Paper:
Representation Learning for Treatment Effect Estimation from Observational Data
Estimating individual treatment effect (ITE) is a challenging problem in causal inference, due to the missing counterfactuals and the selection bias. Existing ITE estimation methods mainly focus on balancing the distributions of control and treated groups, but ignore the local similarity information that provides meaningful constraints on the ITE estimation. In this paper, we propose a local similarity preserved individual treatment effect (SITE) estimation method based on deep representation learning. SITE preserves local similarity and balances data distributions simultaneously, by focusing on several hard samples in each mini-batch. Experimental results on synthetic and three real-world datasets demonstrate the advantages of the proposed SITE method, compared with the state-of-the-art ITE estimation methods.

Review:
# Summary  This paper proposes a method for estimating individual treatment effects. The basic approach is to propose a regression y_i = g(f(x_i), t_i) where f(x_i) is a learned representation of the covariates, and g predicts the response using this representation and the treatment. The main novelty is in the latent representation g(x_i). The given motivation is that points that are close in the covariate space should also be close in the representation space. This is achieved by adding two terms to the mini-batch loss function.   # Strengths  The problem is self evidently important, the idea is creative, and seems to work well under to an (apparently) broad battery of empirical tests.     # Weaknesses  I had trouble understanding this paper, but I'm not sure if that's due to the exposition or because it's a little ways outside my normal area of expertise. In particular, I don't immediately see the answer to:  1. When, if ever, is SITE a consistent estimator of the true average ITE? What assumptions are required for the estimator to be a valid estimator of the causal effect? In particular, the loss function is only defined over minibatches, so the objective function for the regression is left implicit. Presupposing that SGD does in fact converge, does this oddball objective function cause any issues?  2. Is the intuitive motivation (representation preserves local similarity) actually supported by the empirical results? It's clear that SITE does somewhat better than the comparitor methods, but it's not clear to me why this is---could it attributed simply to higher model capacity?  Experiments showing that SITE actually learns representations that do a better job of preserving local similarity, and that this matters, would strengthen the paper.  I note that the authors claim (line 263-265) that the experiments show this already, but I don't understand how.    More broadly, the whole procedure in this paper feels a bit ad hoc. It's not clear to me which parts of the model are really important for the results to hold.   # Overview   Based on the above critiques, I've voted (weakly) to reject. However, if good answers to the above points of confusion can be incorporated into the text, I'd be happy to reconsider.    # Further questions and comments 1. The learning procedure described in the paper seems to take propensity scores as inputs. E.g. triplet pair selection relies on this. How are the required propensity scores determined? 2. Does the SGD actually converge? It seems possible that selecting triplets within the mini-batch may lead to issues. 3. What is the summation (\Sum) in equation 7 over? I thought there was exactly one \hat{i}, \hat{j}, etc. per minibatch 4. Is the correct interpretation of the experiment in section 3.2 that the covariates x are generated according to one of the two normal distributions, the response is generated independent of T, and the ground truth ITE is 0? Assuming this is correct, the text should be rewritten to be clearer. I'm also unclear what the inputs to the KL distance are, and why KL is chosen as the distance       #### Update  I thank the authors for responding to my comments and questions.  1. The ablation study with PDDM is helpful. I think the paper would be improved by adding this, and also one for MPDM loss term.   The presented results show that PDDM improves the ITE estimate, but, as far as I can see, it does not show that the PDDM term actually causes the learned representations to better preserve local similarity.      2. I'm still confused by when, if ever, the method described in the paper is a correct estimator for ITE (defining 'correct' sensibly is part of the challenge here). The author response didn't cleared this up for me. For example, it was still unclear why assumptions 2.1 and 2.2 are included given that, as far as I can tell, neither is actually referenced again in the paper.   I was sufficiently confused by this that I went back and read the related prior work ("Learning Representations for Counterfactual Inference" Johansson, Shalit, Sontag, and "Estimating Individual Treatment Effect: Generalization Bounds and Algorithms", ref [28] in the paper). These papers establish a clear meaning for the use of representation learning for causal inference: the PEHE is bounded by an expression that includes the distance between P(r | t=0) and P(r | t=1), the distributions over the representations for the treated and untreated. I'm convinced this could provide a clear motivation and (hand wavy) justification for SITE. However, I don't think the paper explains this well---if the method is justified by ref [28] then the key results and the connection should be summarized in the paper!  There is presumably some analogous idea making use of the assumption that similar units will have similar responses, but I'm again unsure what such a result is or exactly how it might apply to the proposed method.  Although I'm now convinced that the method can probably be justified properly, I don't think this is done in the paper, and I view the the confusing presentation as a serious problem.  For this reason, I'm still voting to reject. However, I note that reviewer 1 has essentially the same criticism (to wit: this method doesn't seem to actually estimate ITE), but doesn't view this is a serious issue.