Pattern-Guided Adaptive Prior for Structure Learning

Learning the causality between variables, known as DAG structure learning, is critical yet challenging due to issues such as insufficient data and noise. While prior knowledge can improve the learning process and refine the DAG structure, incorporating prior knowledge is not without pitfalls. In particular, we find that the gap between the imprecise prior knowledge and the exact weights modeled by existing methods may result in deviation in edge weights. Such deviation can subsequently cause significant inaccuracies when learning the DAG structure. This paper addresses this challenge by providing a theoretical analysis of the impact of deviation in edge weights during the optimization process of structure learning. We identify two special graph patterns that arise due to the deviation and show that their occurrence increases as the degree of deviation grows. Building on this analysis, we propose the Pattern-Guided Adaptive Prior (PGAP) framework. PGAP detects these patterns as structural signals during optimization and adaptively adjusts the structure learning process to counteract the identified weight deviation, thereby improving the integration of prior knowledge. Experiments verify the effectiveness and robustness of the proposed method.