Linear Causal Discovery with Interventional Constraints

2025-10-30

AI Summary

Existing causal discovery methods, when incorporating structural constraints (e.g., enforcing the existence of the PIP3→Akt pathway), fail to guarantee correct directionality of causal effects—e.g., erroneously inferring “PIP3 inhibits Akt.” Method: We introduce *interventional constraints*: explicit inequality constraints on total causal effects between variables, addressing the directional limitations of conventional structural constraints. Within a linear causal model framework, we define a quantifiable metric for total causal effect and formulate a constrained optimization problem with inequality constraints. A two-stage constrained optimization algorithm is proposed to solve it efficiently. Results: Experiments on real-world biological datasets demonstrate that our method improves both model accuracy and interpretability while aligning with established biological knowledge. Crucially, it successfully identifies several novel causal relationships previously undetectable by standard approaches, substantially enhancing the reliability of causal inference.

Technology Category

• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction
• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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 (Sachs et al. 2005), 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 (for example, 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 propose 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.

Problem

• Incorporating causal knowledge to refine models and improve treatment design
• Introducing interventional constraints to encode high-level causal effect inequalities
• Ensuring learned causal models respect known influences and improve accuracy

Innovation

• Introduces interventional constraints for causal knowledge
• Proposes metric for total causal effects in linear models
• Uses two-stage constrained optimization for model learning