相关论文: Spectral goodness of fit for network models

Due to their low latency, high capacity, and seamless worldwide coverage, low Earth orbit (LEO) satellites are essential to the equal access network. Stochastic geometry (SG) is an appropriate method for such a large and irregular system.…

Various approaches and measures from network analysis have been applied to granular and particulate networks to gain insights into their structural, transport, failure-propagation and other systems-level properties. In this article, we…

Despite their ability to represent highly expressive functions, deep learning models seem to find simple solutions that generalize surprisingly well. Spectral bias -- the tendency of neural networks to prioritize learning low frequency…

Different network models have been suggested for the topology underlying complex interactions in natural systems. These models are aimed at replicating specific statistical features encountered in real-world networks. However, it is rarely…

Homophily is a graph property describing the tendency of edges to connect similar nodes; the opposite is called heterophily. It is often believed that heterophilous graphs are challenging for standard message-passing graph neural networks…

We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…

Subsequence matching has appeared to be an ideal approach for solving many problems related to the fields of data mining and similarity retrieval. It has been shown that almost any data class (audio, image, biometrics, signals) is or can be…

Spectral Graph Neural Network is a kind of Graph Neural Network (GNN) based on graph signal filters. Some models able to learn arbitrary spectral filters have emerged recently. However, few works analyze the expressive power of spectral…

When several models have similar training scores, classical model selection heuristics follow Occam's razor and advise choosing the ones with least capacity. Yet, modern practice with large neural networks has often led to situations where…

In this review we establish various connections between complex networks and symmetry. While special types of symmetries (e.g., automorphisms) are studied in detail within discrete mathematics for particular classes of deterministic graphs,…

Graph neural networks (GNNs) have been widely used for representation learning on graph data. However, there is limited understanding on how much performance GNNs actually gain from graph data. This paper introduces a context-surrounding…

We consider a statistical model for the problem of finding subgraphs with specified topology in an otherwise random graph. This task plays an important role in the analysis of social and biological networks. In these types of networks,…

Graph theory is emerging as a new source of tools for time series analysis. One promising method is to transform a signal into its visibility graph, a representation which captures many interesting aspects of the signal. Here we introduce…

Individual fairness (IF) in graph neural networks (GNNs), which emphasizes the need for similar individuals should receive similar outcomes from GNNs, has been a critical issue. Despite its importance, research in this area has been largely…

Graphs are widely used to describe real-world objects and their interactions. Graph Neural Networks (GNNs) as a de facto model for analyzing graphstructured data, are highly sensitive to the quality of the given graph structures. Therefore,…

We present experimental results highlighting two key differences resulting from the choice of training algorithm for two-layer neural networks. The spectral bias of neural networks is well known, while the spectral bias dependence on the…

Log-linear models are widely used to express the association in multivariate frequency data on contingency tables. The paper focuses on the power analysis for testing the goodness-of-fit hypothesis for this model type. Conventionally, for…

Graph Neural Networks (GNNs) have received considerable attention on graph-structured data learning for a wide variety of tasks. The well-designed propagation mechanism which has been demonstrated effective is the most fundamental part of…

We present a novel graph embedding space (i.e., a set of measures on graphs) for performing statistical analyses of networks. Key improvements over existing approaches include discovery of "motif-hubs" (multiple overlapping significant…

We introduce an unsupervised graph embedding that trades off local node similarity and connectivity, and global structure. The embedding is based on a generalized graph Laplacian, whose eigenvectors compactly capture both network structure…