Algorithms for Solving Nonlinear Binary Optimization Problems in Robust Causal Inference

Identifying cause-effect relation among variables is a key step in the decision-making process. While causal inference requires randomized experiments, researchers and policymakers are increasingly using observational studies to test causal hypotheses due to the wide availability of observational data and the infeasibility of experiments. The matching method is the most used technique to make causal inference from observational data. However, the pair assignment process in one-to-one matching creates uncertainty in the inference because of different choices made by the experimenter. Recently, discrete optimization models are proposed to tackle such uncertainty. Although a robust inference is possible with discrete optimization models, they produce nonlinear problems and lack scalability. In this work, we propose greedy algorithms to solve the robust causal inference test instances from observational data with continuous outcomes. We propose a unique framework to reformulate the nonlinear binary optimization problems as feasibility problems. By leveraging the structure of the feasibility formulation, we develop greedy schemes that are efficient in solving robust test problems. In many cases, the proposed algorithms achieve global optimal solution. We perform experiments on three real-world datasets to demonstrate the effectiveness of the proposed algorithms and compare our result with the state-of-the-art solver. Our experiments show that the proposed algorithms significantly outperform the exact method in terms of computation time while achieving the same conclusion for causal tests. Both numerical experiments and complexity analysis demonstrate that the proposed algorithms ensure the scalability required for harnessing the power of big data in the decision-making process.