Off-policy causal estimation in social network studies

Music City Center 

In the setting of no interference between experimental units, wherein the treatment of one unit cannot influence the outcome of another, the average treatment effect is the main causal estimand of interest and its value does not depend on the experiment design policy. However, in social networks where units are connected, this assumption is often incorrect and its relaxation yields a profusion of causal estimands whose value depends on the design. Say, the expected average direct and indirect effects respectively capture the average effect of flipping the treatment of a unit on its own and on another unit's outcome, marginalized over the experiment design. The nontrivial dependence of these estimands on the design implies an off-policy estimation challenge: can we estimate arbitrary causal estimands under a design policy different from the one the data were collected under? Considering causal estimands as Boolean functions, we describe unbiased estimators for off-policy estimation in full generality and show precisely how interference assumptions interplay with the sparsity of the interference network for a given variance of these estimators. For any causal estimator, including the proposed off-policy estimator(s), we show that its variance is generally nonidentifiable but there are unbiased estimators for a conservative bound on the variance and the bound can be made tighter when one restricts interference. Notably, considering causal estimands as Boolean functions allows us to view the profusion of causal estimands as providing higher-order corrections to a Taylor expansion of the expected average outcome curve around the actual design policy, which presents promising directions for optimal design to estimate the complete off-policy curve.

social networks

network interference

off-policy estimation

experiment design