[Paper Review] Learning sources of variability from high-dimensional observational studies

Eric Bridgeford, Jaewon Chung+7 more|arXiv (Cornell University)|Jul 26, 2023

Advanced Causal Inference TechniquesMathematics3 citations

TL;DR

This paper proposes Causal cDcorr, a novel framework that generalizes causal inference to high-dimensional, arbitrary-distribution outcomes and nominal treatment variables by transforming conditional independence tests into universally consistent causal discrepancy tests. It improves finite-sample validity and power over existing methods, especially under model misspecification or covariate imbalance.

ABSTRACT

Causal inference studies whether the presence of a variable influences an observed outcome. As measured by quantities such as the "average treatment effect," this paradigm is employed across numerous biological fields, from vaccine and drug development to policy interventions. Unfortunately, the majority of these methods are often limited to univariate outcomes. Our work generalizes causal estimands to outcomes with any number of dimensions or any measurable space, and formulates traditional causal estimands for nominal variables as causal discrepancy tests. We propose a simple technique for adjusting universally consistent conditional independence tests and prove that these tests are universally consistent causal discrepancy tests. Numerical experiments illustrate that our method, Causal CDcorr, leads to improvements in both finite sample validity and power when compared to existing strategies. Our methods are all open source and available at github.com/ebridge2/cdcorr.

Motivation & Objective

• To address the gap in causal inference methods that can handle high-dimensional, arbitrary-distribution outcomes and nominal treatment variables.
• To unify conditional independence testing with causal discrepancy testing under general statistical assumptions.
• To improve finite-sample performance of causal inference in observational studies where standard assumptions may be violated.
• To extend causal estimands beyond binary treatments to multi-level nominal treatments.
• To provide a theoretically grounded, open-source framework for robust causal structure learning with nominal variables.

Proposed method

• The framework establishes that any universally consistent conditional independence test can be repurposed as a causal discrepancy test under mild regularity conditions.
• It introduces a transformation of observed data to better reflect the positivity assumption in observational studies, especially under covariate imbalance.
• Causal cDcorr is derived by modifying the cDcorr test to incorporate assumption-driven pre-processing that enhances sensitivity and specificity.
• The method leverages generalized propensity scores to re-weight samples, improving finite-sample behavior under continuous or multivariate treatments.
• The approach is designed to maintain asymptotic theoretical guarantees while enhancing empirical performance in small samples.
• The framework supports both conditional and unconditional causal discrepancy testing, with direct extension to K-sample problems beyond binary treatments.

Experimental results

Research questions

• RQ1 Can conditional independence tests be systematically repurposed as causal discrepancy tests under general assumptions?
• RQ2 How can existing conditional independence tests be modified to improve finite-sample validity and power in observational studies?
• RQ3 To what extent does the proposed framework generalize beyond binary treatments to multi-level nominal treatments?
• RQ4 How does the method perform under model misspecification or covariate imbalance, common in high-dimensional observational data?
• RQ5 Can the framework be extended to continuous or multivariate treatments using generalized propensity scores?

Key findings

• Causal cDcorr demonstrates substantial improvements in finite-sample validity compared to existing methods like kernelCDTest in null experiments.
• The method shows increased statistical power with larger effect sizes, indicating stronger detection capability under alternative hypotheses.
• Causal cDcorr generalizes naturally to more than two treatment levels, enabling causal discrepancy testing in multi-group settings.
• The framework provides theoretical justification for using conditional independence tests as causal discrepancy tests under mild regularity conditions.
• The method maintains empirical validity and improves performance even when underlying assumptions of standard causal inference are violated.
• The open-source implementation at github.com/ebridge2/cdcorr enables reproducibility and extension to new applications in causal structure learning.