Related papers: Sparse graphs using exchangeable random measures
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…
Many statistical methods for network data parameterize the edge-probability by attributing latent traits to the vertices such as block structure and assume exchangeability in the sense of the Aldous-Hoover representation theorem. Empirical…
A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is…
We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process, and naturally generalizes existing probabilistic models with…
In this paper we generalize the Aldous-Hoover-Kallenberg theorem concerning representations of distributions of exchangeable arrays via collections of measurable maps. We give criteria when such a representation theorem exists for arrays…
A projective network model is a model that enables predictions to be made based on a subsample of the network data, with the predictions remaining unchanged if a larger sample is taken into consideration. An exchangeable model is a model…
Network data appear in a number of applications, such as online social networks and biological networks, and there is growing interest in both developing models for networks as well as studying the properties of such data. Since individual…
We introduce a class of random graphs that we argue meets many of the desiderata one would demand of a model to serve as the foundation for a statistical analysis of real-world networks. The class of random graphs is defined by a…
The two components for infinite exchangeability of a sequence of distributions $(P_n)$ are (i) consistency, and (ii) finite exchangeability for each $n$. A consequence of the Aldous-Hoover theorem is that any node-exchangeable,…
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay…
Even though power-law or close-to-power-law degree distributions are ubiquitously observed in a great variety of large real networks, the mathematically satisfactory treatment of random power-law graphs satisfying basic statistical…
Exchangeability is a desired statistical property of network ensembles requiring their invariance upon relabelling of the nodes. However combining sparsity of network ensembles with exchangeability is challenging. Here we propose a…
We study conditional independence relationships for random networks and their interplay with exchangeability. We show that, for finitely exchangeable network models, the empirical subgraph densities are maximum likelihood estimates of their…
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…
We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…
Exchangeable random graphs serve as an important probabilistic framework for the statistical analysis of network data. In this work we develop an alternative parameterization for a large class of exchangeable random graphs, where the nodes…
Exchangeable models for countable vertex-labeled graphs cannot replicate the large sample behaviors of sparsity and power law degree distribution observed in many network datasets. Out of this mathematical impossibility emerges the question…
A variety of machine learning tasks---e.g., matrix factorization, topic modelling, and feature allocation---can be viewed as learning the parameters of a probability distribution over bipartite graphs. Recently, a new class of models for…
We consider a non-projective class of inhomogeneous random graph models with interpretable parameters and a number of interesting asymptotic properties. Using the results of Bollob\'as et al. [2007], we show that i) the class of models is…
Sparse exchangeable graphs on $\mathbb{R}_+$, and the associated graphex framework for sparse graphs, generalize exchangeable graphs on $\mathbb{N}$, and the associated graphon framework for dense graphs. We develop the graphex framework as…