Neighborhood Adaptive Estimators for Causal Inference under Network Interference

Information Systems and Operations Management 

Intervenant: Alex Belloni (Duke U, Fuqua)

Salle Bernard Ramanantsoa

Abstract

Estimating causal effects has become an integral part of most applied fields. Solving these modern causal questions requires tackling violations of many classical causal assumptions. In this work we consider the violation of the classical no-interference assumption, meaning that the treatment of one individuals might affect the outcomes of another. To make interference tractable, we consider a known network that describes how interference may travel. However, unlike previous work in this area, the radius (and intensity) of the interference experienced by a unit is unknown and can depend on different (local) sub-networks and the assigned treatments to these corresponding units.

We study estimators for the average direct treatment effect on the treated in such a setting under additive treatment effects. Although we cover more general cases, our main result pertains to the case that there is selection on the treatment assignment but those are independent across units given observables. We address several challenges steaming from the data-driven creation of the interference patterns (i.e. feature engineering) and the network dependence. In addition to rates of convergence, under mild regularity conditions, we show that one of the proposed estimators is asymptotically normal and unbiased. The proposed estimator builds upon a Lepski-like procedure that searches over the possible relevant radii for each (local) treatment assignment patterns. In contrast to previous work, the proposed aims to approximate the relevant network interference patterns that leads to good estimates of the interference. We establish oracle inequalities and corresponding adaptive rates for the estimation of the interference function.

Paper: https://arxiv.org/abs/2212.03683