Data-Driven Information-Theoretic Causal Bounds under Unmeasured Confounding
Yonghan Jung, Bogyeong Kang
TL;DR
This work addresses the challenge of causal effect identification under unmeasured confounding by introducing a data-driven, information-theoretic framework for sharp partial identification. It derives an upper bound on the $f$-divergence between the observational law $P_{a,x}$ and the interventional law $Q_{a,x}$ as $D_f(P_{a,x}\| Q_{a,x})\le B_f(e_a(x))$, where $e_a(x)=\Pr(A=a\mid X=x)$ and $B_f(e)=e f(1/e)+(1-e)f(0)$. These divergence bounds enable covariate-conditional causal bounds for $\theta(a,x)=\mathbb{E}_{Q_{a,x}}[\varphi(Y)]$ that hold without outcome-bounding assumptions or external inputs, and without requiring full SCM modeling. A debiased semiparametric estimator satisfying Neyman orthogonality enables $\sqrt{n}$-consistent inference with flexible machine-learning nuisance functions, and ensemble aggregation over multiple divergences yields tight, valid bounds across data-generating processes. Empirical results on synthetic and semi-synthetic data demonstrate robust, tight bounds and valid coverage, showcasing the method’s practical impact for causal analysis under unmeasured confounding.
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.