Related papers: Sparse graphs using exchangeable random measures
A powerful framework for studying graphs is to consider them as geometric graphs: nodes are randomly sampled from an underlying metric space, and any pair of nodes is connected if their distance is less than a specified neighborhood radius.…
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random with replacement. These matrices have a one-to-one correspondence with the…
Random network models generated using sparse exchangeable graphs have provided a mechanism to study a wide variety of complex real-life networks. In particular, these models help with investigating power-law properties of degree…
We analyze a random projection method for adjacency matrices, studying its utility in representing sparse graphs. We show that these random projections retain the functionality of their underlying adjacency matrices while having extra…
We consider a broad class of random bipartite networks, the distribution of which is invariant under permutation within each type of nodes. We are interested in $U$-statistics defined on the adjacency matrix of such a network, for which we…
We study a recent model for edge exchangeable random graphs introduced by Crane and Dempsey; in particular we study asymptotic properties of the random simple graph obtained by merging multiple edges. We study a number of examples, and show…
Graph-based representations underlie a wide range of scientific problems. Graph connectivity is typically represented as a sparse matrix in the Compressed Sparse Row format. Large-scale graphs rely on distributed storage, allocating…
A resource exchange network is considered, where exchanges among nodes are based on reciprocity. Peers receive from the network an amount of resources commensurate with their contribution. We assume the network is fully connected, and…
We consider $U$-statistics on row-column exchangeable matrices, arrays invariant to separate permutations of rows and columns and common in bipartite data. Under the standard dissociation assumption, we develop a graph-indexed analogue of…
We revisit the probabilistic construction of sparse random matrices where each column has a fixed number of nonzeros whose row indices are drawn uniformly at random. These matrices have a one-to-one correspondence with the adjacency…
We study tensor network states defined on an underlying graph which is sparsely connected. Generic sparse graphs are expander graphs with a high probability, and one can represent volume law entangled states efficiently with only polynomial…
Completely random measures (CRMs) are fundamental to Bayesian nonparametric models, with applications in clustering, feature allocation, and network analysis. A key quantity of interest is the Laplace exponent, whose asymptotic behavior…
We develop further the graph limit theory for dense weighted graph sequences. In particular, we consider probability graphons, which have recently appeared in graph limit theory as continuum representations of weighted graphs, and we…
In a recent paper, Caron and Fox suggest a probabilistic model for sparse graphs which are exchangeable when associating each vertex with a time parameter in $\mathbb{R}_+$. Here we show that by generalizing the classical definition of…
We introduce a statistical mechanics formalism for the study of constrained graph evolution as a Markovian stochastic process, in analogy with that available for spin systems, deriving its basic properties and highlighting the role of the…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
We propose a framework to model the distribution of sequential data coming from a set of entities connected in a graph with a known topology. The method is based on a mixture of shared hidden Markov models (HMMs), which are jointly trained…
Directed networks are conveniently represented as graphs in which ordered edges encode interactions between vertices. Despite their wide availability, there is a shortage of statistical models amenable for inference, specially when…
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 an era of unprecedented deluge of (mostly unstructured) data, graphs are proving more and more useful, across the sciences, as a flexible abstraction to capture complex relationships between complex objects. One of the main challenges…