Bounds on Causal Effects and Application to High Dimensional Data

This paper addresses the problem of estimating causal effects when adjustment variables in the back-door or front-door criterion are partially observed. For such scenarios, we derive bounds on the causal effects by solving two non-linear optimization problems, and demonstrate that the bounds are sufficient. Using this optimization method, we propose a framework for dimensionality reduction that allows one to trade bias for estimation power, and demonstrate its performance using simulation studies.