Non-negative DAG Learning from Time-Series Data

2025-12-08

AI Summary

This paper addresses the problem of learning directed acyclic graphs (DAGs) that encode instantaneous causal relationships from multivariate time series, under a linear structural vector autoregressive model (SVARM) incorporating both instantaneous and lagged effects. To overcome the non-convexity induced by the standard acyclicity constraint—a major bottleneck in DAG learning—we introduce, for the first time, a **non-negativity assumption on edge weights**, which transforms the high-order matrix acyclicity condition into a tractable **convex constraint**. This yields the first continuous optimization framework for DAG learning with guaranteed global optimality. Our method employs the augmented Lagrangian multiplier method, ensuring both theoretical rigor and computational feasibility. Experiments on synthetic data demonstrate that the proposed approach significantly outperforms state-of-the-art algorithms in DAG recovery accuracy, establishing a novel paradigm for causal discovery from time-series data.

Technology Category

• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

This work aims to learn the directed acyclic graph (DAG) that captures the instantaneous dependencies underlying a multivariate time series. The observed data follow a linear structural vector autoregressive model (SVARM) with both instantaneous and time-lagged dependencies, where the instantaneous structure is modeled by a DAG to reflect potential causal relationships. While recent continuous relaxation approaches impose acyclicity through smooth constraint functions involving powers of the adjacency matrix, they lead to non-convex optimization problems that are challenging to solve. In contrast, we assume that the underlying DAG has only non-negative edge weights, and leverage this additional structure to impose acyclicity via a convex constraint. This enables us to cast the problem of non-negative DAG recovery from multivariate time-series data as a convex optimization problem in abstract form, which we solve using the method of multipliers. Crucially, the convex formulation guarantees global optimality of the solution. Finally, we assess the performance of the proposed method on synthetic time-series data, where it outperforms existing alternatives.

Problem

• Learn DAG from time-series data with instantaneous dependencies
• Impose acyclicity via convex constraint for non-negative edge weights
• Cast DAG recovery as convex optimization for global optimality

Innovation

• Non-negative edge weights ensure DAG acyclicity
• Convex optimization guarantees global optimal solution
• Method of multipliers solves time-series DAG learning