  We consider learning ancestral causal relationships in high dimensions. Our
approach is driven by a supervised learning perspective, with discrete
indicators of causal relationships treated as labels to be learned from
available data. We focus on the setting in which some causal (ancestral)
relationships are known (via background knowledge or experimental data) and put
forward a general approach that scales to large problems. This is motivated by
problems in human biology which are characterized by high dimensionality and
potentially many latent variables. We present a case study involving
interventional data from human cells with total dimension $p \! \sim \!
19{,}000$. Performance is assessed empirically by testing model output against
previously unseen interventional data. The proposed approach is highly
effective and demonstrably scalable to the human genome-wide setting. We
consider sensitivity to background knowledge and find that results are robust
to nontrivial perturbations of the input information. We consider also the
case, relevant to some applications, where the only prior information available
concerns a small number of known ancestral relationships.
