Related papers: Maximum entropy based testing in network models: E…
A new method is proposed for analyzing complexity and studying the information in random geometric networks using Tsallis entropy tool. Tsallis entropy of the ensemble of random geometric networks is calculated based on the components of…
Natural and social multivariate systems are commonly studied through sets of simultaneous and time-spaced measurements of the observables that drive their dynamics, i.e., through sets of time series. Typically, this is done via hypothesis…
The principle of maximum entropy provides a useful method for inferring statistical mechanics models from observations in correlated systems, and is widely used in a variety of fields where accurate data are available. While the assumptions…
A class of models that have been widely used are the exponential random graph (ERG) models, which form a comprehensive family of models that include independent and dyadic edge models, Markov random graphs, and many other graph…
Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions.…
The $\boldsymbol{\beta}$-model for random graphs is commonly used for representing pairwise interactions in a network with degree heterogeneity. Going beyond pairwise interactions, Stasi et al. (2014) introduced the hypergraph…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…
Exponential random graph models (ERGMs) are a widely used framework for network data, enabling hypothesis testing on the structural mechanisms underlying observed networks. Bayesian ERGMs provide principled uncertainty quantification and…
Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…
The recent extension of permutation entropy and its derivatives to graph signals has opened up new horizons for the analysis of complex, high-dimensional systems evolving on networks. However, these measures are all fundamentally rooted in…
A major line of contemporary research on complex networks is based on the development of statistical models that specify the local motifs associated with macro-structural properties observed in actual networks. This statistical approach…
In many realistic systems, maximum entropy principle (MEP) analysis provides an effective characterization of the probability distribution of network states. However, to implement the MEP analysis, a sufficiently long-time data recording in…
This paper studies a classic maximum entropy sampling problem (MESP), which aims to select the most informative principal submatrix of a prespecified size from a covariance matrix. MESP has been widely applied to many areas, including…
With the growth of interest in network data across fields, the Exponential Random Graph Model (ERGM) has emerged as the leading approach to the statistical analysis of network data. ERGM parameter estimation requires the approximation of an…
Exponential random graph models (ERGMs) are very flexible for modeling network formation but pose difficult estimation challenges due to their intractable normalizing constant. Existing methods, such as MCMC-MLE, rely on sequential…
Recent years have seen the rise of convolutional neural network techniques in exemplar-based image synthesis. These methods often rely on the minimization of some variational formulation on the image space for which the minimizers are…
Inferring the input parameters of simulators from observations is a crucial challenge with applications from epidemiology to molecular dynamics. Here we show a simple approach in the regime of sparse data and approximately correct models,…
Exponential-family random graph models (ERGMs) provide a principled way to model and simulate features common in human social networks, such as propensities for homophily and friend-of-a-friend triad closure. We show that, without…
Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief…
Inspired by applications to theories of coding and communication in networks of nervous tissue, we study maximum entropy distributions on weighted graphs with a given expected degree sequence. These distributions are characterized by…