mlsanityData to 7 Oct 2026

Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding

arXiv 2103.15106 ↗First posted 28 Mar 2021stat.ML cs.LGcited by 9

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Abstract (arXiv)

Unobserved confounding is one of the greatest challenges for causal discovery. The case in which unobserved variables have a widespread effect on many of the observed ones is particularly difficult because most pairs of variables are conditionally dependent given any other subset, rendering the causal effect unidentifiable. In this paper we show that beyond conditional independencies, under the principle of independent mechanisms, unobserved confounding in this setting leaves a statistical footprint in the observed data distribution that allows for disentangling spurious and causal effects. Using this insight, we demonstrate that a sparse linear Gaussian directed acyclic graph among observed variables may be recovered approximately and propose an adjusted score-based causal discovery algorithm that may be implemented with general purpose solvers and scales to high-dimensional problems. We find, in addition, that despite the conditions we pose to guarantee causal recovery, performance in practice is robust to large deviations in model assumptions.

Key facts. Cited by 9 papers in the map (data through 7 Oct 2026). Builds on 21 of its 47 references that are in the map. First posted on arXiv 28 Mar 2021.

Builds on

21 of 47 references.

References · 21

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  2. 2019Learning Sparse Nonparametric DAGscited by 207
  3. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 186
  4. 2017Learning Independent Causal Mechanismscited by 104
  5. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 86
  6. 2013Learning Equivalence Classes of Bayesian Networks Structurescited by 75
  7. 2018Blessing of dimensionality: mathematical foundations of the statistical physics of datacited by 55
  8. 2013Learning Sparse Causal Models is not NP-hardcited by 48
  9. 2019Conditional Independence Testing using Generative Adversarial Networkscited by 36
  10. 2019Ordering-Based Causal Structure Learning in the Presence of Latent Variablescited by 26
  11. 2017Adaptive Estimation in Structured Factor Models with Applications to Overlapping Clusteringcited by 19
  12. 2017Robust causal structure learning with some hidden variablescited by 17
9 more
  1. 2018Detecting non-causal artifacts in multivariate linear regression modelscited by 16
  2. 2017Detecting confounding in multivariate linear models via spectral analysiscited by 14
  3. 2020Accounting for Unobserved Confounding in Domain Generalizationcited by 14
  4. 2015Learning Directed Acyclic Graphs with Penalized Neighbourhood Regressioncited by 12
  5. 2018Spectral Deconfounding via Perturbed Sparse Linear Modelscited by 12
  6. 2017Causal Dantzig: fast inference in linear structural equation models with hidden variables under additive interventionscited by 10
  7. 2015A lava attack on the recovery of sums of dense and sparse signalscited by 6
  8. 2015Large Covariance Estimation through Elliptical Factor Modelscited by 5
  9. 2018Who Learns Better Bayesian Network Structures: Accuracy and Speed of Structure Learning Algorithmscited by 4

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 3; 2024: 3; 2025: 1; 2026: 1.

9 papers.

  1. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  2. 2023Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learningcited by 15
  3. 2023Towards Bounding Causal Effects under Markov Equivalencecited by 8
  4. 2024psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learningcited by 3
  5. 2024Differentiable Causal Discovery For Latent Hierarchical Causal Modelscited by 3
  6. 2026Score-Based Causal Discovery of Latent Variable Causal Modelscited by 2
  7. 2022A Consistent Estimator for Confounding Strengthcited by 1
  8. 2024Revisiting Differentiable Structure Learning: Inconsistency of ℓ1 Penalty and Beyondcited by 1
  9. 2025Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Modelscited by 1