Doubly robust identification of treatment effects from multiple environments

TL;DR

RAMEN tackles the challenge of identifying treatment effects from observational data in the presence of bad controls and unobserved variables by exploiting heterogeneity across multiple environments. It introduces a doubly robust identification framework that requires only partial knowledge of the causal graph: either the parents of the treatment are observed and invariant, or the parents of the outcome are observed and invariant, across environments. The methodology combines a population-level invariant-set formulation with practical finite-sample estimators, including a kernelized invariance loss and a differentiable Gumbel-trick approach for scalable covariate selection. Empirical evaluations on synthetic, semi-synthetic, and real-world data demonstrate strong performance relative to baselines, with a real-world maternal smoking–birth weight analysis aligning with established epidemiological findings. Together, these contributions advance causal identification under bad controls and unobserved confounding by leveraging cross-environment heterogeneity for robust ATE estimation.

Abstract

Practical and ethical constraints often require the use of observational data for causal inference, particularly in medicine and social sciences. Yet, observational datasets are prone to confounding, potentially compromising the validity of causal conclusions. While it is possible to correct for biases if the underlying causal graph is known, this is rarely a feasible ask in practical scenarios. A common strategy is to adjust for all available covariates, yet this approach can yield biased treatment effect estimates, especially when post-treatment or unobserved variables are present. We propose RAMEN, an algorithm that produces unbiased treatment effect estimates by leveraging the heterogeneity of multiple data sources without the need to know or learn the underlying causal graph. Notably, RAMEN achieves doubly robust identification: it can identify the treatment effect whenever the causal parents of the treatment or those of the outcome are observed, and the node whose parents are observed satisfies an invariance assumption. Empirical evaluations on synthetic and real-world datasets show that our approach outperforms existing methods.

Figures (10)

• Figure 1: Two causal graphs illustrating when the set of all covariates is or is not a valid adjustment set: (a) $\{X_1, X_2\}$ blocks all backdoor paths between $T$ and $Y$, making it a valid adjustment set; (b) $X_1$ opens a backdoor path between $T$ and $Y$, introducing bias in the treatment effect estimate if adjusted for. Unobserved variables are dashed and colored in white, bad controls are colored in red, and good controls---covariates that can be included in the adjustment set---are colored in green.
• Figure 2: (Top row) Graphical models illustrating three scenarios in which the unobserved confounder $U$ may break different invariances between $T$, $Y$, and the observed covariates $X$. In each graph, dashed arrows denote optional edges, dashed nodes indicate unobserved variables, green and red nodes indicate good and bad controls, respectively. Panel (a) shows the case where $U$ does not break any invariance. Panel (b) shows the case where $U$ breaks the invariance between $X_p$ and $T$. Panel (c) shows the case where $U$ breaks the invariance between $X_p$ and $Y$. (Bottom row) Mean absolute errors are shown across $5$ environments ($n=2500$, $d=5$ observed covariates), with error bars representing standard errors over 20 runs.
• Figure 3: We plot the mean absolute error averaged across environments when the $T$-invariance is preserved. We sample $n=2000$ points for each environment; we report mean and standard error over $100$ runs.
• Figure 4: Mean absolute error averaged across environments for the IHDP dataset when different invariances are preserved (T, Y, or both). We consider five environments with $n=748$ points each; mean and standard error are reported over $20$ runs.
• Figure 5: ATE estimates for the Cattaneo2 dataset using different baselines. We report the mean and standard deviation over $100$ initializations of the random seeds in the algorithms.

Theorems & Definitions (3)

• Theorem 1: Doubly robust identification
• Example C.1: Post-treatment variables
• Example D.1: Post-treatment variables