Distributional Equivalence and Structure Learning for Bow-free Acyclic Path Diagrams

TL;DR

This paper introduces a new method for learning the structure of bow-free acyclic path diagrams (BAPs), which generalize DAG models with hidden variables, using a greedy search and distributional equivalence conditions.

Contribution

It presents the first greedy score-based algorithm for BAP structure learning and provides conditions for distributional equivalence to improve causal inference.

Findings

Effective structure learning for BAPs demonstrated on real and simulated data.

Algorithm computes nearly equivalent models to infer causal effects.

Open-source R package implementation available.

Abstract

We consider the problem of structure learning for bow-free acyclic path diagrams (BAPs). BAPs can be viewed as a generalization of linear Gaussian DAG models that allow for certain hidden variables. We present a first method for this problem using a greedy score-based search algorithm. We also prove some necessary and some sufficient conditions for distributional equivalence of BAPs which are used in an algorithmic ap- proach to compute (nearly) equivalent model structures. This allows us to infer lower bounds of causal effects. We also present applications to real and simulated datasets using our publicly available R-package.