COMPACT: Spectral Adjustment Scores from a Complete and Irreducible Causal Criterion

2026-08-10

AI Summary

This study addresses the challenges in estimating causal effects from observational data, which are often hindered by uncertainty in confounder selection and the dispersed nature of confounding information. The authors propose the first adjustment scoring method grounded in a complete causal invariance criterion, constructing graph-specific optimal adjustment scores by identifying sets of dependencies invariant to causal direction. Their approach integrates generalized eigenvalue decomposition to jointly span a space informed by both covariate balance and outcome-guided coordinates. To ensure robust inference in the presence of latent variables, the method leverages proxy variables and bootstrap techniques. Extensive experiments demonstrate that the proposed method significantly outperforms existing approaches on both synthetic and real-world datasets, accurately recovering causal effects even when the true adjustment variables are not directly observed.

Abstract

Observational datasets frequently contain many baseline variables, yet investigators estimating causal effects may not know which variables to include in the adjustment set. Confounding information may also be distributed weakly across many variables. Propensity scores can simplify adjustment by reducing high-dimensional covariates to a scalar with binary treatment. Although the propensity score is the coarsest balancing score, this distributional optimality does not imply maximal specificity over causal graphs. We instead examine all causal graphs among a candidate score, treatment, and outcome while allowing latent variables. Under faithfulness, we identify the largest set of unconditional and conditional dependence relations whose truth is invariant to whether treatment causes the outcome, leaving treatment-effect estimation to the downstream analysis. This criterion defines the maximally specific graph class expressible through these relations. We then develop the proposed algorithm, which operationalizes the criterion through a generalized eigenvalue problem whose score space targets the span of a balancing coordinate and an outcome-guided coordinate. We show that sufficiently informative proxies can recover this span without direct observation of the adjustment variables, characterize the resulting estimation and causal errors, and establish bootstrap validity for the complete procedure. Simulations and a real-data application demonstrate superior performance over several alternatives.

Problem

• causal inference
• confounding
• adjustment set
• observational data
• balancing score

Innovation

• causal inference
• spectral adjustment
• balancing score
• latent variables
• generalized eigenvalue problem