Integer Programming Based Methods and Heuristics for Causal Graph Learning
Abstract: Acyclic directed mixed graphs (ADMG) –
graphs that contain both directed and bidi-
rected edges but no directed cycles – are used
to model causal and conditional independence
relationships between a set of random vari-
ables in the presence of latent or unmeasured
variables. Bow-free ADMGs, Arid ADMGs,
and Ancestral ADMGs (AADMG) are three
widely studied classes of ADMGs where each
class is contained in the previously mentioned
class. There are a number of published meth-
ods – primarily heuristic ones – to find score-
maximizing AADMGs from data. Bow-free
and Arid ADMGs can model certain equal-
ity restrictions – such as Verma constraints
– between observed variables that maximal
AADMGs cannot. In this work, we develop
the first exact methods – based on integer
programming – to find score-maximizing Bow-
free and Arid ADMGs. Our methods work for
data that follows a continuous Gaussian distri-
bution and for scores that linearly decompose
into the sum of scores of c-components of
an ADMG. To improve scaling, we develop
an effective linear-programming based heuris-
tic that yields solutions with high parent set
sizes and/or large districts. We show that
our proposed algorithms obtain better scores
than other state-of-the-art methods and re-
turn graphs that have excellent fits to data.
Submission Number: 482
Loading