mlsanityData to 14 Oct 2026

Markov Equivalence and Consistency in Differentiable Structure Learning

arXiv 2410.06163 ↗First posted 8 Oct 2024stat.ML cs.LG math.STcited by 7

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Abstract (arXiv)

Existing approaches to differentiable structure learning of directed acyclic graphs (DAGs) rely on strong identifiability assumptions in order to guarantee that global minimizers of the acyclicity-constrained optimization problem identifies the true DAG. Moreover, it has been observed empirically that the optimizer may exploit undesirable artifacts in the loss function. We explain and remedy these issues by studying the behavior of differentiable acyclicity-constrained programs under general likelihoods with multiple global minimizers. By carefully regularizing the likelihood, it is possible to identify the sparsest model in the Markov equivalence class, even in the absence of an identifiable parametrization. We first study the Gaussian case in detail, showing how proper regularization of the likelihood defines a score that identifies the sparsest model. Assuming faithfulness, it also recovers the Markov equivalence class. These results are then generalized to general models and likelihoods, where the same claims hold. These theoretical results are validated empirically, showing how this can be done using standard gradient-based optimizers, thus paving the way for differentiable structure learning under general models and losses.

Key facts. Cited by 7 papers in the map (data through 14 Oct 2026). Builds on 33 of its 72 references that are in the map. First posted on arXiv 8 Oct 2024.

Builds on

33 of 72 references.

References · 33

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21 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 3; 2026: 4.

7 papers.

  1. 2025DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confoundingcited by 2
  2. 2025Causal Mechanism Estimation in Multi-Sensor Systems Across Multiple Domainscited by 0
  3. 2025Differentiable Structure Learning and Causal Discovery for General Binary Datacited by 0
  4. 2026Structure Learning on Clustered Datacited by 0
  5. 2026Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificatescited by 0
  6. 2026xWhyL: Causal Interactive Learningcited by 0
  7. 2026Learning Non-Gaussian SEMs with Conditional Risk, and Why the Direction of Recursion Matterscited by 0