Localised Natural Causal Learning Algorithms for Weak Consistency Conditions

TL;DR

This paper introduces localized natural structure learning algorithms (LoNS) that relax traditional conditions for causal discovery, providing theoretical guarantees and practical algorithms with comparisons to existing methods through simulations.

Contribution

It defines LoNS algorithms with relaxed assumptions, offers necessary and sufficient conditions for their consistency, and presents a practical exponential-time algorithm with empirical evaluations.

Findings

LoNS algorithms generalize existing structure learning methods.

Theoretical conditions for LoNS consistency are established.

Simulation results compare LoNS with PC/SGS and sparsest permutation algorithms.

Abstract

By relaxing conditions for natural structure learning algorithms, a family of constraint-based algorithms containing all exact structure learning algorithms under the faithfulness assumption, we define localised natural structure learning algorithms (LoNS). We also provide a set of necessary and sufficient assumptions for consistency of LoNS, which can be thought of as a strict relaxation of the restricted faithfulness assumption. We provide a practical LoNS algorithm that runs in exponential time, which is then compared with related existing structure learning algorithms, namely PC/SGS and the relatively recent sparsest permutation algorithm. Simulation studies are also provided.