Scalable Causal Structure Learning via Amortized Conditional Independence Testing

James Leiner, Brian Manzo, Aaditya Ramdas, Wesley Tansey

Keywords: Causal Inference, Hypothesis Testing, Directed Acyclic Graphs

TL;DR: We leverage discrete optimization techniques to more efficiently perform causal structure learning and apply the technique to an example in computational oncology.

Abstract:

Controlling false positives (Type I errors) through statistical hypothesis testing is a foundation
of modern scientific data analysis. Existing causal structure discovery algorithms either do not
provide Type I error control or cannot scale to the size of modern scientific datasets. We consider
a variant of the causal discovery problem with two sets of nodes, where the only edges of interest
form a bipartite causal subgraph between the sets. We develop Scalable Causal Structure Learning
(SCSL), a method for causal structure discovery on bipartite subgraphs that provides Type I error
control. SCSL recasts the discovery problem as a simultaneous hypothesis testing problem and
uses discrete optimization over the set of possible confounders to obtain an upper bound on the
test statistic for each edge. Semi-synthetic simulations demonstrate that SCSL scales to handle
graphs with hundreds of nodes while maintaining error control and good power. We demonstrate the
practical applicability of the method by applying it to a cancer dataset to reveal connections between
somatic gene mutations and metastases to different tissues.

Submission Number: 113