Estimating Treatment Effects with Independent Component Analysis
This work provides a novel method for causal inference researchers, bridging two previously independent fields to improve estimation in partially linear regression settings.
The paper tackles the problem of estimating treatment effects in causal inference by connecting it to Independent Component Analysis (ICA), showing that linear ICA can accurately estimate multiple treatment effects even with Gaussian confounders or nonlinear nuisance.
The field of causal inference has developed a variety of methods to accurately estimate treatment effects in the presence of nuisance. Meanwhile, the field of identifiability theory has developed methods like Independent Component Analysis (ICA) to identify latent sources and mixing weights from data. While these two research communities have developed largely independently, they aim to achieve similar goals: the accurate and sample-efficient estimation of model parameters. In the partially linear regression (PLR) setting, Mackey et al. (2018) recently found that estimation consistency can be improved with non-Gaussian treatment noise. Non-Gaussianity is also a crucial assumption for identifying latent factors in ICA. We provide the first theoretical and empirical insights into this connection, showing that ICA can be used for causal effect estimation in the PLR model. Surprisingly, we find that linear ICA can accurately estimate multiple treatment effects even in the presence of Gaussian confounders or nonlinear nuisance.