# ExDBN: Learning Dynamic Bayesian Networks using Extended Mixed-Integer Programming Formulations

arXiv: https://arxiv.org/abs/2410.16100 · HTML: https://mlsanity.com/paper/2410.16100/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 43 references that are in the map.
- First posted on arXiv 21 Oct 2024.

## Builds on (most cited first, 13 of 13)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [DYNOTEARS: Structure Learning from Time-Series Data](https://mlsanity.com/paper/2002.00498/) (2020)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Discovering contemporaneous and lagged causal relations in autocorrelated nonlinear time series datasets](https://mlsanity.com/paper/2003.03685/) (2020)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Unsuitability of NOTEARS for Causal Graph Discovery](https://mlsanity.com/paper/2104.05441/) (2021)
- [Neural graphical modelling in continuous-time: consistency guarantees and algorithms](https://mlsanity.com/paper/2105.02522/) (2021)
- [Fast Scalable and Accurate Discovery of DAGs Using the Best Order Score Search and Grow-Shrink Trees](https://mlsanity.com/paper/2310.17679/) (2023)
- [Complexity theoretic limitations on learning DNF's](https://mlsanity.com/paper/1404.3378/) (2014)
- [Integer Programming for Learning Directed Acyclic Graphs from Continuous Data](https://mlsanity.com/paper/1904.10574/) (2019)
- [Dynamic Network Models for Forecasting](https://mlsanity.com/paper/1303.5396/) (2013)
- [Causal inference in drug discovery and development](https://mlsanity.com/paper/2209.14664/) (2022)
- [Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Models](https://mlsanity.com/paper/2404.12592/) (2024)

## Abstract (arXiv)

Causal learning from data has received much attention recently. Bayesian networks can be used to capture causal relationships. There, one recovers a weighted directed acyclic graph in which random variables are represented by vertices, and the weights associated with each edge represent the strengths of the causal relationships between them. This concept is extended to capture dynamic effects by introducing a dependency on past data, which may be captured by the structural equation model. This formalism is utilized in the present contribution to propose a score-based learning algorithm. A mixed-integer quadratic program is formulated and an algorithmic solution proposed, in which the pre-generation of exponentially many acyclicity constraints is avoided by utilizing the so-called branch-and-cut (``lazy constraint'') method. Comparing the novel approach to the state-of-the-art, we show that the proposed approach turns out to produce more accurate results when applied to small and medium-sized synthetic instances containing up to 80 time series. Lastly, two interesting applications in bioscience and finance, to which the method is directly applied, further stress the importance of developing highly accurate, globally convergent solvers that can handle instances of modest size.