# Detecting Unobserved Confounders: A Kernelized Regression Approach

arXiv: https://arxiv.org/abs/2601.00200 · HTML: https://mlsanity.com/paper/2601.00200/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 37 references that are in the map.
- First posted on arXiv 1 Jan 2026.

## Builds on (most cited first, 13 of 13)

- [Kernel Mean Embedding of Distributions: A Review and Beyond](https://mlsanity.com/paper/1605.09522/) (2016)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Removing Hidden Confounding by Experimental Grounding](https://mlsanity.com/paper/1810.11646/) (2018)
- [Proximal Causal Learning with Kernels: Two-Stage Estimation and Moment Restriction](https://mlsanity.com/paper/2105.04544/) (2021)
- [Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesis](https://mlsanity.com/paper/2206.02013/) (2022)
- [Kernel-based Tests for Joint Independence](https://mlsanity.com/paper/1603.00285/) (2016)
- [Detecting confounding in multivariate linear models via spectral analysis](https://mlsanity.com/paper/1704.01430/) (2017)
- [Detecting hidden confounding in observational data using multiple environments](https://mlsanity.com/paper/2205.13935/) (2022)
- [Multiple Robust Learning for Recommendation](https://mlsanity.com/paper/2207.10796/) (2022)
- [Kernel Balancing: A flexible non-parametric weighting procedure for estimating causal effects](https://mlsanity.com/paper/1605.00155/) (2016)
- [Label Distribution Learning with Biased Annotations by Learning Multi-Label Representation](https://mlsanity.com/paper/2502.01170/) (2025)
- [Higher-order least squares: assessing partial goodness of fit of linear causal models](https://mlsanity.com/paper/2109.14544/) (2021)
- [Confounder Detection in High Dimensional Linear Models using First Moments of Spectral Measures](https://mlsanity.com/paper/1803.06852/) (2018)

## Built on by (most cited first, 2 of 2)

- [When Tabular Foundation Models Meet Strategic Tabular Data: A Prior Alignment Approach](https://mlsanity.com/paper/2605.19662/) (2026)
- [Beyond Rational Illusion: Behaviorally Realistic Strategic Classification](https://mlsanity.com/paper/2605.19674/) (2026)

## Abstract (arXiv)

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.