COMPACT algorithm improves causal inference without pre-specified adjustment sets
New spectral method identifies causal adjustment scores from proxies alone, beating propensity scores.
Causal inference from observational data typically requires researchers to choose which confounding variables to adjust for—a process that is error-prone and fails when confounding is weak but distributed across many variables. Eric V. Strobl's new paper, COMPACT: Spectral Adjustment Scores from a Complete and Irreducible Causal Criterion (arXiv:2608.10305), takes a fundamentally different approach. Rather than relying on pre-specified adjustment sets, COMPACT examines all possible causal graphs among a candidate score, treatment, and outcome while allowing for latent (unmeasured) confounders. Under faithfulness assumptions, it derives the largest class of conditional and unconditional dependence relations whose truth is invariant to whether treatment actually causes the outcome, thereby defining the maximally specific graph class expressible through these relations.
COMPACT operationalizes this criterion through a generalized eigenvalue problem whose score space targets a balancing coordinate plus an outcome-guided coordinate. The theoretical analysis shows that sufficiently informative proxy variables can recover this span without directly observing the adjustment variables, which is crucial in applied settings where confounders are only measured indirectly. Strobl also characterizes estimation and causal errors and establishes bootstrap validity for the full procedure, meaning practitioners get reliable confidence intervals. Simulation studies and a real-data application demonstrate that COMPACT outperforms several existing alternatives, including propensity-score-based methods. With accompanying R code released, COMPACT offers a principled, automated path to more accurate treatment-effect estimation from messy, high-dimensional observational data.
- COMPACT solves a generalized eigenvalue problem to construct adjustment scores without requiring a pre-specified covariate set.
- It handles latent variables and proxy measurements, recovering the balancing/outcome-guided span under sufficient information conditions.
- Bootstrap-valid inference is established; COMPACT outperforms propensity-score alternatives in simulations and a real-data application.
Why It Matters
More reliable causal estimates from observational data means better decisions in medicine, economics, and machine learning—without hand-picking covariates.