A novel hybrid approach for positive-valued DAG learning

Researcher Yao Zhao has introduced a new algorithm, the Hybrid Moment-Ratio Scoring (H-MRS), designed to tackle a specific but widespread challenge in causal discovery: learning causal structures from data where all variables are inherently positive. This scenario is common in fields like genomics, where gene expression levels are measured, and economics, where metrics like asset prices or company revenues are analyzed. Traditional causal discovery methods often assume additive relationships, but positive-valued data frequently follows multiplicative dynamics, making standard approaches less effective.

The H-MRS algorithm proposes a novel hybrid approach. Its core innovation is using a moment ratio—specifically, the ratio of the raw second moment of a variable to the second moment of its conditional expectation—as a criterion for determining causal ordering among variables. The method first uses log-scale Ridge regression to estimate these moment ratios efficiently. It then employs a greedy procedure to establish a causal order based on the raw-scale ratios, followed by a final parent selection step using Elastic Net regression to recover the complete Directed Acyclic Graph (DAG) structure.

Experiments on synthetic log-linear data, as detailed in the paper accepted at the CLeaR 2026 conference, demonstrate that H-MRS achieves competitive performance in terms of precision and recall for graph recovery. The authors highlight that the method is computationally efficient and naturally respects the positivity constraints of the data. This makes it a practical new tool for researchers and data scientists working in domains where understanding causality from observational, positive-only data is critical, potentially leading to more accurate models in bioinformatics and econometrics.