High Dimensional Causal Inference with Variational Backdoor Adjustment
Daniel Israel Aditya Grover Guy Van den Broeck
Backdoor adjustment is a technique in causal inference for estimating
interventional quantities from purely observational data. For example, in
medical settings, backdoor adjustment can be used to control for confounding
and estimate the effectiveness of a treatment. However, high dimensional
treatments and confounders pose a series of potential pitfalls: tractability,
identifiability, optimization. In this work, we take a generative modeling
approach to backdoor adjustment for high dimensional treatments and
confounders. We cast backdoor adjustment as an optimization problem in
variational inference without reliance on proxy variables and hidden
confounders. Empirically, our method is able to estimate interventional
likelihood in a variety of high dimensional settings, including semi-synthetic
X-ray medical data. To the best of our knowledge, this is the first application
of backdoor adjustment in which all the relevant variables are high
dimensional.