Under stringent model type and variable distribution assumptions, differentiable score-based causal discovery methods learn a directed acyclic graph (DAG) from observational data by evaluating candidate graphs over an average score function. Despite great success in low-dimensional linear systems, it has been observed that these approaches overly exploit easier-to-fit samples, thus inevitably learning spurious edges. Worse still, inherent mostly in these methods the common homogeneity assumption can be easily violated, due to the widespread existence of heterogeneous data in the real world, resulting in performance vulnerability when noise distributions vary. We propose a simple yet effective model-agnostic framework to boost causal discovery performance by dynamically learning the adaptive weights for the Reweighted Score function, ReScore for short, where the weights tailor quantitatively to the importance degree of each sample. Intuitively, we leverage the bilevel optimization scheme to \wx{alternately train a standard DAG learner and reweight samples -- that is, upweight the samples the learner fails to fit and downweight the samples that the learner easily extracts the spurious information from. Extensive experiments on both synthetic and real-world datasets are carried out to validate the effectiveness of ReScore. We observe consistent and significant boosts in structure learning performance. Furthermore, we visualize that ReScore concurrently mitigates the influence of spurious edges and generalizes to heterogeneous data. Finally, we perform the theoretical analysis to guarantee the structure identifiability and the weight adaptive properties of ReScore in linear systems. Our codes are available at https://github.com/anzhang314/ReScore.

翻译：在严格的模型类型和变量分布假设下，基于可微分评分函数的因果发现方法通过评估候选图在平均评分函数上的表现，从观测数据中学习有向无环图（DAG）。尽管在低维线性系统中取得了巨大成功，但已有研究表明，这些方法过度利用易于拟合的样本，从而不可避免地学习到虚假边。更严重的是，由于现实世界中异质性数据的广泛存在，这些方法中普遍隐含的同质性假设极易被违背，导致在噪声分布变化时性能脆弱。我们提出了一种简单而有效的模型无关框架，通过动态学习自适应样本权重来提升因果发现性能，简称ReScore（重加权评分函数），其中权重定量地定制每个样本的重要程度。直观上，我们利用双层优化方案交替训练标准DAG学习器与重加权样本——即上调学习器难以拟合的样本权重，下调学习器易于提取虚假信息的样本权重。在合成和真实数据集上的大量实验验证了ReScore的有效性。我们观察到结构学习性能得到一致且显著的提升。此外，我们可视化证明了ReScore能够同时减轻虚假边的影响并泛化到异质性数据。最后，我们进行了理论分析，保证了线性系统中ReScore的结构可辨识性与权重自适应特性。我们的代码可在https://github.com/anzhang314/ReScore获取。