High Dimensional Causal Inference with Variational Backdoor Adjustment
This addresses a bottleneck in causal inference for domains like medicine where variables are high-dimensional, representing an incremental advance by applying known techniques to new high-dimensional scenarios.
The paper tackles the problem of high-dimensional treatments and confounders in causal inference by proposing a generative modeling approach for backdoor adjustment, achieving estimation of interventional likelihood in settings like semi-synthetic X-ray medical data.
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.