Detecting Unobserved Confounders: A Kernelized Regression Approach

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 higher-order 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.

Authors

• Yikai Chen National University of Defense Technology
• Yunxin Mao National University of Defense Technology
• Chunyuan Zheng Peking University
• Hao Zou Tsinghua University
• Shanzhi Gu National University of Defense Technology
• Shixuan Liu Australian National University
• Yang Shi School of Software, Shandong University, Jinan 250101, China
• Wenjing Yang National University of Defense Technology
• Kun Kuang Zhejiang University
• Haotian Wang JD Logistic

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