mlsanityData to 14 Oct 2026

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

arXiv 2610.18075 ↗First posted 13 Oct 2026cs.LGcited by 0

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Abstract (arXiv)

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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References · 17

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  2. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  3. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 178
  4. 2013Causal Inference in the Presence of Latent Variables and Selection Biascited by 166
  5. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 111
  6. 2023Causal-learn: Causal Discovery in Pythoncited by 109
  7. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 66
  8. 2022Greedy Relaxations of the Sparsest Permutation Algorithmcited by 64
  9. 2023Scalable Causal Discovery with Score Matchingcited by 45
  10. 2017Inference via low-dimensional couplingscited by 44
  11. 2022Local Constraint-Based Causal Discovery under Selection Biascited by 16
  12. 2018FASK with Interventional Knowledge Recovers Edges from the Sachs Modelcited by 14
5 more
  1. 2024Score matching through the roof: linear, nonlinear, and latent variables causal discoverycited by 10
  2. 2025When Selection Meets Intervention: Additional Complexities in Causal Discoverycited by 10
  3. 2025Gene Regulatory Network Inference in the Presence of Selection Bias and Latent Confounderscited by 7
  4. 2025Latent Variable Causal Discovery under Selection Biascited by 7
  5. 2023Causal Discovery and Optimal Experimental Design for Genome-Scale Biological Network Recoverycited by 2

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