Ordering-based Causal Discovery via Generalized Score Matching

TL;DR

This paper extends score matching methods for causal discovery to discrete data, enabling accurate inference of causal orderings and improving existing methods' performance across various datasets.

Contribution

It introduces a novel leaf discriminant criterion based on the discrete score function, enhancing causal order inference from discrete data.

Findings

Accurate causal order inference from discrete data.

Significant improvement over baseline methods.

Validated on simulated and real-world datasets.

Abstract

Learning DAG structures from purely observational data remains a long-standing challenge across scientific domains. An emerging line of research leverages the score of the data distribution to initially identify a topological order of the underlying DAG via leaf node detection and subsequently performs edge pruning for graph recovery. This paper extends the score matching framework for causal discovery, which is originally designated for continuous data, and introduces a novel leaf discriminant criterion based on the discrete score function. Through simulated and real-world experiments, we demonstrate that our theory enables accurate inference of true causal orders from observed discrete data and the identified ordering can significantly boost the accuracy of existing causal discovery baselines on nearly all of the settings.