A Free Lunch with Influence Functions? An Empirical Evaluation of Influence Functions for Average Treatment Effect Estimation

Matthew James Vowels, Sina Akbari, Necati Cihan Camgöz, Richard Bowden

Abstract: The applications of causal inference may be life-critical, including the evaluation of vaccinations, medicine, and social policy. However, when undertaking estimation for causal inference, practitioners rarely have access to what might be called `ground-truth' in a supervised learning setting, meaning the chosen estimation methods cannot be evaluated and must be assumed to be reliable. It is therefore crucial that we have a good understanding of the performance consistency of typical methods available to practitioners. In this work we provide a comprehensive evaluation of recent semiparametric methods (including neural network approaches) for average treatment effect estimation. Such methods have been proposed as a means to derive unbiased causal effect estimates and statistically valid confidence intervals, even when using otherwise non-parametric, data-adaptive machine learning techniques. We also propose a new estimator `MultiNet', and a variation on the semiparametric update step `MultiStep', which we evaluate alongside existing approaches. The performance of both semiparametric and `regular' methods are found to be dataset dependent, indicating an interaction between the methods used, the sample size, and nature of the data generating process. Our experiments highlight the need for practitioners to check the consistency of their findings, potentially by undertaking multiple analyses with different combinations of estimators.