Comment on "Blessings of Multiple Causes"

TL;DR

This comment critically examines the deconfounder method proposed by Wang and Blei, arguing that its core premise is incorrect and that it cannot reliably control for unmeasured confounding without additional assumptions.

Contribution

It provides a critical analysis showing that the deconfounder’s key assumption about conditional independence and confounding control is invalid.

Findings

The deconfounder premise is incorrect.

Methods relying solely on observed data cannot verify ignorability.

Additional assumptions are necessary for valid causal inference.

Abstract

(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.