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arXiv Machine Learning

On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models

The paper investigates identifiability in linear parametric models where variables follow either an ordered logit or a one‑parameter exponential family distribution. It proves that the direction of every edge linking an ordinal node to an exponential‑family node can be determined from the joint distribution, provided each node has at least three categories or support points, respectively. Numerical experiments confirm that these orientations can be distinguished even when conditional independence tests cannot separate them.

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arXiv Machine Learning
Sep 18

Epidemiological Causal Graph Identification: Challenges, Identifiability and Algorithms

The paper addresses causal discovery in Directed Acyclic Graphs where nodes are either ordinal (modeled with an ordered logit) or follow a one‑parameter exponential family distribution. It proves that the direction of edges between such nodes is identifiable for generic parameter values, extending prior Ordinal‑Poisson results. The authors also propose a score‑based exhaustive search and a masked continuous optimization method using DAGMA, and demonstrate through simulations that these approaches recover orientations that are otherwise unidentifiable under classical structural equation models.

By Sambit Mishra, Yingying Wang, Christine K. Johnson, Urbashi Mitra
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arXiv Machine Learning
Jun 30

Towards Complete Causal Explanation with Expert Knowledge

arXiv:2407. 07338v4 Announce Type: replace-cross Abstract: We study the problem of restricting a Markov equivalence class of maximal ancestral graphs (MAGs) to only those MAGs that contain certain edge marks, which we refer to as expert or orientation knowledge.

By Aparajithan Venkateswaran, Emilija Perkovi\'c
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arXiv Machine Learning
Sep 11

The observational partial order of causal structures with latent variables

The paper studies observational dominance among causal structures with latent variables, defining one structure as dominating another if it can realize all distributions that the other can over the same visible variables. It provides a full characterization of this dominance partial order for three visible variables and a partial one for four, and shows that many equivalence classes are distinguished by nontrivial inequality constraints similar to Bell or instrumental inequalities. The authors also demonstrate that constraint‑based causal discovery algorithms relying only on conditional independence are much less powerful than those incorporating nested Markov and inequality constraints.

By Marina Maciel Ansanelli, Elie Wolfe, Robert W. Spekkens
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arXiv AI
Jul 16

Partially Observed Structural Causal Models

arXiv:2605. 03268v2 Announce Type: replace-cross Abstract: Here we introduce Partially Observed Structural Causal Models (POSCMs) as an extension of structural causal models (SCMs) to settings where upstream contexts co-determine both the interaction structure and downstream mechanisms on observed variables.

By Turan Orujlu, Jordan Matelsky, Martin V. Butz, Charley M. Wu, Konrad P. Kording
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