Branch-Price-and-Cut for Causal Discovery

James Cussens

Keywords: Causal discovery, integer linear programming, pricing

TL;DR: The integer programming (IP) approach to learning DAGs is extended to allow IP variables to be added during solving/learning.

Abstract:

We show how to extend the integer programming (IP) approach to
score-based causal discovery by including pricing. Pricing
allows the addition of new IP variables during solving, rather than
requiring them all to be present initially. The dual values of
acyclicity constraints allow this addition to be done in a
principled way. We have extended the GOBNILP algorithm to effect
a branch-price-and-cut method for DAG learning. Empirical results
show that implementing a delayed pricing approach can be
beneficial. The current pricing algorithm in GOBNILP is slow, so
further work on fast pricing is required.