arXiv research

New graph types help identify complex relationships.

Characterizes Bayesian networks up to unconditional equivalence.

Graph Interplay (GIP) improves GSSL performance by enhancing graph-level communications.

Knowing when a graphical model is perfect to a distribution is essential in order to relate separation in the graph to conditional independence in the distribution, and this is particularly important when performing inference from data. When the model is perfect, there is a one-to-one correspondence between conditional…

We establish bounds on the KL divergence between two multivariate Gaussian distributions in terms of the Hamming distance between the edge sets of the corresponding graphical models. We show that the KL divergence is bounded below by a constant when the graphs differ by at least one edge; this is essentially the tighte…

Paper tackles graph class-incremental learning with task profiling and prompting.

New constructions from non-separating planar graphs improve understanding of graph linkability and knotability.

Characterizes minor-minimal separating projective planar graphs and their generalizations.

Enhances graph neural networks by creating virtual data examples.

The complement of a non-separating planar graph contains a K_n minor.

Classifies essential annuli in a genus two handlebody exterior.

New algorithms verify and search causal graphs with minimal interventions.

Automorphisms of fine curve graphs match surface homeomorphisms for planar surfaces.

New measures assess differences in causal graphs' separations.

New complex connects graph separability to group properties.

We prove that the separating curve graph of a connected, compact, orientable surface with genus at least 3 and a single boundary component is not relatively hyperbolic. This completes the classification of when the separating curve graph is hyperbolic and relatively hyperbolic initiated by previous works of the authors…

We extend a recently proposed 1-nearest-neighbor based multiclass learning algorithm and prove that our modification is universally strongly Bayes-consistent in all metric spaces admitting any such learner, making it an "optimistically universal" Bayes-consistent learner. This is the first learning algorithm known to e…

Study restricts causal graphs with expert knowledge.

Develops a new framework for causal models on cyclic graphs, solving unique solvability issues.

This work evaluates graph models' robustness to structural distributional shifts.

A non-separating multicurve of a surface S of genus g with m punctures is a multicurve c so that S-c is connected. For k>0 define the graph of non-separting k-multicurves to be the graph whose vertices are non-separating multicurves with k components and where two such multicurves are connected by an edge if they can b…

New framework for cyclic quantum causal models with graph separation property.

Study essential diagrams of knots in $S_{g} imes S^{1}$ and their relation to virtual knots.

We construct a hyperbolic 3-manifold $M$ (with $\partial M$ totally geodesic) which contains no essential closed surfaces, but for any even integer $g> 0$ there are infinitely many separating slopes $r$ on $\partial M$ so that $M[r]$, the 3-manifold obtained by attaching 2-handle to $M$ along $r$, contains an essential…

We consider perturbed quadharmonic operators, $Δ^4 + V$, acting on sections of a Hermitian vector bundle over a complete Riemannian manifold, with the potential $V$ satisfying a bound from below by a non-positive function depending on the distance from a point. Under a bounded geometry assumption on the Hermitian vecto…

Proposes a new model for clustering passenger trajectories with graphs.

We construct a small, hyperbolic 3-manifold $M$ such that, for any integer $g\geq 2$, there are infinitely many separating slopes $r$ in $\partial M$ so that $M(r)$, the 3-manifold obtained by attaching a 2-handle to $M$ along $r$, is hyperbolic and contains an essential separating closed surface of genus $g$. The resu…

An embedding of a metric graph $(G, d)$ on a closed hyperbolic surface is \emph{essential}, if each complementary region has a negative Euler characteristic. We show, by construction, that given any metric graph, its metric can be rescaled so that it admits an essential and isometric embedding on a closed hyperbolic su…

We solve minimal separator problems in AMP chain graphs and improve structure learning algorithms.

The paper explores how different patterns of heterophily affect Graph Neural Networks.

We use the theory of group actions on profinite trees to prove that the fundamental group of a finite, 1-acylindrical graph of free groups with finitely generated edge groups is conjugacy separable. This has several applications: we prove that positive, $C'(1/6)$ one-relator groups are conjugacy separable; we provide a…

Let $T$ be a graph in a compact, orientable 3--manifold $M$ and let $Γ$ be a subgraph. $T$ can be placed in bridge position with respect to a Heegaard surface $H$. We show that if $H$ is what we call $(T,Γ)$-c-weakly reducible in the complement of $T$ then either a "degenerate" situation occurs or $H$ can be untelescop…

Gradient methods avoid overfitting on separable data.

The study embeds graphs on translation surfaces, proving essential-systolic embeddings and estimating surface genera.

Graph convolution improves linear separability and generalizes to out-of-distribution data.

Study shows surfaces without certain curves have infinite orbit graph.

GCNs distinguish graph models based on embeddings, but depth matters.

New findings on hyperbolicity of fine curve graphs and their subgraphs.

Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the cov…

In many video coding systems, separable transforms (such as two-dimensional DCT-2) have been used to code block residual signals obtained after prediction. This paper proposes a parametric approach to build graph-based separable transforms (GBSTs) for video coding. Specifically, a GBST is derived from a pair of line gr…

We consider the minimum cost intervention design problem: Given the essential graph of a causal graph and a cost to intervene on a variable, identify the set of interventions with minimum total cost that can learn any causal graph with the given essential graph. We first show that this problem is NP-hard. We then prove…

New graph kernels capture spatio-temporal interactions.

Essential curves in certain graph manifolds imply non-linear groups.

Poly-GNNs achieve similar performance regardless of depth, highlighting graph noise's dominance.

We study the existence and uniqueness of the heat kernel on infinite, locally finite, connected graphs. For general graphs, a uniqueness criterion, shown to be optimal, is given in terms of the maximal valence on spheres about a fixed vertex. A sufficient condition for non-uniqueness is also presented. Furthermore, we …

New PCstar algorithm discovers causal structure of max-linear Bayesian networks.

Improved graph neural networks by separating feature aggregation and depth.

Study on hyperbolic groups, focusing on separability and splittings.