Comment on "Blessings of Multiple Causes"
This is an incremental critique highlighting fundamental limitations in a specific causal inference method, relevant for researchers in statistics and machine learning.
The comment critiques the deconfounder method by arguing that its premise—that a variable making multiple causes conditionally independent controls for unmeasured confounding—is incorrect, as observed data alone cannot verify ignorability, and such methods generally do not offer weaker assumptions than standard causal inference approaches.
(This comment has been updated to respond to Wang and Blei's rejoinder [arXiv:1910.07320].) The premise of the deconfounder method proposed in "Blessings of Multiple Causes" by Wang and Blei [arXiv:1805.06826], namely that a variable that renders multiple causes conditionally independent also controls for unmeasured multi-cause confounding, is incorrect. This can be seen by noting that no fact about the observed data alone can be informative about ignorability, since ignorability is compatible with any observed data distribution. Methods to control for unmeasured confounding may be valid with additional assumptions in specific settings, but they cannot, in general, provide a checkable approach to causal inference, and they do not, in general, require weaker assumptions than the assumptions that are commonly used for causal inference. While this is outside the scope of this comment, we note that much recent work on applying ideas from latent variable modeling to causal inference problems suffers from similar issues.