PaperActive

The observational partial order of causal structures with latent variables

quality89

Updated 6 h ago · first seen 11 Sept 2026

paper_01M294FSQZ3TS79SFED5BKRS9C

Published: 11 Sept 2026; T1 · 6 h ago
arXiv: 2502.07891; T1 · 6 h ago
Category: stat.ML; T1 · 6 h ago

Abstract

-cross Abstract: For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the visible variables realizable by the second. Knowing such dominance relations is useful for adjudicating between these structures given observational data. Here, we consider the problem of determining the partial order of equivalence classes of causal structures with latent variables relative to observational dominance. We provide a complete characterization of the dominance order in the case of three visible variables, and a partial characterization in the case of four visible variables. Our techniques also help to identify which observational equivalence classes have a set of realizable distributions that is characterized by nontrivial inequality constraints, analogous to Bell inequalities and instrumental inequalities. We find evidence that as one increases the number of visible variables, the equivalence classes satisfying nontrivial inequality constraints become ubiquitous. (Because such classes are the ones for which there can be a difference in the distributions that are quantumly and classically realizable, this implies that the potential for quantum-classical gaps is also ubiquitous.) Furthermore, we find evidence that constraint-based causal discovery algorithms that rely solely on conditional independence constraints have a significantly weaker distinguishing power among observational equivalence classes than algorithms that go beyond these (i.e., algorithms that also leverage nested Markov constraints and inequality constraints).

Authors 3

Marina Maciel Ansanelli, Elie Wolfe, Robert W. Spekkens

Specification

Official page: arxiv.org/abs/2502.07891
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Arxiv announce type: replace
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
arXiv id: 2502.07891
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Categories: stat.ML, cs.LG, quant-ph
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
DOI: 10.1515/jci-2025-0009
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
PDF: arxiv.org/pdf/2502.07891
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Primary category: stat.ML
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh
Published: 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 6 h agohigh

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T110

Freshest observation

6 h ago

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None

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10 claims · 10 properties

Official pageofficial_url1

Claim history for Official page
Value	Valid from → to	Status	Source	Confidence	Extractor
https://arxiv.org/abs/2502.07891	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Abstractabstract1

Claim history for Abstract
Value	Valid from → to	Status	Source	Confidence	Extractor
-cross Abstract: For two causal structures with the same set of visible variables, one is said to observationally dominate the other if the set of distributions over the visible variables realizable by the first contains the set of distributions over the visible variables realizable by the second. Knowing such dominance relations is useful for adjudicating between these structures given observational data. Here, we consider the problem of determining the partial order of equivalence classes of causal structures with latent variables relative to observational dominance. We provide a complete characterization of the dominance order in the case of three visible variables, and a partial characterization in the case of four visible variables. Our techniques also help to identify which observational equivalence classes have a set of realizable distributions that is characterized by nontrivial inequality constraints, analogous to Bell inequalities and instrumental inequalities. We find evidence that as one increases the number of visible variables, the equivalence classes satisfying nontrivial inequality constraints become ubiquitous. (Because such classes are the ones for which there can be a difference in the distributions that are quantumly and classically realizable, this implies that the potential for quantum-classical gaps is also ubiquitous.) Furthermore, we find evidence that constraint-based causal discovery algorithms that rely solely on conditional independence constraints have a significantly weaker distinguishing power among observational equivalence classes than algorithms that go beyond these (i.e., algorithms that also leverage nested Markov constraints and inequality constraints).	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Arxiv announce typearxiv_announce_type1

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Value	Valid from → to	Status	Source	Confidence	Extractor
replace	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

arXiv idarxiv_id1

Claim history for arXiv id
Value	Valid from → to	Status	Source	Confidence	Extractor
2502.07891	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Authorsauthors1

Claim history for Authors
Value	Valid from → to	Status	Source	Confidence	Extractor
Marina Maciel Ansanelli, Elie Wolfe, Robert W. Spekkens	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Categoriescategories1

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Value	Valid from → to	Status	Source	Confidence	Extractor
stat.ML, cs.LG, quant-ph	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

DOIdoi1

Claim history for DOI
Value	Valid from → to	Status	Source	Confidence	Extractor
10.1515/jci-2025-0009	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

PDFpdf_url1

Claim history for PDF
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https://arxiv.org/pdf/2502.07891	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Primary categoryprimary_category1

Claim history for Primary category
Value	Valid from → to	Status	Source	Confidence	Extractor
stat.ML	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Publishedpublished_at1

Claim history for Published
Value	Valid from → to	Status	Source	Confidence	Extractor
11 Sept 2026	11 Sept 2026 21:02 UTC → current	current	arXiv (Atom API + RSS)T1	high	deterministic

Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →

Source documents
Source	Document	Type	Tier	Last observed	Snapshots
arXiv (Atom API + RSS)	rss.arxiv.org/rss/cs.LG	feed	T1· Official	5 h ago	1

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