Detecting Unobserved Confounders: A Kernelized Regression Approach

• URL: http://arxiv.org/abs/2601.00200v1
• Date: Thu, 01 Jan 2026 04:26:02 GMT
• Title: Detecting Unobserved Confounders: A Kernelized Regression Approach
• Authors: Yikai Chen, Yunxin Mao, Chunyuan Zheng, Hao Zou, Shanzhi Gu, Shixuan Liu, Yang Shi, Wenjing Yang, Kun Kuang, Haotian Wang,
• Abstract summary: Kernel Regression Confounder Detection (KRCD) is a novel method for detecting unobserved confounding in nonlinear observational data under single-environment conditions.<n>Test statistic whose significant deviation from zero indicates unobserved confounding.<n>Experiments on synthetic benchmarks and the Twins dataset demonstrate that KRCD not only outperforms existing baselines but also achieves superior computational efficiency.
• Score: 46.52607207396279
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Sharp Convergence Rates for Masked Diffusion Models [53.117058231393834]
  We develop a total-variation based analysis for the Euler method that overcomes limitations.<n>Our results relax assumptions on score estimation, improve parameter dependencies, and establish convergence guarantees.<n>Overall, our analysis introduces a direct TV-based error decomposition along the CTMC trajectory and a decoupling-based path-wise analysis for FHS.
  arXiv  Detail & Related papers  (2026-02-26T00:47:51Z)
• Towards Self-Supervised Covariance Estimation in Deep Heteroscedastic Regression [102.24287051757469]
  We study self-supervised covariance estimation in deep heteroscedastic regression.<n>We derive an upper bound on the 2-Wasserstein distance between normal distributions.<n>Experiments over a wide range of synthetic and real datasets demonstrate that the proposed 2-Wasserstein bound coupled with pseudo label annotations results in a computationally cheaper yet accurate deep heteroscedastic regression.
  arXiv  Detail & Related papers  (2025-02-14T22:37:11Z)
• A Partial Initialization Strategy to Mitigate the Overfitting Problem in CATE Estimation with Hidden Confounding [44.874826691991565]
  Estimating the conditional average treatment effect (CATE) from observational data plays a crucial role in areas such as e-commerce, healthcare, and economics.<n>Existing studies mainly rely on the strong ignorability assumption that there are no hidden confounders.<n>Data collected from randomized controlled trials (RCT) do not suffer from confounding but are usually limited by a small sample size.
  arXiv  Detail & Related papers  (2025-01-15T15:58:16Z)
• On the Wasserstein Convergence and Straightness of Rectified Flow [54.580605276017096]
  Rectified Flow (RF) is a generative model that aims to learn straight flow trajectories from noise to data.<n>We provide a theoretical analysis of the Wasserstein distance between the sampling distribution of RF and the target distribution.<n>We present general conditions guaranteeing uniqueness and straightness of 1-RF, which is in line with previous empirical findings.
  arXiv  Detail & Related papers  (2024-10-19T02:36:11Z)
• Theory on Score-Mismatched Diffusion Models and Zero-Shot Conditional Samplers [49.97755400231656]
  We present the first performance guarantee with explicit dimensional dependencies for general score-mismatched diffusion samplers.<n>We show that score mismatches result in an distributional bias between the target and sampling distributions, proportional to the accumulated mismatch between the target and training distributions.<n>This result can be directly applied to zero-shot conditional samplers for any conditional model, irrespective of measurement noise.
  arXiv  Detail & Related papers  (2024-10-17T16:42:12Z)
• Selective Nonparametric Regression via Testing [54.20569354303575]
  We develop an abstention procedure via testing the hypothesis on the value of the conditional variance at a given point. Unlike existing methods, the proposed one allows to account not only for the value of the variance itself but also for the uncertainty of the corresponding variance predictor.
  arXiv  Detail & Related papers  (2023-09-28T13:04:11Z)
• Online Bootstrap Inference with Nonconvex Stochastic Gradient Descent Estimator [0.0]
  In this paper, we investigate the theoretical properties of gradient descent (SGD) for statistical inference in the context of convex problems. We propose two coferential procedures which may contain multiple error minima.
  arXiv  Detail & Related papers  (2023-06-03T22:08:10Z)
• Convergence of uncertainty estimates in Ensemble and Bayesian sparse model discovery [4.446017969073817]
  We show empirical success in terms of accuracy and robustness to noise with bootstrapping-based sequential thresholding least-squares estimator. We show that this bootstrapping-based ensembling technique can perform a provably correct variable selection procedure with an exponential convergence rate of the error rate.
  arXiv  Detail & Related papers  (2023-01-30T04:07:59Z)
• Data thinning for convolution-closed distributions [2.299914829977005]
  We propose data thinning, an approach for splitting an observation into two or more independent parts that sum to the original observation. We show that data thinning can be used to validate the results of unsupervised learning approaches.
  arXiv  Detail & Related papers  (2023-01-18T02:47:41Z)
• Binary Independent Component Analysis via Non-stationarity [7.283533791778359]
  We consider independent component analysis of binary data. We start by assuming a linear mixing model in a continuous-valued latent space, followed by a binary observation model. In stark contrast to the continuous-valued case, we prove non-identifiability of the model with few observed variables.
  arXiv  Detail & Related papers  (2021-11-30T14:23:53Z)
• Binary Classification of Gaussian Mixtures: Abundance of Support Vectors, Benign Overfitting and Regularization [39.35822033674126]
  We study binary linear classification under a generative Gaussian mixture model. We derive novel non-asymptotic bounds on the classification error of the latter. Our results extend to a noisy model with constant probability noise flips.
  arXiv  Detail & Related papers  (2020-11-18T07:59:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.