# Direct Estimation of Differences in Causal Graphs

arXiv: https://arxiv.org/abs/1802.05631 · HTML: https://mlsanity.com/paper/1802.05631/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2018.

## Built on by (most cited first, 14 of 14)

- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning](https://mlsanity.com/paper/2406.14302/) (2024)
- [Scalable Intervention Target Estimation in Linear Models](https://mlsanity.com/paper/2111.07512/) (2021)
- [An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis](https://mlsanity.com/paper/2311.18048/) (2023)
- [Identifying Patient-Specific Root Causes of Disease](https://mlsanity.com/paper/2205.11627/) (2022)
- [iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Models](https://mlsanity.com/paper/2306.17361/) (2023)
- [Identifying General Mechanism Shifts in Linear Causal Representations](https://mlsanity.com/paper/2410.24059/) (2024)
- [Root Cause Analysis of Outliers in Unknown Cyclic Graphs](https://mlsanity.com/paper/2510.06995/) (2025)
- [dotears: Scalable, consistent DAG estimation using observational and interventional data](https://mlsanity.com/paper/2305.19215/) (2023)
- [Bayesian causal discovery from unknown general interventions](https://mlsanity.com/paper/2312.00509/) (2023)
- [Causal reasoning in difference graphs](https://mlsanity.com/paper/2411.01292/) (2024)
- [Identifying biological perturbation targets through causal differential networks](https://mlsanity.com/paper/2410.03380/) (2024)
- [Detecting Changes in Causal Dependence with Kernels and Copulas](https://mlsanity.com/paper/2605.05809/) (2026)
- [Root cause analysis via difference graph discovery from linear time-series data](https://mlsanity.com/paper/2608.21117/) (2026)

## Abstract (arXiv)

We consider the problem of estimating the differences between two causal directed acyclic graph (DAG) models with a shared topological order given i.i.d. samples from each model. This is of interest for example in genomics, where changes in the structure or edge weights of the underlying causal graphs reflect alterations in the gene regulatory networks. We here provide the first provably consistent method for directly estimating the differences in a pair of causal DAGs without separately learning two possibly large and dense DAG models and computing their difference. Our two-step algorithm first uses invariance tests between regression coefficients of the two data sets to estimate the skeleton of the difference graph and then orients some of the edges using invariance tests between regression residual variances. We demonstrate the properties of our method through a simulation study and apply it to the analysis of gene expression data from ovarian cancer and during T-cell activation.