# Large-Scale Bayesian Causal Discovery with Interventional Data

arXiv: https://arxiv.org/abs/2510.01562 · HTML: https://mlsanity.com/paper/2510.01562/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 52 references that are in the map.
- First posted on arXiv 2 Oct 2025.

## Builds on (most cited first, 21 of 21)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [BCD Nets: Scalable Variational Approaches for Bayesian Causal Discovery](https://mlsanity.com/paper/2112.02761/) (2021)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions](https://mlsanity.com/paper/1301.6697/) (2013)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [BayesDAG: Gradient-Based Posterior Inference for Causal Discovery](https://mlsanity.com/paper/2307.13917/) (2023)
- [Stable Differentiable Causal Discovery](https://mlsanity.com/paper/2311.10263/) (2023)
- [Pathfinder: Parallel quasi-Newton variational inference](https://mlsanity.com/paper/2108.03782/) (2021)
- [BaCaDI: Bayesian Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2206.01665/) (2022)
- [Instrumental Variables: An Econometrician's Perspective](https://mlsanity.com/paper/1410.0163/) (2014)
- [Minimal I-MAP MCMC for Scalable Structure Discovery in Causal DAG Models](https://mlsanity.com/paper/1803.05554/) (2018)
- [Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders](https://mlsanity.com/paper/2402.14781/) (2024)
- [dotears: Scalable, consistent DAG estimation using observational and interventional data](https://mlsanity.com/paper/2305.19215/) (2023)
- [Nonparametric identification and efficient estimation of causal effects with instrumental variables](https://mlsanity.com/paper/2402.09332/) (2024)

## Abstract (arXiv)

Inferring the causal relationships among a set of variables in the form of a directed acyclic graph (DAG) is an important but notoriously challenging problem. Recently, advancements in high-throughput genomic perturbation screens have inspired development of methods that leverage interventional data to improve model identification. However, existing methods still suffer poor performance on large-scale tasks and fail to quantify uncertainty. Here, we propose Interventional Bayesian Causal Discovery (IBCD), an empirical Bayesian framework for causal discovery with interventional data. Our approach models the likelihood of the matrix of total causal effects, which can be approximated by a matrix normal distribution, rather than the full data matrix. We place a spike-and-slab horseshoe prior on the edges and separately learn data-driven weights for scale-free and ErdHos-R'enyi structures from observational data, treating each edge as a latent variable to enable uncertainty-aware inference. Through extensive simulation, we show that IBCD achieves superior structure recovery compared to existing baselines. We apply IBCD to CRISPR perturbation (Perturb-seq) data on 521 genes, demonstrating that edge posterior inclusion probabilities enable identification of robust graph structures.