Non-negative DAG Learning from Time-Series Data

2025/12/08 by Rey, Samuel, Mateos, Gonzalo
Computer Science · Mathematics · #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Machine Learning in Healthcare #Signal Processing (eess.SP) #Statistical Methods and Inference #Time Series Analysis and Forecasting #electronic engineering #information engineering

paper · doi:10.48550/arxiv.2512.07267

openalex publication_date 2025/12/08 · openalex created_date 2025/12/10 · openalex updated_date 2026/07/28

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.

Citations

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• Network Topology Inference from Spectral Templates
• How to learn a graph from smooth signals
• Выпуклая оптимизация
• Large-Sample Learning of Bayesian Networks is NP-Hard

Related

• Causal Structural Learning from Time Series: A Convex Optimization Approach
• Non-negative Weighted DAG Structure Learning
• LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Data
• Bayesian Inference for High-dimensional Time Series with a Stationary Directed Acyclic Graphical Structure
• A polynomial-time algorithm for learning nonparametric causal graphs