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

arXiv: https://arxiv.org/abs/2001.06555 · HTML: https://mlsanity.com/paper/2001.06555/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2020.

## Built on by (most cited first, 8 of 8)

- [Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders](https://mlsanity.com/paper/2303.02320/) (2023)
- [Why Do Probabilistic Clinical Models Fail To Transport Between Sites?](https://mlsanity.com/paper/2311.04787/) (2023)
- [Estimating Social Influence from Observational Data](https://mlsanity.com/paper/2204.01633/) (2022)
- [Two-way Deconfounder for Off-policy Evaluation in Causal Reinforcement Learning](https://mlsanity.com/paper/2412.05783/) (2024)
- [Synthetic Potential Outcomes and Causal Mixture Identifiability](https://mlsanity.com/paper/2405.19225/) (2024)
- [Causal Inference with Categorical Unobserved Confounder via Mixture Learning](https://mlsanity.com/paper/2605.19006/) (2026)
- [Substitute adjustment via recovery of latent variables](https://mlsanity.com/paper/2403.00202/) (2024)
- [The Spectral Structure of Latent Treatment Effects](https://mlsanity.com/paper/2607.10926/) (2026)

## Abstract (arXiv)

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.