# Exact Estimation of Multiple Directed Acyclic Graphs

arXiv: https://arxiv.org/abs/1404.1238 · HTML: https://mlsanity.com/paper/1404.1238/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2014.

## Built on by (most cited first, 5 of 5)

- [The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applications](https://mlsanity.com/paper/2412.01953/) (2024)
- [MM-DAG: Multi-task DAG Learning for Multi-modal Data -- with Application for Traffic Congestion Analysis](https://mlsanity.com/paper/2306.02831/) (2023)
- [NOTMAD: Estimating Bayesian Networks with Sample-Specific Structures and Parameters](https://mlsanity.com/paper/2111.01104/) (2021)
- [Leveraging heterogeneity for identifiability: Bayesian order-based learning of multiple DAGs](https://mlsanity.com/paper/2605.15639/) (2026)
- [Structure Learning on Clustered Data](https://mlsanity.com/paper/2607.08238/) (2026)

## Abstract (arXiv)

This paper considers the problem of estimating the structure of multiple related directed acyclic graph (DAG) models. Building on recent developments in exact estimation of DAGs using integer linear programming (ILP), we present an ILP approach for joint estimation over multiple DAGs, that does not require that the vertices in each DAG share a common ordering. Furthermore, we allow also for (potentially unknown) dependency structure between the DAGs. Results are presented on both simulated data and fMRI data obtained from multiple subjects.