Estimating Direct Effects under Interference: A Spectral Experimental Design

Abstract:
From clinical trials to corporate strategy, randomized experiments are a reliable methodological tool for estimating causal effects. In recent years, there has been a growing interest in causal inference under interference, where treatment given to one unit can affect outcomes of other units. While the literature on interference has focused primarily on unbiased and consistent estimation, designing randomized network experiments to insure tight rates of convergence is relatively under-explored for many settings.

In this talk, we study the problem of direct effect estimation under interference. Here, the interference between experimental subjects is captured by a network and the experimenter seeks to estimate the direct effect, which is the difference between the outcomes when (i) a unit is treated and its neighbors receive control and (ii) the unit and its neighbors receive control. We present a new experimental design under which the normalized variance of a Horvitz—Thompson style estimator is bounded as $n * Var <= O( \lambda )$, where $\lambda$ is the largest eigenvalue of the adjacency matrix of the graph. This experimental approach achieves consistency when $\lambda = o(n)$, which is a much weaker condition on the network than most similar approaches which require the maximum degree to be bounded. This experimental design, which relies on insights from spectral graph theory, establishes the best known rate of convergence for this problem; in fact, we offer lower bounds for any experimental design, which match our rates in certain instances. In addition, we present a variance estimator and CLT which facilitate the construction of asymptotically valid confidence intervals. Finally, simulations using data from a real network experiment corroborate the theoretical claims. Joint work with Vardis Kandiros, Charis Pipis, and Costis Daskalakis.

Bio:
Christopher Harshaw is an Assistant Professor in the Statistics Department at Columbia University, with research that lies at the interface of causal inference and algorithm design.
His recent work develops algorithmic tools for improving the design and analysis of randomized experiments. He has focused on experiments with interference as well as sequential experiments. More broadly, he is interested in the intersection of computation and statistics.  He obtained his PhD in Computer Science from Yale, and has been a FODSI postdoctoral fellow and a postdoctoral fellow at the Simons Institute in the Causality program.