A novel hybrid approach for positive-valued DAG learning

Yao Zhao
Proceedings of the Fifth Conference on Causal Learning and Reasoning, PMLR 323:297-323, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v323-zhao26a, title = {A novel hybrid approach for positive-valued DAG learning}, author = {Zhao, Yao}, booktitle = {Proceedings of the Fifth Conference on Causal Learning and Reasoning}, pages = {297--323}, year = {2026}, editor = {Mazaheri, Bijan and Hanson, Niels Richard}, volume = {323}, series = {Proceedings of Machine Learning Research}, month = {06--08 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v323/main/assets/zhao26a/zhao26a.pdf}, url = {https://proceedings.mlr.press/v323/zhao26a.html}, 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.} }
Endnote
%0 Conference Paper %T A novel hybrid approach for positive-valued DAG learning %A Yao Zhao %B Proceedings of the Fifth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2026 %E Bijan Mazaheri %E Niels Richard Hanson %F pmlr-v323-zhao26a %I PMLR %P 297--323 %U https://proceedings.mlr.press/v323/zhao26a.html %V 323 %X 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.
APA
Zhao, Y.. (2026). A novel hybrid approach for positive-valued DAG learning. Proceedings of the Fifth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 323:297-323 Available from https://proceedings.mlr.press/v323/zhao26a.html.

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