PACER: Acyclic Causal Discovery from Large-scale Interventional Data

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.

Understanding cause-and-effect relationships is a fundamental goal in science, often represented by diagrams called Directed Acyclic Graphs (DAGs). These diagrams use arrows to show how one variable influences another without creating infinite loops. Discovering these networks from massive datasets (like genetic information or protein signals) is incredibly difficult. We developed PACER, a new framework designed to find these causal networks more efficiently. Unlike previous methods that try to "punish" a program for creating loops, PACER is built so it physically cannot create invalid cycles. It achieves this by simultaneously learning the correct order of variables and the strength of the connections between them. Because PACER is mathematically streamlined, it can handle thousands of variables at once, far more than previous tools. In our tests on biological data, PACER was not only more accurate but also hundreds of times faster than competing methods. By providing a faster, more reliable way to map complex systems, PACER helps researchers turn massive amounts of experimental data into clear, actionable blueprints of cause-and-effect relationships in nature.