Statistics Seminar

Title: Low-rank models in statistical network analysis

Abstract: Networks are ubiquitous in the sciences. As a result, a fundamental goal of statistical network analysis is to develop network analogues of classical statistical procedures. Recent years have seen a surge of interest in causal inference, and the widespread presence of network data in the social sciences necessitates network analogues of causal inference methods. Unfortunately, the complicated dependency structure of network data presents an obstacle to many popular causal inference procedures. In this talk, we consider the task of mediation analysis for network data. We present a model in which mediation occurs in a latent node embedding space. Under this model, node-level interventions have causal effects on nodal outcomes, and these effects can be partitioned into a direct effect independent of the network, and an indirect effect, which is induced by homophily. To estimate these network-mediated effects, we embed nodes into a low-dimensional Euclidean space. We then use these embeddings to fit two ordinary least squares models: (1) an outcome model that characterizes how nodal outcomes vary with nodal treatment, controls, and position in latent space; and (2) a mediator model that characterizes how latent positions vary with nodal treatment and controls. We prove that the estimated coefficients are asymptotically normal about the true coefficients under an extension of the random dot product graph, a widely-used latent space network model. Further, we show that these coefficients can be used in product-of-coefficients estimators for causal inference. If time allows, we will also discuss extensions of this work, and related work I have done since joining UW-Madison.