  The recent availability of huge, many-dimensional data sets, like those
arising from genome-wide association studies (GWAS), provides many
opportunities for strengthening causal inference. One popular approach is to
utilize these many-dimensional measurements as instrumental variables
(instruments) for improving the causal effect estimate between other pairs of
variables. Unfortunately, searching for proper instruments in a
many-dimensional set of candidates is a daunting task due to the intractable
model space and the fact that we cannot directly test which of these candidates
are valid, so most existing search methods either rely on overly stringent
modeling assumptions or fail to capture the inherent model uncertainty in the
selection process. We show that, as long as at least some of the candidates are
(close to) valid, without knowing a priori which ones, they collectively still
pose enough restrictions on the target interaction to obtain a reliable causal
effect estimate. We propose a general and efficient causal inference algorithm
that accounts for model uncertainty by performing Bayesian model averaging over
the most promising many-dimensional instrumental variable models, while at the
same time employing weaker assumptions regarding the data generating process.
We showcase the efficiency, robustness and predictive performance of our
algorithm through experimental results on both simulated and real-world data.
