Two Time-Slices Help Topological Ordering for Learning Directed Acyclic Graphs

Anpeng Wu, Haoxuan Li, Kun Kuang, Zhang Keli, Fei Wu

Primary Area: causal reasoning

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Keywords: Two Time-Slices, Topology-based Algorithm, Descendant Hierarchical Topology, Conditional Independence Criterion

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TL;DR: We propose a novel topology-based algorithm called DHT-CIT, which introduces auxiliary instrumental variables in two time-slices to improve topological ordering and to learn the true DAGs rather than the Markov equivalence class.

Abstract: Learning causal relations from observational data is an important task in the real world, yet it remains challenging due to the super-exponential search space and the acyclicity constraint. To address these issues, practitioners develop promising topology-based methods to generate a complete topological ordering, reducing the search space and automatically maintaining the acyclicity constraint. However, these methods typically produce non-unique topological orderings with numerous spurious edges, resulting in decreased accuracy and efficiency in downstream search tasks. While using interventional data can quickly identify (non-)descendants for each node and construct a more precise topological ordering, full interventions are often expensive, unethical, or even infeasible. Therefore, we explore how the more readily available two time-slices data can replace intervention data to improve topological ordering. Based on a conditional independence criterion using two time-slices as auxiliary instrumental variables, we propose a novel Descendant Hierarchical Topology algorithm with Conditional Independence Test (DHT-CIT) to learn causal relations more efficiently, with a smaller search space and fewer spurious edges. Empirical results on both synthetic and real-world datasets demonstrate the superiority of our DHT-CIT algorithm.

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Submission Number: 1639