Towards Effective Causal Partitioning by Edge Cutting of Adjoint Graph

Causal partitioning
is an effective approach for causal discovery based on the divide-and-conquer strategy. Up to now, various heuristic methods based on conditional independence (CI) tests have been proposed for causal partitioning. However, most of these methods fail to achieve satisfactory partitioning without violating
$d$
-separation, leading to poor inference performance. In this work, we transform causal partitioning into an alternative problem that can be more easily solved. Concretely, we first construct a superstructure
$G$
of the true causal graph
$G_{\mathcal {T}}$
by performing a set of low-order CI tests on the observed data
$D$
. Then, we leverage point-line duality to obtain a graph
$G_\mathcal {A}$
adjoint to
$G$
. We show that the solution of
minimizing edge-cut ratio
on
$G_\mathcal {A}$
can lead to a valid causal partitioning with
smaller causal-cut ratio
on
$G$
and
without violating $d$d-separation
. We design an efficient algorithm to solve this problem. Extensive experiments show that the proposed method can achieve significantly better causal partitioning without violating
$d$
-separation than the existing methods.