mlsanityData to 14 Oct 2026

Global Optimality in Bivariate Gradient-based DAG Learning

arXiv 2306.17378 ↗First posted 30 Jun 2023cs.LG stat.MLcited by 10

Not on the map. Why?

Abstract (arXiv)

Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order optimization schemes to solve this problem, proving the global optimality of such approaches has proven elusive. The difficulty lies in the fact that unlike other non-convex problems in the literature, this problem is not "benign", and possesses multiple spurious solutions that standard approaches can easily get trapped in. In this paper, we prove that a simple path-following optimization scheme globally converges to the global minimum of the population loss in the bivariate setting.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 30 of its 57 references that are in the map. First posted on arXiv 30 Jun 2023.

Builds on

30 of 57 references.

References · 30

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  3. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 331
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18 more
  1. 2017Theoretical insights into the optimization landscape of over-parameterized shallow neural networkscited by 128
  2. 2016Matrix Completion has No Spurious Local Minimumcited by 125
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  5. 2020DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networkscited by 66
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 1; 2024: 5; 2025: 2; 2026: 2.

10 papers.

  1. 2023CoLiDE: Concomitant Linear DAG Estimationcited by 13
  2. 2024Non-negative Weighted DAG Structure Learningcited by 7
  3. 2024psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learningcited by 4
  4. 2026Concomitant DAG Learning: On the Roles of Noise Adaptivity, Sparsity, and Non-negativitycited by 2
  5. 2024Interventional Causal Structure Discovery over Graphical Models with Convergence and Optimality Guaranteescited by 1
  6. 2024Revisiting Differentiable Structure Learning: Inconsistency of ℓ1 Penalty and Beyondcited by 1
  7. 2024Causal Order Discovery based on Monotonic SCMscited by 1
  8. 2025Differentiable Structure Learning and Causal Discovery for General Binary Datacited by 0
  9. 2025Non-negative DAG Learning from Time-Series Datacited by 0
  10. 2026Structure Learning on Clustered Datacited by 0