# Causal Structural Learning from Time Series: A Convex Optimization Approach

arXiv: https://arxiv.org/abs/2301.11336 · HTML: https://mlsanity.com/paper/2301.11336/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 25 references that are in the map.
- First posted on arXiv 26 Jan 2023.

## Builds on (most cited first, 12 of 12)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [On Low Rank Directed Acyclic Graphs and Causal Structure Learning](https://mlsanity.com/paper/2006.05691/) (2020)
- [Integer Programming for Learning Directed Acyclic Graphs from Continuous Data](https://mlsanity.com/paper/1904.10574/) (2019)
- [Learning Network of Multivariate Hawkes Processes: A Time Series Approach](https://mlsanity.com/paper/1603.04319/) (2016)

## Abstract (arXiv)

Structural learning, which aims to learn directed acyclic graphs (DAGs) from observational data, is foundational to causal reasoning and scientific discovery. Recent advancements formulate structural learning into a continuous optimization problem; however, DAG learning remains a highly non-convex problem, and there has not been much work on leveraging well-developed convex optimization techniques for causal structural learning. We fill this gap by proposing a data-adaptive linear approach for causal structural learning from time series data, which can be conveniently cast into a convex optimization problem using a recently developed monotone operator variational inequality (VI) formulation. Furthermore, we establish non-asymptotic recovery guarantee of the VI-based approach and show the superior performance of our proposed method on structure recovery over existing methods via extensive numerical experiments.