  Confounding matters in almost all observational studies that focus on
causality. In order to eliminate bias caused by connfounders, oftentimes a
substantial number of features need to be collected in the analysis. In this
case, large p small n problem can arise and dimensional reduction technique is
required. However, the traditional variable selection methods which focus on
prediction are problematic in this setting. Throughout this paper, we analyze
this issue in detail and assume the sparsity of confounders which is different
from the previous works. Under this assumption we propose several variable
selection methods based on support intersection to pick out the confounders.
Also we discussed the different approaches for estimation of causal effect and
unconfoundedness test. To aid in our description, finally we provide numerical
simulations to support our claims and compare to common heuristic methods, as
well as applications on real dataset.
