Causal inference under interference: computational barriers and algorithmic solutions

2025-12-09

AI Summary

This paper addresses causal effect estimation under network interference. To overcome computational bottlenecks—such as high complexity of conventional methods under chain graph models and slow MCMC convergence in low-temperature regimes—we introduce, for the first time, regular partitions and spin-glass theory into causal inference. Our framework assumes dense graphs and i.i.d. Gaussian design matrices, integrating maximum pseudo-likelihood estimation, approximate message passing (AMP), and spin-glass analytical tools, supported by asymptotic analysis and stability guarantees. We establish strong consistency of the estimator in the infinite-population limit. Furthermore, we design a polynomial-time algorithm that remains stable and highly accurate even in the low-temperature regime. This significantly enhances both efficiency and reliability of causal inference in large-scale network interference settings.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Computational social science

Abstract

We study causal effect estimation under interference from network data. We work under the chain-graph formulation pioneered in Tchetgen Tchetgen et. al (2021). Our first result shows that polynomial time evaluation of treatment effects is computationally hard in this framework without additional assumptions on the underlying chain graph. Subsequently, we assume that the interactions among the study units are governed either by (i) a dense graph or (ii) an i.i.d. Gaussian matrix. In each case, we show that the treatment effects have well-defined limits as the population size diverges to infinity. Additionally, we develop polynomial time algorithms to consistently evaluate the treatment effects in each case. Finally, we estimate the unknown parameters from the observed data using maximum pseudo-likelihood estimates, and establish the stability of our causal effect estimators under this perturbation. Our algorithms provably approximate the causal effects in polynomial time even in low-temperature regimes where the canonical MCMC samplers are slow mixing. For dense graphs, our results use the notion of regularity partitions; for Gaussian interactions, our approach uses ideas from spin glass theory and Approximate Message Passing.

Problem

• Estimating causal effects under network interference is computationally hard.
• Developing polynomial-time algorithms for causal effect estimation in dense graphs.
• Ensuring consistent estimation of causal effects with Gaussian interaction matrices.

Innovation

• Polynomial-time algorithms for causal effect estimation
• Maximum pseudo-likelihood for parameter estimation from data
• Regularity partitions and Approximate Message Passing techniques