We consider the challenge of estimating treatment effects from observational data; and point out that, in general, only some factors based on the observed covariates X contribute to selection of the treatment T , and only some to determining the outcomes Y . We model this by considering three underlying sources of { X, T, Y } and show that explicitly modeling these sources offers great insight to guide designing models that better handle selection bias. This paper is an attempt to conceptualize this line of thought and provide a path to explore it further. In this work, we propose an algorithm to (1) identify disentangled representations of the above-mentioned underlying factors from any given observational dataset D and (2) leverage this knowledge to reduce, as well as account for, the negative impact of selection bias on estimating the treatment effects from D. Our empirical results show that the proposed method (i) achieves state-of-the-art performance in both individual and population based evaluation measures and (ii) is highly robust under various data generating scenarios.
Summary:
   The authors consider the problem of estimating average treatment effects when observed X and treatment T causes Y. Observational data for X,T,Y is available and strong ignorability is assumed. Previous work (Shalit et al 2017) introduced learning a representation that is invariant in distribution across treatment and control groups and using that with treatment to estimate Y. However, authors point out that this representation being forced to be invariant still does not drive the selection bias to zero. A follow up work (Hassanpour and Greiner 2019) - corrects for this by using additional importance weighting that estimates the treatment selection bias given the learnt representation. However, the authors point out even this is not complete in general, as X could be determined by three latent factors, one that is the actual confounder between treatment and outcome and the other that affects only the outcome and the other that affects only the treatment. Therefore, the authors propose to have three representations and enforce independence between representation that solely determines outcome and the treatment and make other appropriate terms depend on the respective latent factors. This gives a modified objective with respect to these two prior works.
The authors implement optimize this joint system on synthetic and real world datasets. They show that they outperform all these previous works because of explicitly accounting for confounder, latent factors that solely control only outcome and treatment assignment respectively. 
Pros:
  This paper directly addresses the problems due to Shalit 2017 that are still left open. The experimental results seems convincing on standard benchmarks. 
I vote for accepting the paper. I don't have many concerns about this paper.
Cons:
  - I have one question for the authors - if T and Y(0),Y(1) are independent given X is assumed, then how are we sure that the composite representations (of the three latent factors) are going to necessarily satisfy ignorability provably ?? I guess this cannot be formally established. It would be great for the authors to comment on this.