A novel hybrid approach for positive-valued DAG learning

arXiv stat.ML / 4/13/2026

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Key Points

The paper introduces Hybrid Moment-Ratio Scoring (H-MRS), a causal discovery method for learning DAG structures from observational data where variables are inherently positive.
It leverages a moment-ratio criterion, \(\mathbb{E}[X_j^2]/\mathbb{E}[(\mathbb{E}[X_j\mid S])^2]\), to infer causal ordering using candidate parent sets in positive-valued domains.
H-MRS combines log-scale Ridge regression to estimate moment ratios with a greedy ordering step based on raw-scale moment ratios, then uses Elastic Net to select parents and form the final DAG.
Experiments on synthetic log-linear data show competitive precision and recall, and the approach is designed to be computationally efficient while respecting positivity constraints.
The authors argue the method is well-suited to real-world settings such as genomics and economics where multiplicative dynamics and nonnegative measurements are common.

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.