A novel hybrid approach for positive-valued DAG learning

Yao Zhao

Keywords: Causal discovery, Directed acyclic graphs, Log-linear models, Moment-ratio scoring, Positive-valued data

TL;DR: We propose H-MRS, a polynomial-time algorithm for causal discovery from positive-valued data that combines log-scale regression with moment-ratio scoring to recover interpretable DAGs.

Abstract: 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 naturally follow multiplicative rather than additive dynamics. We propose the Hybrid Moment-Ratio Scoring (H-MRS) algorithm, a novel approach for learning directed acyclic graphs (DAGs) from positive-valued data that combines moment-based scoring with log-scale regression. The key insight is that for positive-valued variables, the moment ratio $\frac{\mathbb{E}\left[X_j^2\right]}{\mathbb{E}\left[\left(\mathbb{E}\left[X_j \mid S\right]\right)^2\right]}$ provides an effective criterion for causal ordering, where $S$ denotes candidate parent sets. H-MRS combines log-scale Ridge regression for moment-ratio estimation with greedy ordering construction based on raw-scale moment ratios, followed by ElasticNet-based parent selection to recover the final DAG structure. We evaluate H-MRS on synthetic log-linear data, showing that it achieves competitive precision and recall. The algorithm is computationally efficient and naturally respects positivity constraints, making it well-suited for applications such as genomics and economics. Our results highlight that combining log-scale modeling with raw-scale moment ratios offers a practical and robust framework for causal discovery in positive-valued domains.

Submission Number: 20