Ordering-based Causal Discovery via Generalized Score Matching
Vy Vo, He Zhao, Trung Le, Edwin V. Bonilla, Dinh Phung
TL;DR
This work addresses causal discovery from observational discrete data by introducing an ordering-based framework that recovers a true topological order via leaf-node detection using a discrete score function. It extends generalized score matching to the discrete domain and proves an identifiability result under a non-decreasing randomness condition, enabling recovery of the causal order and improved downstream DAG estimation. The method, supported by a practical order-diagnostic tool and extensive experiments on synthetic and real discrete networks, demonstrates robust improvements over existing baselines in both edge precision and causal reliability, even under noise and relaxed assumptions. The approach broadens the applicability of score-based causal discovery to categorical data and offers a scalable pathway to leverage learned orders in diverse application domains.
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.