相关论文: Unifying DAGs and UGs

Estimating the structure of directed acyclic graphs (DAGs, also known as Bayesian networks) is a challenging problem since the search space of DAGs is combinatorial and scales superexponentially with the number of nodes. Existing approaches…

Acyclic model, often depicted as a directed acyclic graph (DAG), has been widely employed to represent directional causal relations among collected nodes. In this article, we propose an efficient method to learn linear non-Gaussian DAG in…

Graph Neural Networks (GNNs) have emerged as a powerful tool to capture intricate network patterns, achieving success across different domains. However, existing GNNs require careful domain-specific architecture designs and training from…

Despite the enormous success of graph neural networks (GNNs), most existing GNNs can only be applicable to undirected graphs where relationships among connected nodes are two-way symmetric (i.e., information can be passed back and forth).…

Oriented graph complexes, in which graphs are not allowed to have oriented cycles, govern for example the quantization of Lie bialgebras and infinite dimensional deformation quantization. It is shown that the oriented graph complex GC^or_n…

Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or…

Across the sciences, the statistical analysis of networks is central to the production of knowledge on relational phenomena. Because of their ability to model the structural generation of networks, exponential random graph models are a…

Motivated by the problem of designing inference-friendly Bayesian nonparametric models in probabilistic programming languages, we introduce a general class of partially exchangeable random arrays which generalizes the notion of hierarchical…

Directed acyclic graphs (DAGs) serve as crucial data representations in domains such as hardware synthesis and compiler/program optimization for computing systems. DAG generative models facilitate the creation of synthetic DAGs, which can…

Directed acyclic graphs (DAGs) can be characterised as directed graphs whose strongly connected components are isolated vertices. Using this restriction on the strong components, we discover that when $m = cn$, where $m$ is the number of…

Randomising networks using a naive `accept-all' edge-swap algorithm is generally biased. Building on recent results for nondirected graphs, we construct an ergodic detailed balance Markov chain with non-trivial acceptance probabilities for…

In this note, we introduce a family of bipartite graphs called path restricted ordered bipartite graphs and present it as an abstract generalization of some well known geometric graphs like unit distance graphs on convex point sets. In the…

Causal processes in biomedicine may contain cycles, evolve over time or differ between populations. However, many graphical models cannot accommodate these conditions. We propose to model causation using a mixture of directed cyclic graphs…

We study a special class of graphs with a strong transience feature called uniform transience. We characterize uniform transience via a Feller-type property and via validity of an isoperimetric inequality. We then give a further…

Transformer models have recently gained popularity in graph representation learning as they have the potential to learn complex relationships beyond the ones captured by regular graph neural networks. The main research question is how to…

We present a new notion of limits of weighted directed graphs of growing size based on convergence of their random quotients. These limits are specified in terms of random exchangeable measures on the unit square. We call our limits…

We consider a a collection of categorical random variables. Of special interest is the causal effect on an outcome variable following an intervention on another variable. Conditionally on a Directed Acyclic Graph (DAG), we assume that the…

A classical enumerative result states that, given a graph $G$ and a vertex $u$, the number of connected subgraphs of $G$ is equal to the number of orientations of $G$ such that every vertex can reach $u$ by a directed path. We show that…

In 2001, Davies, Gladwell, Leydold, and Stadler proved discrete nodal domain theorems for eigenfunctions of generalized Laplacians, i.e., symmetric matrices with non-positive off-diagonal entries. In this paper, we establish nodal domain…

Semi-supervised learning on graphs is a widely applicable problem in network science and machine learning. Two standard algorithms -- label propagation and graph neural networks -- both operate by repeatedly passing information along edges,…