Equivalence Class Searcher

as part of the

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

Haoyue Dai, Immanuel Albrecht, Peter Spirtes, Kun Zhang

Appears at ICLR 2026 (Oral Presentation)

The CPDAG-like representation of this distributional equivalence class is as follows:
Explanation
  • The whole equivalence class can be partitioned into subclasses, where each subclass consists of digraphs mutually reachable via sequences of admissible edge additions and deletions, but without cycle reversals.
  • The left panel shows the maximally inclusive digraph of a subclass.
  • Solid edges appear in all digraphs within the subclass.
  • Dashed edges appear in some but not all digraphs within the subclass.
  • Such representations of different subclasses are connected by simple cycle reversals, with edge types carried along.
  • Further details are provided in Appendix C.3 of the paper.
There are 82 irreducible digraphs (unique up to L-labeling) in this distributional equivalence class. 41 of them are acyclic.
There are 22 digraphs with 14 edges. The first 16 of them are acyclic. (click to expand)
Page 1 of 3 (Digraphs 1 to 10 of 22)
There are 33 digraphs with 15 edges. The first 17 of them are acyclic. (click to expand)
Page 1 of 4 (Digraphs 1 to 10 of 33)
There are 20 digraphs with 16 edges. The first 7 of them are acyclic. (click to expand)
Page 1 of 2 (Digraphs 1 to 10 of 20)
There are 6 digraphs with 17 edges. The first 1 of them are acyclic. (click to expand)
Page 1 of 1 (Digraphs 1 to 6 of 6)
There are 1 digraphs with 18 edges. None of them are acyclic. (click to expand)
Page 1 of 1 (Digraphs 1 to 1 of 1)
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