Matching on Balanced Nonlinear Representations for Treatment Effects Estimation
Estimating treatment effects from observational data is challenging due to the missing counterfactuals. Matching is an effective strategy to tackle this problem. The widely used matching estimators such as nearest neighbor matching (NNM) pair the treated units with the most similar control units in terms of covariates, and then estimate treatment effects accordingly. However, the existing matching estimators have poor performance when the distributions of control and treatment groups are unbalanced. Moreover, theoretical analysis suggests that the bias of causal effect estimation would increase with the dimension of covariates. In this paper, we aim to address these problems by learning low-dimensional balanced and nonlinear representations (BNR) for observational data. In particular, we convert counterfactual prediction as a classification problem, develop a kernel learning model with domain adaptation constraint, and design a novel matching estimator. The dimension of covariates will be significantly reduced after projecting data to a low-dimensional subspace. Experiments on several synthetic and real-world datasets demonstrate the effectiveness of our approach.
The paper proposes a new matching algorithm for estimation of treatment effects in observational studies. The algorithm is appropriate when the number of covariates is large. It finds a projection of the original covariate space into a lower dimensional one and applies a standard matching approach such as nearest neighbor matching in this new space. The proposed low dimensional nonlinear projection has two objectives: (1) maximize separation between outcomes and (2) maximize the overlap between cases and controls. The new algorithm is evaluated on one synthetic and two real data sets. The results indicate the proposed method is better than several alternatives. 
  Positives:
+ the proposed objective function is intuitively appealing
+ the experiments were well designed and the results are positive
+ the paper is easy to read
  Negatives:
- the proposed ordinal scatter discrepancy criterion is a heuristic that is sounds reasonable. However, it would require a deeper experimental or theoretical study to truly understand its advantages and drawbacks. 
- Any type of causal study on the observational data needs to come with caveats and understanding of potential pitfalls. This paper is not discussing it and presents the algorithm only in a positive light. It would be useful for the paper to at least have a "buyer beware" discussion.
- There are several moving parts required to make the proposed algorithm work, such as discretizing the outcomes, selecting the kernel, deciding on the dimensionality, selecting the hyperparameters. It would be important to see how sensitive the algorithm is to those choices. From the presented results, it is fair to ask if the shown results might be due to some overfitting
- the paper will need to be carefully proofread -- there are numerous grammar mistakes throughout.