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Spectral embedding is a procedure which can be used to obtain vector representations of the nodes of a graph. This paper proposes a generalisation of the latent position network model known as the random dot product graph, to allow…
The stochastic block model is able to generate different network partitions, ranging from traditional assortative communities to disassortative structures. Since the degree-corrected stochastic block model does not specify which mixing…
For a multi-agent system state estimation resting upon noisy measurements constitutes a problem related to several application scenarios. Adopting the standard least-squares approach, in this work we derive both the (centralized) analytic…
This paper explores the estimation of a panel data model with cross-sectional interaction that is flexible both in its approach to specifying the network of connections between cross-sectional units, and in controlling for unobserved…
In this paper, we propose the first exact Markov model for connection blocking analysis in elastic optical networks, based on the occupancy status of spectrum slices on all links due to arrivals and departures of various classes of…
The stochastic block model (SBM) has been widely used to analyze network data. Various goodness-of-fit tests have been proposed to assess the adequacy of model structures. To the best of our knowledge, however, none of the existing…
In the standard stochastic block model for networks, the probability of a connection between two nodes, often referred to as the edge probability, depends on the unobserved communities each of these nodes belongs to. We consider a flexible…
We study the expected adjacency matrix of a uniformly random multigraph with fixed degree sequence $\mathbf{d} \in \mathbb{Z}_+^n$. This matrix arises in a variety of analyses of networked data sets, including modularity-maximization and…
We propose a Bayesian approach, called the posterior spectral embedding, for estimating the latent positions in random dot product graphs, and prove its optimality. Unlike the classical spectral-based adjacency/Laplacian spectral embedding,…
Several classical adaptive optimization algorithms, such as line search and trust region methods, have been recently extended to stochastic settings where function values, gradients, and Hessians in some cases, are estimated via stochastic…
This article develops limit laws for network sampling based estimates of subgraph counts and clustering coefficient of a large population network, and uses them for predictive inference. A model based approach is used, where the population…
We present a method to estimate block membership of nodes in a random graph generated by a stochastic blockmodel. We use an embedding procedure motivated by the random dot product graph model, a particular example of the latent position…
We present a new approach, based on graphon theory, to finding the limiting spectral distributions of general Wigner-type matrices. This approach determines the moments of the limiting measures and the equations of their Stieltjes…
Graph-based representations play a key role in machine learning. The fundamental step in these representations is the association of a graph structure to a dataset. In this paper, we propose a method that aims at finding a block sparse…
In network analysis, developing a unified theoretical framework that can compare methods under different models is an interesting problem. This paper proposes a partial solution to this problem. We summarize the idea of using separation…
Stochastic network influences complicate graph filter design by producing uncertainty in network iteration matrix eigenvalues, the points at which the graph filter response is defined. While joint statistics for the eigenvalues typically…
In this paper we consider the trace regression model where $n$ entries or linear combinations of entries of an unknown $m_1\times m_2$ matrix $A_0$ corrupted by noise are observed. We establish for the nuclear-norm penalized estimator of…
To learn (statistical) dependencies among random variables requires exponentially large sample size in the number of observed random variables if any arbitrary joint probability distribution can occur. We consider the case that sparse data…
Graphical models use graphs to compactly capture stochastic dependencies amongst a collection of random variables. Inference over graphical models corresponds to finding marginal probability distributions given joint probability…
We develop a new algorithmic technique that allows to transfer some constant time approximation algorithms for general graphs into random order streaming algorithms. We illustrate our technique by proving that in random order streams with…