Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variables

TL;DR

This paper introduces removable order (r-order) methods for learning the maximal ancestral graph in structural equation models with unobserved variables, offering advantages over traditional causal order approaches.

Contribution

It proposes a novel r-order framework that is invariant within Markov equivalence classes and easier to optimize, improving causal structure learning in SEMs with hidden variables.

Findings

r-orders are invariant within MECs and include c-orders as a subset

The optimization for r-orders can be solved exactly or approximately, enhancing flexibility

Proposed methods show improved performance and scalability on real and synthetic networks

Abstract

We propose ordering-based approaches for learning the maximal ancestral graph (MAG) of a structural equation model (SEM) up to its Markov equivalence class (MEC) in the presence of unobserved variables. Existing ordering-based methods in the literature recover a graph through learning a causal order (c-order). We advocate for a novel order called removable order (r-order) as they are advantageous over c-orders for structure learning. This is because r-orders are the minimizers of an appropriately defined optimization problem that could be either solved exactly (using a reinforcement learning approach) or approximately (using a hill-climbing search). Moreover, the r-orders (unlike c-orders) are invariant among all the graphs in a MEC and include c-orders as a subset. Given that set of r-orders is often significantly larger than the set of c-orders, it is easier for the optimization problem to find an r-order instead of a c-order. We evaluate the performance and the scalability of our proposed approaches on both real-world and randomly generated networks.