mlsanityData to 7 Oct 2026

Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning

arXiv 2603.04780 ↗First posted 5 Mar 2026cs.LG stat.MLcited by 4

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Abstract (arXiv)

Causal discovery with latent variables is a fundamental task. Yet most existing methods rely on strong structural assumptions, such as enforcing specific indicator patterns for latents or restricting how they can interact with others. We argue that a core obstacle to a general, structural-assumption-free approach is the lack of an equivalence characterization: without knowing what can be identified, one generally cannot design methods for how to identify it. In this work, we aim to close this gap for linear non-Gaussian models. We establish the graphical criterion for when two graphs with arbitrary latent structure and cycles are distributionally equivalent, that is, they induce the same observed distribution set. Key to our approach is a new tool, edge rank constraints, which fills a missing piece in the toolbox for latent-variable causal discovery in even broader settings. We further provide a procedure to traverse the whole equivalence class and develop an algorithm to recover models from data up to such equivalence. To our knowledge, this is the first equivalence characterization with latent variables in any parametric setting without structural assumptions, and hence the first structural-assumption-free discovery method. Code and an interactive demo are available at https://equiv.cc.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 61 of its 152 references that are in the map. First posted on arXiv 5 Mar 2026.

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61 of 152 references.

References · 61

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  2. 2019Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changescited by 166
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38 more
  1. 2017Nested Markov Properties for Acyclic Directed Mixed Graphscited by 38
  2. 2015backShift: Learning causal cyclic graphs from unknown shift interventionscited by 37
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  4. 2023A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variablescited by 33
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  6. 2017Markov Properties for Graphical Models with Cycles and Latent Variablescited by 32
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  8. 2020Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cyclescited by 31
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50 most cited of 61 All 61 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 4.

4 papers.

  1. 2026Coarsening Linear Non-Gaussian Causal Models with Cyclescited by 2
  2. 2026Equilibrium Causal Games: Separation, Identification, and the Identifiability of Cyclic Latent Statescited by 0
  3. 2026Decoupled Causal Discoverycited by 0
  4. 2026The Statistical Cost of Causal Discovery with Feedbackcited by 0