Information-Theoretic Causal Bounds under Unmeasured Confounding

2026-01-23

AI Summary

This work proposes a data-driven information-theoretic framework for sharp partial identification of conditional causal effects in the presence of unobserved confounding. The approach relies solely on an upper bound on the f-divergence between the propensity scores under treatment and control, without requiring instrumental variables, sensitivity parameters, or structural modeling assumptions. By integrating f-divergence constraints, propensity score modeling, Neyman-orthogonal semiparametric estimators, and flexible machine learning methods, the framework overcomes key limitations in existing literature—such as restrictions to discrete or bounded outcomes, dependence on parametric structural models, and the inability to account for covariate-specific conditional effects—within a unified setting. Simulations and real-data analyses demonstrate that the method yields tight and valid bounds on causal effects across diverse data-generating mechanisms.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

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
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

We develop a data-driven information-theoretic framework for sharp partial identification of causal effects under unmeasured confounding. Existing approaches often rely on restrictive assumptions, such as bounded or discrete outcomes; require external inputs (for example, instrumental variables, proxies, or user-specified sensitivity parameters); necessitate full structural causal model specifications; or focus solely on population-level averages while neglecting covariate-conditional treatment effects. We overcome all four limitations simultaneously by establishing novel information-theoretic, data-driven divergence bounds. Our key theoretical contribution shows that the f-divergence between the observational distribution P(Y | A = a, X = x) and the interventional distribution P(Y | do(A = a), X = x) is upper bounded by a function of the propensity score alone. This result enables sharp partial identification of conditional causal effects directly from observational data, without requiring external sensitivity parameters, auxiliary variables, full structural specifications, or outcome boundedness assumptions. For practical implementation, we develop a semiparametric estimator satisfying Neyman orthogonality (Chernozhukov et al., 2018), which ensures square-root-n consistent inference even when nuisance functions are estimated using flexible machine learning methods. Simulation studies and real-world data applications, implemented in the GitHub repository (https://github.com/yonghanjung/Information-Theretic-Bounds), demonstrate that our framework provides tight and valid causal bounds across a wide range of data-generating processes.

Problem

• unmeasured confounding
• causal inference
• partial identification
• information theory
• conditional treatment effects

Innovation

• information-theoretic bounds
• unmeasured confounding
• partial identification
• f-divergence
• Neyman orthogonality