---
title: "Learning Kernelized Hypothesis for Hidden Confounder Detection"
authors:
  - "Yikai Chen"
  - "Haotian Wang"
  - "Yunxin Mao"
  - "Xinpeng Lv"
  - "Shaowu Yang"
  - "Kun Kuang"
  - "Xinwang Liu"
  - "Wenjing Yang"
doi: "10.24963/ijcai.2026/467"
url: "https://ijcai.org/proceedings/2026/467"
pdf: "https://ijcai.org/proceedings/2026/0467.pdf"
venue: "Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence"
year: 2026
pages: "4197-4205"
track: "Main Track"
keywords:
  - "Machine Learning: Causality"
---

# Learning Kernelized Hypothesis for Hidden Confounder Detection

Yikai Chen, Haotian Wang, Yunxin Mao, Xinpeng Lv, Shaowu Yang, Kun Kuang, Xinwang Liu, Wenjing Yang

*Proceedings of the Thirty-Fifth International Joint Conference on Artificial Intelligence*, pages 4197-4205. DOI: [10.24963/ijcai.2026/467](https://doi.org/10.24963/ijcai.2026/467)

## Abstract

Detecting hidden confounding is crucial for reliable causal analysis from observational data, directly determining which downstream causal inference method to be deployed. Inspired by the theory of higher-order regression, recent sample-efficient hypothesis testing strategies overcome the restrictive requirement of multiple heterogeneous data environment. Despite their progress on single-environment confounder detection, such methods suffer from intrinsic flaws that the structural functions of the causal models should be specified in prior (linear or specific kernel functions). By contrast, real-world data acquisition exhibits diverse, unknown forms of structural functions, imposing an important but challenging gap between theories of higher-order regressions to practical confounder detection. In this paper, we contribute a Bi-level Kernel Confounder Detection (BiKCD) framework by learning adaptive kernelized structural space of structural functions. Subsequently, our BiKCD constructs hypothesis testing by comparing coefficients from the higher-order regression and the classical ordinary least squares in learned kernelized space. Finally, the hypothesis is calibrated to ensure valid inference under adaptivity. Theoretically, we establish an oracle-type risk bound for the selected structural space over a candidate kernel family, with the Type-I error control for the downstream test. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed BiKCD.