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Counterexamples to "The Blessings of Multiple Causes" by Wang and Blei

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arxiv 2001.06555 v3 pith:PYI2ABOV submitted 2020-01-17 stat.ME stat.ML

Elizabeth L. Ogburn , Ilya Shpitser , Eric J. Tchetgen Tchetgen This is my paper · ORCID
classification stat.MEstat.ML
keywords bleiindependencewangdeconfounderattemptingblessingscausesconditional
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This note has been updated (April, 2020) to respond to "Towards Clarifying the Theory of the Deconfounder" by Yixin Wang, David M. Blei (arXiv:2003.04948). This original note, posted in January, 2020, is meant to complement our previous comment on "The Blessings of Multiple Causes" by Wang and Blei (2019). We provide a more succinct and transparent explanation of the fact that the deconfounder does not control for multi-cause confounding. The argument given in Wang and Blei (2019) makes two mistakes: (1) attempting to infer independence conditional on one variable from independence conditional on a different, unrelated variable, and (2) attempting to infer joint independence from pairwise independence. We give two simple counterexamples to the deconfounder claim.

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Cited by 2 Pith papers

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    After shared-subspace compression, the difference of treatment-arm proxy quotient operators is similar to the diagonal of latent treatment effects, whose eigenvalues and lifted eigenvectors recover the full mixture.

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    Causal effects are identifiable for categorical unobserved confounders via mixture learning and tensor decomposition, yielding consistent estimators with non-asymptotic guarantees.

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