Detecting Unobserved Confounders: A Kernelized Regression Approach

TL;DR

This paper introduces KRCD, a kernel-based method for detecting unobserved confounders in nonlinear observational data within a single environment, addressing limitations of existing approaches.

Contribution

KRCD is the first method to detect unobserved confounders in nonlinear single-environment settings using kernel regression techniques.

Findings

KRCD outperforms existing methods on synthetic benchmarks.

KRCD achieves higher computational efficiency.

Theoretical guarantees link regression coefficients to confounder presence.

Abstract

Detecting unobserved confounders is crucial for reliable causal inference in observational studies. Existing methods require either linearity assumptions or multiple heterogeneous environments, limiting applicability to nonlinear single-environment settings. To bridge this gap, we propose Kernel Regression Confounder Detection (KRCD), a novel method for detecting unobserved confounding in nonlinear observational data under single-environment conditions. KRCD leverages reproducing kernel Hilbert spaces to model complex dependencies. By comparing standard and higherorder kernel regressions, we derive a test statistic whose significant deviation from zero indicates unobserved confounding. Theoretically, we prove two key results: First, in infinite samples, regression coefficients coincide if and only if no unobserved confounders exist. Second, finite-sample differences converge to zero-mean Gaussian distributions with tractable variance. Extensive experiments on synthetic benchmarks and the Twins dataset demonstrate that KRCD not only outperforms existing baselines but also achieves superior computational efficiency.