Efficient Symbolic Computations for Identifying Causal Effects

2026-04-22

AI Summary

This work addresses the challenge of determining causal effect identifiability in linear structural causal models with latent confounding, a problem traditionally hindered by the double-exponential computational complexity of Gröbner basis methods. The authors propose a novel symbolic computation algorithm that, for the first time, decides rational identifiability of causal effects in quasipolynomial time and efficiently computes the lowest-degree identification formula under a given maximum degree constraint. By integrating techniques from algebraic geometry with causal inference theory, the method substantially enhances algorithmic scalability and practical applicability, thereby overcoming a longstanding computational bottleneck in the field.

Technology Category

Machine Learning: Causal LearningReasoning under Uncertainty: CausalityKnowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semanticsResponsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Determining identifiability of causal effects from observational data under latent confounding is a central challenge in causal inference. For linear structural causal models, identifiability of causal effects is decidable through symbolic computation. However, standard approaches based on Gröbner bases become computationally infeasible beyond small settings due to their doubly exponential complexity. In this work, we study how to practically use symbolic computation for deciding rational identifiability. In particular, we present an efficient algorithm that provably finds the lowest degree identifying formulas. For a causal effect of interest, if there exists an identification formula of a prespecified maximal degree, our algorithm returns such a formula in quasi-polynomial time.

Problem

• causal inference
• identifiability
• symbolic computation
• latent confounding
• structural causal models

Innovation

• symbolic computation
• causal identifiability
• linear structural causal models
• quasi-polynomial algorithm
• rational identifiability