Hierarchical Topological Ordering with Conditional Independence Test for Limited Time Series

TL;DR

This paper introduces HT-CIT, a hierarchical topological ordering algorithm that uses limited time series data and conditional independence tests to efficiently learn sparse DAGs with fewer spurious edges.

Contribution

The paper proposes a novel hierarchical topological ordering method that leverages limited time series data and conditional independence tests to improve DAG learning.

Findings

HT-CIT reduces the number of spurious edges in learned DAGs.

Empirical results show HT-CIT outperforms existing methods on synthetic and real datasets.

The approach efficiently identifies causal structures with limited data.

Abstract

Learning directed acyclic graphs (DAGs) to identify causal relations underlying observational data is crucial but also poses significant challenges. Recently, topology-based methods have emerged as a two-step approach to discovering DAGs by first learning the topological ordering of variables and then eliminating redundant edges, while ensuring that the graph remains acyclic. However, one limitation is that these methods would generate numerous spurious edges that require subsequent pruning. To overcome this limitation, in this paper, we propose an improvement to topology-based methods by introducing limited time series data, consisting of only two cross-sectional records that need not be adjacent in time and are subject to flexible timing. By incorporating conditional instrumental variables as exogenous interventions, we aim to identify descendant nodes for each variable. Following this line, we propose a hierarchical topological ordering algorithm with conditional independence test (HT-CIT), which enables the efficient learning of sparse DAGs with a smaller search space compared to other popular approaches. The HT-CIT algorithm greatly reduces the number of edges that need to be pruned. Empirical results from synthetic and real-world datasets demonstrate the superiority of the proposed HT-CIT algorithm.