Statistical Inference from Networked Data

Statistical estimation has largely focused on settings where observations are independent. This assumption is, however, too strong. In many applications, observations are collected on nodes of a network, or some spatial or temporal domain, and are dependent. Examples abound in financial and meteorological applications, and dependencies naturally arise in social networks through peer effects. We study statistical estimation and causal inference problems in settings where responses at the nodes of a network are not independent conditioning on the nodes’ features and their treatment but are dependent with each other. We model their dependencies through a Markov Random Field with a log-density that captures individual effects, treatment effects and peer effects. Importantly, we allow dependencies to be substantial, i.e do not assume that the Markov Random Field is in high temperature. Our model generalizes standard estimation tasks with independent observations which can be obtained from our model by setting the temperature to infinity. We provide algorithms and statistically efficient estimation methods using novel results for estimating the parameters (i.e. external fields and interaction strengths) of Ising models from a single sample.