Abstract: The estimation of causal effects is increasingly relevant in different applied fields. In this work we consider a causal inference problem in the presence of interference. Our focus is on observational studies where interference across units is governed by a known network interference. However, the radius (and intensity) of interference is unknown and can be dependent on the observed treatment assignments in the relevant subnetwork.  We study causal estimators for average direct treatment effect given the network interference. The proposed estimators build upon a Lepski-like procedure that searches over the possible relevant radius/assignment patterns. In the process we also obtain estimators for the radius of the interference that can be dependent on the treatment assignment of neighbors. Thus it is creating an adaptive estimation of the network interference structure. We establish oracle inequalities and corresponding adaptive rates for the direct average treatment effect estimator. The adaptive network interference can be defined over the labelled subgraphs themselves or on features of these recovering many assumptions previously used in the literature.  We present theoretical examples and numerical simulation that illustrate the performance of the proposed estimators.

Bio: Alexandre Belloni is the John D. Forsyth Professor of Business Administration and Statistical Science at Duke University, and is an Amazon Scholar at SCOT. He received his Ph.D. in Operations Research at MIT and a M.Sc. in Mathematical Economics from IMPA. He was an IBM Herman Goldstein Postdoctoral Fellowship at the IBM Thomas J. Watson Research Center. Professor Belloni’s research interests are on machine learning and statistics, mechanism design (e.g. contracts/auctions), optimization and on their applications. His works appeared at top journals in Economics, Operations Research, and Statistics. He serves as Associate Editor to Annals of Statistics, Management Science and as the Area Editor to Operations Research (Machine Learning and Data Science).