[otterk10]

Thanks! Yes, the concerns you mentioned would also apply to PCA. What we've actually done to help alleviate this is a union of components from y-aware[1] and normal PCA to capture variables that are correlated to both the dependent variables and (hopefully) most of the treatment variables. This seems similar to the double selection approach you mention - the difference being that since we are trying to run this at scale for 1000s of treatment variables, running a feature selection with each of the 1000 treatment variables as the dependent variable isn't super feasible, so the normal PCA acts as proxy for this part of the double selection.

Regardless, we're never going to completely remove omitted variable bias, as we're never going to capture 100% of relevant variables. One way we monitor our model's bias is by looking at the error distribution between users in the treatment vs control. If these aren't similar, there's too much bias in our estimate of the treatment effect, so we wouldn't want to serve an estimate of the treatment effect for this variable to our customers.

The current product is in beta and we're working with some of our current customers to try to re-create our results with A/B tests. I'm hoping that by our GA release in the fall we'll have some case studies with specific examples!

[1] http://www.win-vector.com/blog/2016/05/pcr_part2_yaware/