Linear Causal Discovery with Interventional Constraints

Incorporating causal knowledge and mechanisms is essential for refining causal models and improving downstream tasks, such as designing new treatments. In this paper, we introduce a novel concept in causal discovery, termed <i>interventional constraints</i>, which differs fundamentally from interventional data. While interventional data require direct perturbations of variables, interventional constraints encode high-level causal knowledge in the form of inequality constraints on causal effects. For instance, in the Sachs dataset, Akt has been shown to be <i>activated</i> by PIP3, meaning PIP3 exerts a <i>positive</i> causal effect on Akt. Existing causal discovery methods allow enforcing structural constraints (e.g., requiring a causal path from PIP3 to Akt), but they may still produce incorrect causal conclusions, such as learning that "PIP3 <i>inhibits</i> Akt." Interventional constraints bridge this gap by explicitly constraining the total causal effect between variable pairs, ensuring learned models respect known causal influences. To formalize interventional constraints, we adopt a metric to quantify total causal effects for <i>linear</i> causal models and formulate the problem as a constrained optimization task, solved using a two-stage constrained optimization method. We evaluate our approach on real-world datasets and demonstrate that integrating interventional constraints not only improves model accuracy and ensures consistency with established findings, making models more explainable, but also facilitates the discovery of new causal relationships that would otherwise be costly to identify.