A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New graph types help identify complex relationships.
New constructions from non-separating planar graphs improve understanding of graph linkability and knotability.
Characterizes minor-minimal separating projective planar graphs and their generalizations.
The complement of a non-separating planar graph contains a K_n minor.
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…
Develops a new framework for causal models on cyclic graphs, solving unique solvability issues.
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.
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, one-relator groups are conjugacy separable; we provide a…
Graph convolution improves linear separability and generalizes to out-of-distribution data.
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…
New graph kernels capture spatio-temporal interactions.
Poly-GNNs achieve similar performance regardless of depth, highlighting graph noise's dominance.
New PCstar algorithm discovers causal structure of max-linear Bayesian networks.
Study on hyperbolic groups, focusing on separability and splittings.
Categorical d-separation criterion simplifies probability graph analysis.
We consider the problem of learning causal networks with interventions, when each intervention is limited in size under Pearl's Structural Equation Model with independent errors (SEM-IE). The objective is to minimize the number of experiments to discover the causal directions of all the edges in a causal graph. Previou…
New method separates graph structure from node attributes to recover lost signal.
Characterizes geometric actions on graphs with flexible stabilizers.
We address the problem of finding a minimal separator in an Andersson-Madigan-Perlman chain graph (AMP CG), namely, finding a set Z of nodes that separates a given nonadjacent pair of nodes such that no proper subset of Z separates that pair. We analyze several versions of this problem and offer polynomial-time algorit…
New separation concepts for Anosov representations help bound Thurston asymmetric metric.
Let M be a graph manifold. We prove that fundamental groups of embedded incompressible surfaces in M are separable in the fundamental group of M, and that the double cosets for crossing surfaces are also separable. We deduce that if there is a "sufficient" collection of surfaces in M, then the fundamental group of M is…
AUC-spec optimizes graph-based SSL for complex label distributions.
In this paper, we study classes of graphs with three types of edges that capture the modified independence structure of a directed acyclic graph (DAG) after marginalisation over unobserved variables and conditioning on selection variables using the -separation criterion. These include MC, summary, and ancestral grap…
New proof shows no flat embedding for Petersen family graphs.
Study on self-similar sets on Riemannian manifolds with new separation conditions.
The study of networks leads to a wide range of high dimensional inference problems. In many practical applications, one needs to draw inference from one or few large sparse networks. The present paper studies hypothesis testing of graphs in this high-dimensional regime, where the goal is to test between two populations…
We address the problem of causal discovery from data, making use of the recently proposed causal modeling framework of modular structural causal models (mSCM) to handle cycles, latent confounders and non-linearities. We introduce σ-connection graphs (σ-CG), a new class of mixed graphs (containing undirected, bidirected…
A new method improves graph node embeddings by considering both nearby and distant node similarities.
Convolution Neural Network (CNN) has gained tremendous success in computer vision tasks with its outstanding ability to capture the local latent features. Recently, there has been an increasing interest in extending convolution operations to the non-Euclidean geometry. Although various types of convolution operations h…
This paper restricts efficient geodesics to non-separating curves.
New approach models computer network activity as mixtures of sources.
Paper distinguishes causal structures under latent confounding and selection bias.
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. We investigate the power of GCNs, as a function of their number of layers, to distinguish between different random graph models on the basis of the embeddings of their sample graphs. In particular, the graph models that we c…
Graph Interplay (GIP) improves GSSL performance by enhancing graph-level communications.
Novel graph-spanning algorithm detects changes in high-dimensional data.
Graphs of multicurves are hyperbolic, relatively hyperbolic, or thick.
We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph product of finite groups, a uniform lattice is commensurable with…
We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the pres…
Paper tackles graph class-incremental learning with task profiling and prompting.
Graph convolutional neural networks (GCN) have been the model of choice for graph representation learning, which is mainly due to the effective design of graph convolution that computes the representation of a node by aggregating those of its neighbors. However, existing GCN variants commonly use 1-D graph convolution …
Characterizes Bayesian networks up to unconditional equivalence.
We present a necessary and sufficient condition for existence of a contractible, non-separating and noncontractible separating Hamiltonian cycle in the edge graph of polyhedral maps on surfaces. In particular, we show the existence of contractible Hamiltonian cycle in equivelar triangulated maps. We also present an alg…
A concentration graph associated with a random vector is an undirected graph where each vertex corresponds to one random variable in the vector. The absence of an edge between any pair of vertices (or variables) is equivalent to full conditional independence between these two variables given all the other variables. In…