arXiv:2607. 01057v1 Announce Type: cross Abstract: We study a broad class of graphical models whose independencies correspond to vertex separation in mixed graphs with directed, undirected, and bidirected edges, that are capable of encoding independence structures arising from feedback, latent and selection mechanisms.
arXiv:2607. 20502v1 Announce Type: new Abstract: To allow for principled comparison between two probabilistic graphical models defined over non-identical variable sets, they have to be lifted to a common measurable space.
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.
arXiv:2603.24333v2 Announce Type: replace-cross Abstract: Recently, Forr\'e (arXiv:2104.11547, 2021) introduced transitional conditional independence, a notion of conditional independence that provid...
The paper establishes a precise mathematical link between graph surgery and the do‑operator in deterministic acyclic structural causal models. It shows that deleting arrows in a graph corresponds exactly to replacing the associated mechanisms with constants, proving that “Graph(F^\iota)=Surg(Graph(F),T_\iota)”. The authors further characterize when this equality holds for the full graph, define the intervened model, and demonstrate how sequential interventions combine, concluding that an outcome depends only on interventions at its actual dependency ancestors.
arXiv:2609.16412v1 Announce Type: cross Abstract: Whitney's theorem allows isomorphism testing for connected simple graphs, apart from $K_3$ and $K_{1,3}$, to be formulated as distinguishing their li...
arXiv:2608. 19831v1 Announce Type: new Abstract: Causal Bayesian networks (CBNs) and structural causal models (SCMs) are the dominant frameworks for graphical causal reasoning, but they cannot adequately represent all real-world causal systems.
arXiv:2508. 02158v2 Announce Type: replace-cross Abstract: Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds.
arXiv:2606. 03315v1 Announce Type: new Abstract: Graph foundation models aim to learn transferable knowledge from diverse graphs for generalization to unseen graphs and tasks.
arXiv:2606. 19366v1 Announce Type: cross Abstract: Information lattice learning (ILL) learns interpretable rules of a signal by alternately projecting the signal onto a partition lattice that encodes a hierarchy of abstractions and lifting selected rules back to the signal domain.
arXiv:2603. 14846v3 Announce Type: replace Abstract: We define an information-complexity property for aggregation functions, capturing a vast range of practical aggregations, and prove that any Message-Passing Graph Neural Network (MP-GNN) model with such aggregations induces only a polynomial number of equivalence classes on all graphs - while the number of non-isomorphic graphs is super-exponential (in number of vertices).
arXiv:2607. 17570v1 Announce Type: new Abstract: Graph foundation models (GFMs) with global attention are increasingly used to represent mixed-integer linear programs (MILPs), aiming to capture structure beyond the locality of standard graph neural networks.
arXiv:2608.25598v2 Announce Type: replace Abstract: The purpose of this paper is to provide a general, comprehensive, theoretical framework that allows one to deal with fibrations on graphs labelled...