针对正数变量的因果发现，提出混合方法提升准确性。
A novel hybrid approach for positive-valued DAG learning
- 结合矩比与对数回归，用原始尺度矩比排序，对数尺度估计。
- 合成对数线性数据上精度和召回率表现良好。
- 适合基因组学、经济学等正数变量场景，计算高效。
从观测数据中进行因果发现仍是机器学习与统计学中的基础挑战，尤其当变量代表固有正数量（如基因表达水平、资产价格、公司收入或人口数量）时，这些变量常呈现乘法而非加法动态。我们提出混合矩比评分（H-MRS）算法，一种从正数数据中学习有向无环图（DAG）的新方法，通过将基于矩的评分与对数尺度回归相结合。核心思想是：对于正数变量，其矩比 $\frac{\mathbb{E}[X_j^2]}{\mathbb{E}[(\mathbb{E}[X_j \mid S])^2]}$ 可作为有效的因果排序依据，其中 $S$ 表示候选父集。H-MRS利用对数尺度岭回归估算矩比，并基于原始尺度矩比进行贪心排序，再通过弹性网络实现父节点选择以恢复最终的DAG结构。在合成对数线性数据上的实验表明该方法具有竞争力的精度与召回率。所提方法计算高效且天然满足正数约束，适用于基因组学与经济学等领域。结果表明，结合对数尺度建模与原始尺度矩比可为正数领域因果发现提供实用框架。
原文摘要 · Abstract (English)
Causal discovery from observational data remains a fundamental challenge in machine learning and statistics, particularly when variables represent inherently positive quantities such as gene expression levels, asset prices, company revenues, or population counts, which often follow multiplicative rather than additive dynamics. We propose the Hybrid Moment-Ratio Scoring (H-MRS) algorithm, a novel method for learning directed acyclic graphs (DAGs) from positive-valued data by combining moment-based scoring with log-scale regression. The key idea is that for positive-valued variables, the moment ratio $\frac{\mathbb{E}[X_j^2]}{\mathbb{E}[(\mathbb{E}[X_j \mid S])^2]}$ provides an effective criterion for causal ordering, where $S$ denotes candidate parent sets. H-MRS integrates log-scale Ridge regression for moment-ratio estimation with a greedy ordering procedure based on raw-scale moment ratios, followed by Elastic Net-based parent selection to recover the final DAG structure. Experiments on synthetic log-linear data demonstrate competitive precision and recall. The proposed method is computationally efficient and naturally respects positivity constraints, making it suitable for applications in genomics and economics. These results suggest that combining log-scale modeling with raw-scale moment ratios provides a practical framework for causal discovery in positive-valued domains.
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