Paper:
Causal Effect Inference with Deep Latent-Variable Models
Learning individual-level causal effects from observational data, such as inferring the most effective medication for a specific patient, is a problem of growing importance for policy makers. The most important aspect of inferring causal effects from observational data is the handling of confounders, factors that affect both an intervention and its outcome. A carefully designed observational study attempts to measure all important confounders. However, even if one does not have direct access to all confounders, there may exist noisy and uncertain measurement of proxies for confounders. We build on recent advances in latent variable modeling to simultaneously estimate the unknown latent space summarizing the confounders and the causal effect. Our method is based on Variational Autoencoders (VAE) which follow the causal structure of inference with proxies. We show our method is significantly more robust than existing methods, and matches the state-of-the-art on previous benchmarks focused on individual treatment effects.

Review:
-	The authors utilized Variational Autoencoders (VAE) in order to estimate the individual treatment effect (ITE) and the average treatment effect (ATE) for the causal model in Figure 1. However, five other causal diagrams can also be considered with confounder proxies (see Figure 1 in [Miao et al., 2016]). It would be interesting to check whether the proposed method can be applied to all these causal diagrams or there are some limitations.
-	Please give some justifications why parametrizing the probability distributions in the form of Equations (2-4) would be a good choice for estimating ITE and ATE. For instance, why covariates of x_i are independent given z_i? Is it restricting the expressive power of this method?
-	In your method, do we need to know the dimension of latent variable z? For instance, in Experimental Results section, it is assumed that z is a 20-dimensional variable. Does the performance degrade if D_z is not adjusted correctly?
-	In Table 1, is there any good reason that BNN has a better performance than CEVAE?
-	When z is categorical, it seems that we can just estimate p(x_i|z_i) by your method and then estimate ITE and ATE from the results in [Kuroki and Pearl, 2011]. It would be interesting to compare the performance of this method with CAVAE?
-	Figure 3 shows that model misspecification may increase the sample complexity. It would be interesting to characterize the sample complexity overhead from model misspecification.
-	Under some conditions, can we have a theoretical guarantee that CEVAE gives a good approximation of ITE or ATE? 
-	Some typos:
o	Line 126: p(Z,Xt,y)->p(Z,X,t,y)
o	In equation (2), please define D_x and D_z.