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Grouped data are commonly encountered in applications. The Bernstein polynomial model is proposed as an approximate model in this paper for estimating a univariate density function based on grouped data. The coefficients of the Bernstein…
We analyze the component evolution in inhomogeneous random intersection graphs when the average degree is close to 1. As the average degree increases, the size of the largest component in the random intersection graph goes through a phase…
We study the mean time for a random walk to traverse between two arbitrary sites of the Erdos-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as…
In the past two decades, significant advances have been made in understanding the structural and functional properties of biological networks, via graph-theoretic analysis. In general, most graph-theoretic studies are conducted in the…
The probabilistic graphs framework models the uncertainty inherent in real-world domains by means of probabilistic edges whose value quantifies the likelihood of the edge existence or the strength of the link it represents. The goal of this…
We consider the testing and estimation of change-points -- locations where the distribution abruptly changes -- in a data sequence. A new approach, based on scan statistics utilizing graphs representing the similarity between observations,…
Given a finite sequence of graphs, e.g., coming from technological, biological, and social networks, the paper proposes a methodology to identify possible changes in stationarity in the stochastic process generating the graphs. In order to…
The assumption of using a static graph to represent multivariate time-varying signals oversimplifies the complexity of modeling their interactions over time. We propose a Dynamic Multi-hop model that captures dynamic interactions among…
We revisit the problem of designing sublinear algorithms for estimating the average degree of an $n$-vertex graph. The standard access model for graphs allows for the following queries: sampling a uniform random vertex, the degree of a…
Large crossed data sets, described by generalized linear mixed models, have become increasingly common and provide challenges for statistical analysis. At very large sizes it becomes desirable to have the computational costs of estimation,…
We propose a new model, the Neighbor Mixture Model (NMM), for modeling node labels in a graph. This model aims to capture correlations between the labels of nodes in a local neighborhood. We carefully design the model so it could be an…
We consider sparse random intersection graphs with the property that the clustering coefficient does not vanish as the number of nodes tends to infinity. We find explicit asymptotic expressions for the correlation coefficient of degrees of…
Multiple-subject network data are fast emerging in recent years, where a separate connectivity matrix is measured over a common set of nodes for each individual subject, along with subject covariates information. In this article, we propose…
In this paper the focus is on subsampling as well as reconstructing the second-order statistics of signals residing on nodes of arbitrary undirected graphs. Second-order stationary graph signals may be obtained by graph filtering zero-mean…
Bipartite incidence graph sampling provides a unified representation of many sampling situations for the purpose of estimation, including the existing unconventional sampling methods, such as indirect, network or adaptive cluster sampling,…
We consider the detection and localization of change points in the distribution of an offline sequence of observations. Based on a nonparametric framework that uses a similarity graph among observations, we propose new test statistics when…
This paper studies statistical inference in a network of infinite-server queues, with the aim of estimating the underlying parameters (routing matrix, arrival rates, parameters pertaining to the service times) using observations of the…
Generating random graphs to model networks has a rich history. In this paper, we analyze and improve upon the multifractal network generator (MFNG) introduced by Palla et al. We provide a new result on the probability of subgraphs existing…
Uniform bin width histograms are widely used so this data graphic should represent data as correctly as possible. Method of moments based on familiar mean, variance and Fisher-Pearson skewness cure this problem.
Degree distribution, or equivalently called degree sequence, has been commonly used to be one of most significant measures for studying a large number of complex networks with which some well-known results have been obtained. By contrast,…