Related papers: Hoeffding-type decomposition for $U$-statistics on…
Let H be a graph, and let C_H(G) be the number of (subgraph isomorphic) copies of H contained in a graph G. We investigate the fundamental problem of estimating C_H(G). Previous results cover only a few specific instances of this general…
We define and study the statistical models in exponential family form whose sufficient statistics are the degree distributions and the bi-degree distributions of undirected labelled simple graphs. Graphs that are constrained by the joint…
Simulation-based inference methods that feature correct conditional coverage of confidence sets based on observations that have been compressed to a scalar test statistic require accurate modeling of either the p-value function or the…
In 1948, W. Hoeffding introduced a large class of unbiased estimators called U-statistics, defined as the average value of a real-valued m-variate function h calculated at all possible sets of m points from a random sample. In the present…
We propose a novel method for topological analysis of unweighted graphs which is based on \textit{persistent homology}. The proposed method maps the input graph to a complete weighted graph where the weighting function maps each edge to a…
Previous statistical approaches to hierarchical clustering for social network analysis all construct an "ultrametric" hierarchy. While the assumption of ultrametricity has been discussed and studied in the phylogenetics literature, it has…
Clustering methods are a valuable tool for the identification of patterns in high dimensional data with applications in many scientific problems. However, quantifying uncertainty in clustering is a challenging problem, particularly when…
I study a regression model in which one covariate is an unknown function of a latent driver of link formation in a network. Rather than specify and fit a parametric network formation model, I introduce a new method based on matching pairs…
Recently bipartite graphs have been widely used to represent the relationship two sets of items for information retrieval applications. The Web offers a wide range of data which can be represented by bipartite graphs, such us movies and…
In this paper we propose a distributed algorithm for the estimation and control of the connectivity of ad-hoc networks in the presence of a random topology. First, given a generic random graph, we introduce a novel stochastic power…
Many popular network models rely on the assumption of (vertex) exchangeability, in which the distribution of the graph is invariant to relabelings of the vertices. However, the Aldous-Hoover theorem guarantees that these graphs are dense or…
Methods that learn representations of nodes in a graph play a critical role in network analysis since they enable many downstream learning tasks. We propose Graph2Gauss - an approach that can efficiently learn versatile node embeddings on…
It appeared recently that the classical random graph model used to represent real-world complex networks does not capture their main properties. Since then, various attempts have been made to provide accurate models. We study here a model…
We investigate efficient learning from higher-order graph convolution and learning directly from adjacency matrices for node classification. We revisit the scaled graph residual network and remove ReLU activation from residual layers and…
We establish a strong Gaussian approximation for high-dimensional non-degenerate U-statistics with diverging dimension. Under mild assumptions, we construct, on a sufficiently rich probability space, a Gaussian process that uniformly…
We consider statistical inference for network-linked regression problems, where covariates may include network summary statistics computed for each node. In settings involving network data, it is often natural to posit that latent variables…
We generalize the construction of the Heegaard Floer homology for a singular knot to that for a balanced bipartite graph. For a given graph, we provide a combinatorial description of the Euler characteristic of its Heegaard Floer homology…
Relations between discrete quantities such as people, genes, or streets can be described by networks, which consist of nodes that are connected by edges. Network analysis aims to identify important nodes in a network and to uncover…
Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…
This paper introduces a chordal decomposition approach for scalable analysis of linear networked systems, including stability, $\mathcal{H}_2$ and $\mathcal{H}_{\infty}$ performance. Our main strategy is to exploit any sparsity within these…