  Unobserved confounding is a major hurdle for causal inference from
observational data. Confounders---the variables that affect both the causes and
the outcome---induce spurious non-causal correlations between the two. Wang &
Blei (2018) lower this hurdle with "the blessings of multiple causes," where
the correlation structure of multiple causes provides indirect evidence for
unobserved confounding. They leverage these blessings with an algorithm, called
the deconfounder, that uses probabilistic factor models to correct for the
confounders. In this paper, we take a causal graphical view of the
deconfounder. In a graph that encodes shared confounding, we show how the
multiplicity of causes can help identify intervention distributions. We then
justify the deconfounder, showing that it makes valid inferences of the
intervention. Finally, we expand the class of graphs, and its theory, to those
that include other confounders and selection variables. Our results expand the
theory in Wang & Blei (2018), justify the deconfounder for causal graphs, and
extend the settings where it can be used.
