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arXiv · 2610.18075

Causal Discovery Under Hard Selection Bias: A New Robust Score-Matching Approach

Yiwen Qiu·Francesco Montagna·Shimeng Huang·Francesco Locatello
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Abstract

Selection bias is a difficult yet widespread problem in causal discovery, occurring whenever non-random selection processes lead to data that is not representative of the underlying populations. Due to its practical importance, related works have been proposed to address the problem under local [Versteeg et al., 2022] or interventional settings [Dai et al., 2025a], but general algorithms for observational data remain elusive. In this paper, we focus on truncated data (hard selection), and provide a general result for Additive Noise Models (ANM). We show that score-based methods are a surprisingly suitable candidate due to a special property of the score function ($\nabla \log p(x)$): deterministic truncation preserves both the score of the joint distribution as well as the Jacobian of the score. While established score-matching algorithms still fail in most settings, we actively leverage this observation to propose a new method for causal discovery that is robust under truncated data with ANMs. Overall, our approach offers a general, robust solution that is agnostic to external information about the selection process and still achieves comparable performance to the state-of-the-art approaches when selection is not present.

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Yiwen Qiu, Francesco Montagna, Shimeng Huang, Francesco Locatello. 2026-10-13. Causal Discovery Under Hard Selection Bias: A New Robust Score-Matching Approach. https://arxiv.org/abs/2610.18075

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