# PACER: Acyclic Causal Discovery from Large-Scale Interventional Data

arXiv: https://arxiv.org/abs/2605.15353 · HTML: https://mlsanity.com/paper/2605.15353/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 48 references that are in the map.
- First posted on arXiv 14 May 2026.

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

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [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)
- [Learning Sparse Nonparametric DAGs](https://mlsanity.com/paper/1909.13189/) (2019)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization](https://mlsanity.com/paper/2209.08037/) (2022)
- [Causal-learn: Causal Discovery in Python](https://mlsanity.com/paper/2307.16405/) (2023)
- [Efficient Neural Causal Discovery without Acyclicity Constraints](https://mlsanity.com/paper/2107.10483/) (2021)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [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)
- [Greedy Relaxations of the Sparsest Permutation Algorithm](https://mlsanity.com/paper/2206.05421/) (2022)
- [Large-Scale Differentiable Causal Discovery of Factor Graphs](https://mlsanity.com/paper/2206.07824/) (2022)
- [Fast Scalable and Accurate Discovery of DAGs Using the Best Order Score Search and Grow-Shrink Trees](https://mlsanity.com/paper/2310.17679/) (2023)
- [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)
- [On Low Rank Directed Acyclic Graphs and Causal Structure Learning](https://mlsanity.com/paper/2006.05691/) (2020)
- [A Meta-Learning Approach to Bayesian Causal Discovery](https://mlsanity.com/paper/2412.16577/) (2024)
- [A Tutorial on Regularized Partial Correlation Networks](https://mlsanity.com/paper/1607.01367/) (2016)
- [Low-variance Black-box Gradient Estimates for the Plackett-Luce Distribution](https://mlsanity.com/paper/1911.10036/) (2019)

## Abstract (arXiv)

Inferring the structure of directed acyclic graphs (DAGs) from data is a central challenge in causal discovery, particularly in modern high-dimensional settings where large-scale interventional data are increasingly available. While interventional data can improve identifiability, existing methods remain limited by soft acyclicity constraints, leading to optimization over invalid cyclic graphs, numerical instability, and reduced scalability. We introduce PACER (Perturbation-driven Acyclic Causal Edge Recovery), a scalable framework for causal discovery that guarantees acyclicity by construction. PACER parameterizes a distribution over DAGs through a joint model of variable permutations and edge probabilities, enabling direct optimization over valid causal structures without surrogate penalties. The framework supports a unified likelihood-based treatment of observational and interventional data, flexible conditional density models, and the incorporation of structural prior knowledge. For linear-Gaussian mechanisms, we derive closed-form expressions for the expected interventional log-likelihood and its gradients, yielding substantial computational gains. Empirically, PACER matches or exceeds state-of-the-art methods on protein signaling and large-scale genetic perturbation benchmarks, while scaling efficiently to networks with thousands of variables and achieving up to two orders of magnitude speedups over penalty-based differentiable approaches. These results demonstrate that exact and scalable causal discovery from high-dimensional perturbation data is achievable through principled search space design.