Statistics and Data Seminar

Abstract: Causal inference for observational network data is an area of active interest, owing to the ubiquity of network data in the social sciences. 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 a sub-gamma generalization of the random dot product graph, a widely-used latent space model. Further, we show that these coefficients can be used in product-of-coefficients estimators for causal inference. Our method is easy to implement, scales to networks with millions of edges, and can be extended to accommodate a variety of structured data.

Bio: Keith Levin is an Assistant Professor in the Department of Statistics at University of Wisconsin—Madison, where his research focuses on statistical network analysis, with applications to neuroscience. Keith earned degrees in linguistics and psychology from Northeastern University and completed his Ph.D. in Computer Science at Johns Hopkins University. Prior to joining UW—Madison, he was a postdoctoral research fellow in the Department of Statistics at University of Michigan.