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Identifying cause-effect relations among variables is a key step in thedecision-making process. While causal inference requires randomizedexperiments, researchers and policymakers are increasingly using observationalstudies to test causal hypotheses due to the wide availability of observationaldata and the infeasibility of experiments. The matching method is the most usedtechnique to make causal inference from observational data. However, the pairassignment process in one-to-one matching creates uncertainty in the inferencebecause of different choices made by the experimenter. Recently, discreteoptimization models are proposed to tackle such uncertainty. Although a robustinference is possible with discrete optimization models, they produce nonlinearproblems and lack scalability. In this work, we propose greedy algorithms tosolve the robust causal inference test instances from observational data withcontinuous outcomes. We propose a unique framework to reformulate the nonlinearbinary optimization problems as feasibility problems. By leveraging thestructure of the feasibility formulation, we develop greedy schemes that areefficient in solving robust test problems. In many cases, the proposedalgorithms achieve global optimal solutions. We perform experiments on threereal-world datasets to demonstrate the effectiveness of the proposed algorithmsand compare our result with the state-of-the-art solver. Our experiments showthat the proposed algorithms significantly outperform the exact method in termsof computation time while achieving the same conclusion for causal tests. Bothnumerical experiments and complexity analysis demonstrate that the proposedalgorithms ensure the scalability required for harnessing the power of big datain the decision-making process.

A Computational Framework for Solving Nonlinear Binary OptimizationProblems in Robust Causal Inference