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.

翻译：后门调整是因果推断中的一种技术，用于从纯观测数据中估计干预量。例如在医疗场景中，后门调整可用于控制混杂因素并评估治疗效果。然而，高维度的处理变量和混杂因素会引发一系列潜在问题：可计算性、可识别性、优化困难。本研究针对高维处理变量与混杂因素，采用生成建模方法实现后门调整。我们将后门调整转化为变分推断中的优化问题，无需依赖代理变量和隐藏混杂因素。实验表明，本方法能够在多种高维场景下（包括半合成X光医学数据）有效估计干预似然。据我们所知，这是首次在全部相关变量均为高维的情况下应用后门调整。