Hyperplane Representations of Interventional Characteristic Imset Polytopes

TL;DR

This paper develops a method to compute hyperplane representations of CIM polytopes for causal discovery, enabling linear programming approaches to infer causal structures from observational and interventional data.

Contribution

It introduces a novel approach using toric fiber products and interventional CIM polytopes to explicitly compute hyperplanes for CIM polytopes of tree-structured graphs.

Findings

Derived hyperplanes facilitate linear optimization for causal discovery.

Applied method to learn polytree causal networks from combined data.

Enhanced causal inference accuracy with interventional data integration.

Abstract

Characteristic imsets are 0/1-vectors representing directed acyclic graphs whose edges represent direct cause-effect relations between jointly distributed random variables. A characteristic imset (CIM) polytope is the convex hull of a collection of characteristic imsets. CIM polytopes arise as feasible regions of a linear programming approach to the problem of causal disovery, which aims to infer a cause-effect structure from data. Linear optimization methods typically require a hyperplane representation of the feasible region, which has proven difficult to compute for CIM polytopes despite continued efforts. We solve this problem for CIM polytopes that are the convex hull of imsets associated to DAGs whose underlying graph of adjacencies is a tree. Our methods use the theory of toric fiber products as well as the novel notion of interventional CIM polytopes. Our solution is obtained as a corollary of a more general result for interventional CIM polytopes. The identified hyperplanes are applied to yield a linear optimization-based causal discovery algorithm for learning polytree causal networks from a combination of observational and interventional data.