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An important problem in machine learning and statistics is to identifyfeatures that causally affect the outcome. This is often impossible to do frompurely observational data, and a natural relaxation is to identify featuresthat are correlated with the outcome even conditioned on all other observedfeatures. For example, we want to identify that smoking really is correlatedwith cancer conditioned on demographics. The knockoff procedure is a recentbreakthrough in statistics that, in theory, can identify truly correlatedfeatures while guaranteeing that the false discovery is limited. The idea is tocreate synthetic data -- knockoffs -- that captures correlations amongst thefeatures. However there are substantial computational and practical challengesto generating and using knockoffs. This paper makes several key advances thatenable knockoff application to be more efficient and powerful. We develop anefficient algorithm to generate valid knockoffs from Bayesian Networks. Then wesystematically evaluate knockoff test statistics and develop new statisticswith improved power. The paper combines new mathematical guarantees withsystematic experiments on real and synthetic data.

Knockoffs for the mass: new feature importance statistics with false discovery guarantees