A novel hybrid approach for positive-valued DAG learning
2026-04-10 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed a new method called H-MRS to find cause-and-effect relationships in data where all values are positive, like gene activity or prices. Their method looks at certain statistics (moment ratios) and uses a special type of regression on the log scale to figure out which variables influence others. They tested it on simulated data and found it works well and runs efficiently. This approach is useful for fields like biology and economics where data is naturally positive and changes multiply rather than add.
causal discoverydirected acyclic graph (DAG)moment ratiolog-scale regressionRidge regressionElastic Netcausal orderingpositive-valued datalog-linear modelsgreedy algorithm
Authors
Yao Zhao
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 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.