  To make accurate predictions, understand mechanisms, and design interventions
in systems of many variables, we wish to learn causal graphs from large scale
data. Unfortunately the space of all possible causal graphs is enormous so
scalably and accurately searching for the best fit to the data is a challenge.
In principle we could substantially decrease the search space, or learn the
graph entirely, by testing the conditional independence of variables. However,
deciding if two variables are adjacent in a causal graph may require an
exponential number of tests. Here we build a scalable and flexible method to
evaluate if two variables are adjacent in a causal graph, the Differentiable
Adjacency Test (DAT). DAT replaces an exponential number of tests with a
provably equivalent relaxed problem. It then solves this problem by training
two neural networks. We build a graph learning method based on DAT, DAT-Graph,
that can also learn from data with interventions. DAT-Graph can learn graphs of
1000 variables with state of the art accuracy. Using the graph learned by
DAT-Graph, we also build models that make much more accurate predictions of the
effects of interventions on large scale RNA sequencing data.
