Grand canonical ensembles of sparse networks and Bayesian inference
arXiv:2204.06466 · doi:10.3390/e24050633
Abstract
Maximum entropy network ensembles have been very successful in modelling sparse network topologies and in solving challenging inference problems. However the sparse maximum entropy network models proposed so far have fixed number of nodes and are typically not exchangeable. Here we consider hierarchical models for exchangeable networks in the sparse limit, i.e. with the total number of links scaling linearly with the total number of nodes. The approach is grand canonical, i.e. the number of nodes of the network is not fixed a priori: it is finite but can be arbitrarily large. In this way the grand canonical network ensembles circumvent the difficulties in treating infinite sparse exchangeable networks which according to the Aldous-Hoover theorem must vanish. The approach can treat networks with given degree distribution or networks with given distribution of latent variables. When only a subgraph induced by a subset of nodes is known, this model allows a Bayesian estimation of the network size and the degree sequence (or the sequence of latent variables) of the entire network which can be used for network reconstruction.
arXiv comment(30 pages, 4 figures)
References in corpus (29)
- Emergence of scaling in random networks
- Hyperbolic Geometry of Complex Networks
- Mixed membership stochastic blockmodels
- The statistical mechanics of networks
- The Statistical Physics of Real-World Networks
- Entropy measures for complex networks: Toward an information theory of complex topologies
- The entropy of network ensembles
- Assessing the relevance of node features for network structure
- Generalized network structures: The configuration model and the canonical ensemble of simplicial complexes
- Statistical mechanics of the random K-SAT model
- Quantifying randomness in real networks
- Sparse graphs using exchangeable random measures
- Efficient and exact sampling of simple graphs with given arbitrary degree sequence
- Entropy of stochastic blockmodel ensembles
- Gibbs entropy of networks ensembles by cavity methods
- Sparse exchangeable graphs and their limits via graphon processes
- Entropies of complex networks with hierarchically constrained topologies
- The Class of Random Graphs Arising from Exchangeable Random Measures
- Constructing and sampling directed graphs with given degree sequences
- Statistical physics of complex information dynamics
- Private Graphon Estimation for Sparse Graphs
- Exact sampling of graphs with prescribed degree correlations
- The Grand Canonical ensemble of weighted networks
- Grand canonical validation of the bipartite International Trade Network
- Classical Information Theory of Networks
- Entropic dynamics on Gibbs statistical manifolds
- Size-Invariant Graph Representations for Graph Classification Extrapolations
- Entropy of labeled versus unlabeled networks
- Statistical physics of exchangeable sparse simple networks, multiplex networks and simplicial complexes