A Discovery Algorithm for Directed Cyclic Graphs

TL;DR

This paper introduces a polynomial-time discovery algorithm for inferring causal structures in directed cyclic graphs from sample data, addressing a gap in causal inference beyond acyclic models.

Contribution

The paper presents a novel, large-sample consistent algorithm for causal discovery in directed cyclic graphs, expanding causal inference methods to non-recursive models.

Findings

Algorithm is correct in the large sample limit

Provides information on causal pathways between variables

Efficient for sparse graphs

Abstract

Directed acyclic graphs have been used fruitfully to represent causal strucures (Pearl 1988). However, in the social sciences and elsewhere models are often used which correspond both causally and statistically to directed graphs with directed cycles (Spirtes 1995). Pearl (1993) discussed predicting the effects of intervention in models of this kind, so-called linear non-recursive structural equation models. This raises the question of whether it is possible to make inferences about causal structure with cycles, form sample data. In particular do there exist general, informative, feasible and reliable precedures for inferring causal structure from conditional independence relations among variables in a sample generated by an unknown causal structure? In this paper I present a discovery algorithm that is correct in the large sample limit, given commonly (but often implicitly) made plausible assumptions, and which provides information about the existence or non-existence of causal pathways from one variable to another. The algorithm is polynomial on sparse graphs.