新方法KRCD可检测非线性单环境数据中的隐藏混杂因素。
Detecting Unobserved Confounders: A Kernelized Regression Approach
- 基于核函数空间建模复杂依赖关系，通过高低阶回归比较检测混杂
- 理论证明：无限样本下系数一致仅当无隐藏混杂，有限样本差异服从可计算的正态分布
- 在合成数据和双胞胎数据集上优于现有方法，计算效率高
在观察性研究中，检测隐藏混杂因素对可靠因果推断至关重要。现有方法要么依赖线性假设，要么需要多个异质环境，难以适用于非线性单环境场景。为此，我们提出核回归混杂检测（KRCD），一种用于非线性单环境观测数据中隐藏混杂检测的新方法。KRCD利用再生核希尔伯特空间建模复杂依赖关系，通过比较标准与高阶核回归，构造出一个检验统计量；其显著偏离零值表明存在隐藏混杂。理论上，我们证明了两个关键结果：第一，在无限样本下，回归系数一致当且仅当不存在隐藏混杂；第二，有限样本下系数差异收敛于均值为零的高斯分布，且方差可解析计算。在合成基准和Twins数据集上的大量实验表明，KRCD不仅性能超越现有基线，还具有更优的计算效率。
原文摘要 · Abstract (English)
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.
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