# Causal Graph Discovery from Self and Mutually Exciting Time Series

arXiv: https://arxiv.org/abs/2106.02600 · HTML: https://mlsanity.com/paper/2106.02600/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 99 references that are in the map.
- First posted on arXiv 4 Jun 2021.

## Builds on (most cited first, 27 of 27)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [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)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [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)
- [Counterfactual Off-Policy Evaluation with Gumbel-Max Structural Causal Models](https://mlsanity.com/paper/1905.05824/) (2019)
- [Learning Neural Causal Models from Unknown Interventions](https://mlsanity.com/paper/1910.01075/) (2019)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [Learning Granger Causality for Hawkes Processes](https://mlsanity.com/paper/1602.04511/) (2016)
- [Granger Causality: A Review and Recent Advances](https://mlsanity.com/paper/2105.02675/) (2021)
- [Economy Statistical Recurrent Units For Inferring Nonlinear Granger Causality](https://mlsanity.com/paper/1911.09879/) (2019)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [CAUSE: Learning Granger Causality from Event Sequences using Attribution Methods](https://mlsanity.com/paper/2002.07906/) (2020)
- [Causal models for dynamical systems](https://mlsanity.com/paper/2001.06208/) (2020)
- [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)
- [Neural Granger Causality](https://mlsanity.com/paper/1802.05842/) (2018)
- [Learning Network of Multivariate Hawkes Processes: A Time Series Approach](https://mlsanity.com/paper/1603.04319/) (2016)
- [Scalable Matrix-valued Kernel Learning for High-dimensional Nonlinear Multivariate Regression and Granger Causality](https://mlsanity.com/paper/1408.2066/) (2014)
- [Low Rank and Structured Modeling of High-dimensional Vector Autoregressions](https://mlsanity.com/paper/1812.03568/) (2018)
- [Identifiability and Estimation of Structural Vector Autoregressive Models for Subsampled and Mixed Frequency Time Series](https://mlsanity.com/paper/1704.02519/) (2017)
- [Inferring serial correlation with dynamic backgrounds](https://mlsanity.com/paper/2101.10962/) (2021)

## Abstract (arXiv)

We present a generalized linear structural causal model, coupled with a novel data-adaptive linear regularization, to recover causal directed acyclic graphs (DAGs) from time series. By leveraging a recently developed stochastic monotone Variational Inequality (VI) formulation, we cast the causal discovery problem as a general convex optimization. Furthermore, we develop a non-asymptotic recovery guarantee and quantifiable uncertainty by solving a linear program to establish confidence intervals for a wide range of non-linear monotone link functions. We validate our theoretical results and show the competitive performance of our method via extensive numerical experiments. Most importantly, we demonstrate the effectiveness of our approach in recovering highly interpretable causal DAGs over Sepsis Associated Derangements (SADs) while achieving comparable prediction performance to powerful ``black-box'' models such as XGBoost. Thus, the future adoption of our proposed method to conduct continuous surveillance of high-risk patients by clinicians is much more likely.