Deciding Morality of Graphs is NP-complete

TL;DR

Determining whether a graph can be represented as a DAG projection based on covariance data is computationally hard, being NP-complete, which impacts causal inference methods.

Contribution

This paper proves that deciding the existence of a DAG projection from covariance matrices is NP-complete, highlighting computational limitations in causal graph discovery.

Findings

Deciding DAG existence from covariance matrices is NP-complete.

The result impacts causal inference algorithms.

Highlights computational complexity in causal graph analysis.

Abstract

In order to find a causal explanation for data presented in the form of covariance and concentration matrices it is necessary to decide if the graph formed by such associations is a projection of a directed acyclic graph (dag). We show that the general problem of deciding whether such a dag exists is NP-complete.