  An important problem in machine learning and statistics is to identify
features that causally affect the outcome. This is often impossible to do from
purely observational data, and a natural relaxation is to identify features
that are correlated with the outcome even conditioned on all other observed
features. For example, we want to identify that smoking really is correlated
with cancer conditioned on demographics. The knockoff procedure is a recent
breakthrough in statistics that, in theory, can identify truly correlated
features while guaranteeing that the false discovery is limited. The idea is to
create synthetic data -- knockoffs -- that captures correlations amongst the
features. However there are substantial computational and practical challenges
to generating and using knockoffs. This paper makes several key advances that
enable knockoff application to be more efficient and powerful. We develop an
efficient algorithm to generate valid knockoffs from Bayesian Networks. Then we
systematically evaluate knockoff test statistics and develop new statistics
with improved power. The paper combines new mathematical guarantees with
systematic experiments on real and synthetic data.
