mlsanityData to 14 Oct 2026

DAG Learning on the Permutahedron

arXiv 2301.11898 ↗First posted 27 Jan 2023cs.LG cs.AI stat.MLcited by 9

Not on the map. Why?

Abstract (arXiv)

We propose a continuous optimization framework for discovering a latent directed acyclic graph (DAG) from observational data. Our approach optimizes over the polytope of permutation vectors, the so-called Permutahedron, to learn a topological ordering. Edges can be optimized jointly, or learned conditional on the ordering via a non-differentiable subroutine. Compared to existing continuous optimization approaches our formulation has a number of advantages including: 1. validity: optimizes over exact DAGs as opposed to other relaxations optimizing approximate DAGs; 2. modularity: accommodates any edge-optimization procedure, edge structural parameterization, and optimization loss; 3. end-to-end: either alternately iterates between node-ordering and edge-optimization, or optimizes them jointly. We demonstrate, on real-world data problems in protein-signaling and transcriptional network discovery, that our approach lies on the Pareto frontier of two key metrics, the SID and SHD.

Key facts. Cited by 9 papers in the map (data through 14 Oct 2026). Builds on 36 of its 68 references that are in the map. First posted on arXiv 27 Jan 2023.

Builds on

36 of 68 references.

References · 36

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24 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 6; 2024: 2; 2025: 0; 2026: 1.

9 papers.

  1. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  2. 2023CoLiDE: Concomitant Linear DAG Estimationcited by 13
  3. 2024Ordering-Based Causal Discovery for Linear and Nonlinear Relationscited by 13
  4. 2023Constraint-Free Structure Learning with Smooth Acyclic Orientationscited by 10
  5. 2023Learning DAGs from Data with Few Root Causescited by 8
  6. 2023Order-based Structure Learning with Normalizing Flowscited by 5
  7. 2023Tree Search in DAG Space with Model-based Reinforcement Learning for Causal Discoverycited by 3
  8. 2026Concomitant DAG Learning: On the Roles of Noise Adaptivity, Sparsity, and Non-negativitycited by 2
  9. 2024Causal Order Discovery based on Monotonic SCMscited by 1