# Linear Causal Discovery with Interventional Constraints

## TL;DR

This paper introduces interventional constraints to improve causal discovery by encoding known causal relationships as inequality constraints, leading to more accurate and explainable models.

## Contribution

The novel concept of interventional constraints allows encoding high-level causal knowledge as inequality constraints on causal effects.

## Key findings

- Integrating interventional constraints improves model accuracy and consistency with established findings.
- The method facilitates the discovery of new causal relationships at lower cost.
- The approach is evaluated on real-world datasets and shows promising results.

## Abstract

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 interventional constraints, 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 activated by PIP3, meaning PIP3 exerts a positive 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 inhibits 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 linear 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.