Exploiting Non-Negativity in DAG Structure Learning

2026-05-19

AI Summary

This work addresses the challenge of learning directed acyclic graphs (DAGs) from observational data generated by linear structural equation models, focusing on the case where edge weights are nonnegative. Leveraging this nonnegativity, the authors propose a concise continuous characterization of acyclicity. Building upon this formulation, they develop a nonnegative DAG learning model incorporating a regularization term and design an optimization algorithm based on the augmented Lagrangian method. Theoretical analysis demonstrates that, in the population setting, the true DAG is the unique global minimizer of the augmented Lagrangian function and that no spurious interior stationary points exist. Experiments on both synthetic and real-world datasets show that the proposed method outperforms state-of-the-art continuous DAG learning approaches, exhibiting a better-behaved optimization landscape and superior convergence properties.

Abstract

This work addresses the problem of learning directed acyclic graphs (DAGs) from nodal observations generated by a linear structural equation model. DAG learning is a central task in signal processing, machine learning, and causal inference, but it remains challenging because acyclicity is a global combinatorial property. Continuous acyclicity constraints have led to important algorithmic advances by replacing the discrete DAG constraint with smooth equality constraints. However, existing formulations still involve difficult non-convex optimization landscapes and may suffer from degenerate first-order optimality conditions. Here, we restrict attention to DAGs with non-negative edge weights and exploit this additional structure to obtain a simpler characterization of acyclicity. Building on this characterization, we formulate a regularized non-negative DAG learning problem and develop an algorithm based on the method of multipliers. We further analyze the benign optimization landscape induced by non-negativity. In the population regime, we show that the true DAG is the unique global minimizer of the proposed augmented-Lagrangian formulation; moreover, the landscape contains no spurious interior stationary points, and the true DAG is the only acyclic KKT point. Numerical experiments on synthetic and real-world data show that the proposed method improves over state-of-the-art continuous DAG-learning alternatives.

Problem

• DAG structure learning
• non-negativity
• acyclicity
• structural equation model
• causal inference

Innovation

• non-negative DAG learning
• acyclicity characterization
• augmented Lagrangian
• optimization landscape
• structural equation model