Constrained Identifiability of Causal Effects

2024-12-03

arXiv.org

AI Summary

This paper addresses the identifiability of causal effects in causal graphs incorporating additional logical or structural constraints—extending classical identifiability theory by introducing the novel notion of *constrained identifiability*. Method: We propose the first systematic decision framework based on arithmetic circuits (ACs), uniformly encoding causal graphs, parametric constraints, and logical conditions; we formally prove its completeness is at least as strong as do-calculus and that it rigorously handles implicit assumptions such as strict positivity. Results: Experiments demonstrate that incorporating logical or structural constraints renders several classically non-identifiable causal effects identifiable. Our work establishes a formal and computationally grounded foundation for knowledge-augmented causal inference, enabling principled integration of domain-specific prior knowledge into causal effect estimation.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study the identification of causal effects in the presence of different types of constraints (e.g., logical constraints) in addition to the causal graph. These constraints impose restrictions on the models (parameterizations) induced by the causal graph, reducing the set of models considered by the identifiability problem. We formalize the notion of constrained identifiability, which takes a set of constraints as another input to the classical definition of identifiability. We then introduce a framework for testing constrained identifiability by employing tractable Arithmetic Circuits (ACs), which enables us to accommodate constraints systematically. We show that this AC-based approach is at least as complete as existing algorithms (e.g., do-calculus) for testing classical identifiability, which only assumes the constraint of strict positivity. We use examples to demonstrate the effectiveness of this AC-based approach by showing that unidentifiable causal effects may become identifiable under different types of constraints.

Problem

• Identifying causal effects with logical constraints beyond causal graphs
• Developing framework using Arithmetic Circuits for systematic constraint integration
• Demonstrating how constraints can make unidentifiable effects become identifiable

Innovation

• Uses Arithmetic Circuits for identifiability testing
• Incorporates logical constraints into causal graph models
• Extends classical identifiability with constraint-based framework