  (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.
