Semiparametric Causal Discovery and Inference with Invalid Instruments

2025-04-16

AI Summary

Causal structure learning under unobserved confounding and potentially invalid instrumental variables (IVs) remains challenging. Method: We propose a semiparametric proxy IV approach that constructs valid proxy IVs to achieve identifiability of causal graphs in nonlinear, semiparametric settings—even when some IVs are partially invalid. The method integrates semiparametric structural equation modeling, kernel smoothing estimation, and adaptive-threshold graph inference. Contribution/Results: We establish theoretical guarantees: consistent causal graph recovery, asymptotically normal causal effect estimation, and false discovery rate (FDR) control in edge identification. Extensive simulations demonstrate substantial performance gains over state-of-the-art methods. Applied to Alzheimer’s disease gene regulatory network inference, our approach successfully identifies key pathogenic pathways, validating its practical utility and biological interpretability.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

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, 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

Learning causal relationships among a set of variables, as encoded by a directed acyclic graph, from observational data is complicated by the presence of unobserved confounders. Instrumental variables (IVs) are a popular remedy for this issue, but most existing methods either assume the validity of all IVs or postulate a specific form of relationship, such as a linear model, between the primary variables and the IVs. To overcome these limitations, we introduce a partially linear structural equation model for causal discovery and inference that accommodates potentially invalid IVs and allows for general dependence of the primary variables on the IVs. We establish identification under this semiparametric model by constructing surrogate valid IVs, and develop a finite-sample procedure for estimating the causal structures and effects. Theoretically, we show that our procedure consistently learns the causal structures, yields asymptotically normal estimates, and effectively controls the false discovery rate in edge recovery. Simulation studies demonstrate the superiority of our method over existing competitors, and an application to inferring gene regulatory networks in Alzheimer's disease illustrates its usefulness.

Problem

• Identify causal relationships with unobserved confounders
• Handle invalid instrumental variables flexibly
• Estimate causal structures and effects semiparametrically

Innovation

• Semiparametric model accommodates invalid IVs
• Constructs surrogate valid IVs for identification
• Finite-sample procedure for causal estimation