  To unbiasedly estimate a causal effect on an outcome unconfoundedness is
often assumed. If there is sufficient knowledge on the underlying causal
structure then existing confounder selection criteria can be used to select
subsets of the observed pretreatment covariates, $X$, sufficient for
unconfoundedness, if such subsets exist. Here, estimation of these target
subsets is considered when the underlying causal structure is unknown. The
proposed method is to model the causal structure by a probabilistic graphical
model, e.g., a Markov or Bayesian network, estimate this graph from observed
data and select the target subsets given the estimated graph. The approach is
evaluated by simulation both in a high-dimensional setting where
unconfoundedness holds given $X$ and in a setting where unconfoundedness only
holds given subsets of $X$. Several common target subsets are investigated and
the selected subsets are compared with respect to accuracy in estimating the
average causal effect. The proposed method is implemented with existing
software that can easily handle high-dimensional data, in terms of large
samples and large number of covariates. The results from the simulation study
show that, if unconfoundedness holds given $X$, this approach is very
successful in selecting the target subsets, outperforming alternative
approaches based on random forests and LASSO, and that the subset estimating
the target subset containing all causes of outcome yields smallest MSE in the
average causal effect estimation.
