Stochastic Neural Networks for Causal Inference with Missing Confounders

2026-03-01

AI Summary

This work addresses the challenge of causal inference in the presence of unmeasured confounding in observational data by proposing a causal graph modeling approach based on stochastic neural networks. The method integrates adaptive stochastic gradient Hamiltonian Monte Carlo to impute latent confounders, enabling consistent estimation of average potential outcomes under interventions. Under the assumption of capacity-constrained sparse deep neural networks, the authors establish theoretical guarantees for model identifiability and consistency of causal estimates, proving that the estimator remains invariant within observational equivalence classes. This framework naturally accommodates proxy variables, multiple causes, and overlap diagnostics. Empirical evaluations on both synthetic and benchmark datasets demonstrate that the proposed method achieves high estimation accuracy, favorable scalability, and reliable uncertainty quantification via bootstrap procedures.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

Unmeasured confounding is a fundamental obstacle to causal inference from observational data. Latent-variable methods address this challenge by imputing unobserved confounders, yet many lack explicit model-based identification guarantees and are difficult to extend to richer causal structures. We propose Confounder Imputation with Stochastic Neural Networks (CI-StoNet), which parameterizes the conditional structure of a causal directed acyclic graph using a stochastic neural network and imputes latent confounders via adaptive stochastic-gradient Hamiltonian Monte Carlo. Under SUTVA and overlap, and assuming that the structural components of the data-generating process are well approximated by a capacity-controlled sparse deep neural network class, we establish model identification and consistent estimation of the mean potential outcome under a fixed intervention within this class. Although the latent confounder is identifiable only up to reparameterizations that preserve the joint treatment-outcome distribution, the causal estimand is invariant across this observationally equivalent class. We further characterize the effect of overlap on estimation accuracy. Empirical results on simulated and benchmark datasets demonstrate accurate performance, and the framework extends naturally to proxy-variable and multiple-cause settings with overlap diagnostics and bootstrap-based uncertainty quantification.

Problem

• unmeasured confounding
• causal inference
• latent confounders
• observational data
• missing confounders

Innovation

• Stochastic Neural Networks
• Causal Inference
• Missing Confounders
• Model Identification
• Hamiltonian Monte Carlo