[Paper Review] ASP-based Discovery of Semi-Markovian Causal Models under Weaker Assumptions

Zhalama Zhalama, Jiji Zhang+3 more|arXiv (Cornell University)|Jun 6, 2019

Bayesian Modeling and Causal Inference19 references4 citations

TL;DR

This paper extends weakenings of the Faithfulness assumption to semi-Markovian causal models (SMCMs) with latent confounders using Answer Set Programming (ASP). It demonstrates that conservative relaxations—such as V-adjacency-minimality and NOI-minimality—preserve inferential power while improving computational efficiency in ASP-based discovery, even under latent confounding.

ABSTRACT

In recent years the possibility of relaxing the so-called Faithfulness assumption in automated causal discovery has been investigated. The investigation showed (1) that the Faithfulness assumption can be weakened in various ways that in an important sense preserve its power, and (2) that weakening of Faithfulness may help to speed up methods based on Answer Set Programming. However, this line of work has so far only considered the discovery of causal models without latent variables. In this paper, we study weakenings of Faithfulness for constraint-based discovery of semi-Markovian causal models, which accommodate the possibility of latent variables, and show that both (1) and (2) remain the case in this more realistic setting.

Motivation & Objective

• Address the limitation of prior work on Faithfulness relaxations, which only applied to causally sufficient settings without latent confounders.
• Investigate whether weakenings of the Faithfulness assumption remain valid and beneficial in the more realistic context of semi-Markovian causal models with latent variables.
• Demonstrate that conservative relaxations of Faithfulness—preserving the ability to identify the true causal structure—still hold under semi-Markovian structures.
• Explore the practical impact of these relaxations on the performance of ASP-based causal discovery algorithms in the presence of latent confounders.

Proposed method

• Adopt semi-Markovian causal models (SMCMs) to represent causal structures with latent confounders, using mixed graphs with directed and bidirected edges.
• Introduce and formalize three conservative weakenings of Faithfulness: V-adjacency-minimality, NOE-minimality, and NOI-minimality, adapted to SMCMs and their corresponding MAGs.
• Use the causal Markov assumption as a foundation, ensuring that conditional independence (CI) statements in the data are entailed by the causal graph.
• Prove that these weakenings are logically conservative: they are entailed by Faithfulness but do not entail it, preserving the same inferential power when Faithfulness holds.
• Leverage the correspondence between SMCMs and their marginal ancestral graphs (MAGs) to transfer results from MAGs to SMCMs via the inducing path criterion.
• Apply Answer Set Programming (ASP) as the computational framework to implement and evaluate the proposed relaxations, exploiting their potential for efficiency gains under weaker assumptions.

Experimental results

Research questions

• RQ1 Can the Faithfulness assumption be meaningfully weakened in semi-Markovian causal models that include latent confounders while preserving the ability to identify the true causal structure?
• RQ2 Do the conservative relaxations of Faithfulness—such as V-adjacency-minimality and NOI-minimality—remain logically valid and inferentially powerful in the presence of latent variables?
• RQ3 To what extent do these weakened assumptions improve the computational efficiency of ASP-based causal discovery algorithms when latent confounders are present?
• RQ4 Is the correspondence between SMCMs and their corresponding MAGs sufficient to transfer results from MAG-based relaxations to SMCMs in a way that maintains logical consistency and inferential power?

Key findings

• The Faithfulness assumption can be conservatively weakened in semi-Markovian causal models (SMCMs), with relaxations like V-adjacency-minimality and NOI-minimality preserving the same inferential power as Faithfulness when it holds.
• V-adjacency-minimality is entailed by Faithfulness but does not entail it, and it ensures that no virtual adjacency can be removed without violating the Markov assumption.
• NOI-minimality is logically conservative: for any distribution faithful to an SMCM, a graph satisfying both Markov and NOI-minimality is faithful if and only if it satisfies Faithfulness.
• The results generalize from MAGs to SMCMs via the inducing path criterion, ensuring that conditional independence statements are preserved under the relaxations.
• The theoretical findings are compatible with ASP-based causal discovery, suggesting that these relaxations may retain or even enhance computational efficiency in practice, especially under finite-sample violations of Faithfulness.
• The study extends prior work on Faithfulness relaxations beyond causally sufficient settings, providing a foundation for more robust and scalable causal discovery in the presence of latent confounders.