish efficiency. That is, Thompson sampling learns optimal control actions fast, incurring only a square-root of time regret, and also learns to stabilize the system in a short time period. To our knowledge, this is the first such result for TS in a diffusion process control problem. Moreover, our empirical simulations in three settings that involve blood-glucose and flight control demonstrate that TS significantly improves regret, compared to the state-of-the-art algorithms, suggesting it explores in a more guarded fashion. Our theoretical analysis includes characterization of a certain optimality manifold that relates the geometry of the drift matrices to the optimal control of the diffusion process, among others.

Sadegh Shirani, Mohsen Bayati

Online social networks have transformed the ways in which political mobilization messages are disseminated, raising new questions about how peer influence operates at scale. Building on the landmark 61-million-person Facebook experiment \citep{bond201261}, we develop an agent-based simulation framework that integrates real U.S. Census demographic distributions, authentic Twitter network topology, and heterogeneous large language model (LLM) agents to examine the effect of mobilization messages on voter turnout. Each simulated agent is assigned demographic attributes, a personal political stance, and an LLM variant (\texttt{GPT-4.1}, \texttt{GPT-4.1-Mini}, or \texttt{GPT-4.1-Nano}) reflecting its political sophistication. Agents interact over realistic social network structures, receiving personalized feeds and dynamically updating their engagement behaviors and voting intentions. Experimental conditions replicate the informational and social mobilization treatments of the original Facebook study. Across scenarios, the simulator reproduces qualitative patterns observed in field experiments, including stronger mobilization effects under social message treatments and measurable peer spillovers. Our framework provides a controlled, reproducible environment for testing counterfactual designs and sensitivity analyses in political mobilization research, offering a bridge between high-validity field experiments and flexible computational modeling.\footnote{Code and data available at https://github.com/CausalMP/LLM-SocioPol}

William Overman, Sadegh Shirani, Mohsen Bayati

We study experiments on interacting populations of humans and AI agents, where both unit types and the interaction network remain unobserved. Although causal effects propagate throughout the system, the goal is to estimate effects on humans. Examples include online platforms where human users interact alongside AI-driven accounts. We assume a human-AI prior that gives each unit a probability of being human. While humans cannot be distinguished at the unit level, the prior allows us to compute the average human composition within large subpopulations. We then model outcome dynamics through a causal message passing (CMP) framework and analyze sample-mean outcomes across subpopulations. We show that by constructing subpopulations that vary in expected human composition and treatment exposure, one can consistently recover human-specific causal effects. Our results characterize when distributional knowledge of population composition (without observing unit types or the interaction network) is sufficient for identification. We validate the approach on a simulated human-AI platform driven by behaviorally differentiated LLM agents. Together, these results provide a theoretical and practical framework for experimentation in emerging human-AI systems.

Sadegh Shirani, Mohsen Bayati

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.

Mohsen Bayati, Yuwei Luo, William Overman et al.

Accurate estimation of treatment effects is essential for decision-making across various scientific fields. This task, however, becomes challenging in areas like social sciences and online marketplaces, where treating one experimental unit can influence outcomes for others through direct or indirect interactions. Such interference can lead to biased treatment effect estimates, particularly when the structure of these interactions is unknown. We address this challenge by introducing a new class of estimators based on causal message-passing, specifically designed for settings with pervasive, unknown interference. Our estimator draws on information from the sample mean and variance of unit outcomes and treatments over time, enabling efficient use of observed data to estimate the evolution of the system state. Concretely, we construct non-linear features from the moments of unit outcomes and treatments and then learn a function that maps these features to future mean and variance of unit outcomes. This allows for the estimation of the treatment effect over time. Extensive simulations across multiple domains, using synthetic and real network data, demonstrate the efficacy of our approach in estimating total treatment effect dynamics, even in cases where interference exhibits non-monotonic behavior in the probability of treatment.

Sadegh Shirani, Yuwei Luo, William Overman et al.

Randomized experiments have become a cornerstone of evidence-based decision-making in contexts ranging from online platforms to public health. However, in experimental settings with network interference, a unit's treatment can influence outcomes of other units, challenging both causal effect estimation and its validation. Classic validation approaches fail as outcomes are only observable under a single treatment scenario and exhibit complex correlation patterns due to interference. To address these challenges, we introduce a framework that facilitates the use of machine learning tools for both estimation and validation in causal inference. Central to our approach is the new distribution-preserving network bootstrap, a theoretically-grounded technique that generates multiple statistically-valid subpopulations from a single experiment's data. This amplification of experimental samples enables our second contribution: a counterfactual cross-validation procedure. This procedure adapts the principles of model validation to the unique constraints of causal settings, providing a rigorous, data-driven method for selecting and evaluating estimators. We extend recent causal message-passing developments by incorporating heterogeneous unit-level characteristics and varying local interactions, ensuring reliable finite-sample performance through non-asymptotic analysis. Additionally, we develop and publicly release a comprehensive benchmark toolbox featuring diverse experimental environments, from networks of interacting AI agents to ride-sharing applications. These environments provide known ground truth values while maintaining realistic complexities, enabling systematic evaluation of causal inference methods. Extensive testing across these environments demonstrates our method's robustness to diverse forms of network interference.