Algorithms and Complexities of Matching Variants in Covariate Balancing
研究了观察性研究中协变量平衡问题的计算复杂性，发现两个协变量时可多项式求解，三个及以上则多为困难问题，为使用启发式或聚合方法提供了理论依据。
In an observational study there are two disjointed groups of samples, one of treatment samples and the other of control samples. Each of the samples is characterized by several observed covariates. Covariate balancing problems arise when estimating causal effects using observational data. It is desirable to replicate a randomized experiment by obtaining treatment and control groups with similar covariate distributions. Even though covariate balancing problems have been studied extensively, the complexity status of many variants has not been established. Some of our results demonstrate that 2-covariate balancing problems are polynomial time solvable, whereas almost all problems are hard for three or more covariates. These results have practical implications, such as justifying the use of implicit enumeration techniques or heuristics for the hard cases. A new approach suggested by our results is to use the 2-covariate polynomial cases and relax the problem by aggregating covariates into two sets to be solved efficiently. (accepted paper title: Algorithms and complexities of matching variants in covariate balancing)