相关论文: On Markovian random networks

In this paper we study Eulerian extensions with edge constraints and use the probabilistic method to establish sufficient conditions for a given connected graph to be a subgraph of a Eulerian graph containing $m$ edges, for a given number…

We study modular and integral flow polynomials of graphs by means of subgroup arrangements and lattice polytopes. We introduce an Eulerian equivalence relation on orientations, flow arrangements, and flow polytopes; and we apply the theory…

Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markov approach is used in conventional community detection, ranking, and spreading analysis although it…

Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…

Networks arise in many applications, such as in the analysis of text documents, social interactions and brain activity. We develop a general framework for extrinsic statistical analysis of samples of networks, motivated by networks…

We propose a new framework to estimate the evolution of an ensemble of indistinguishable agents on a hidden Markov chain using only aggregate output data. This work can be viewed as an extension of the recent developments in optimal mass…

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…

Markov random fields area popular model for high-dimensional probability distributions. Over the years, many mathematical, statistical and algorithmic problems on them have been studied. Until recently, the only known algorithms for…

Specify a randomized algorithm that, given a very large graph or network, extracts a random subgraph. What can we learn about the input graph from a single subsample? We derive laws of large numbers for the sampler output, by relating…

In earlier work we introduced the graph bracket polynomial of graphs with marked vertices, motivated by the fact that the Kauffman bracket of a link diagram D is determined by a looped, marked version of the interlacement graph associated…

We introduce a general framework for undirected graphical models. It generalizes Gaussian graphical models to a wide range of continuous, discrete, and combinations of different types of data. The models in the framework, called exponential…

Discrete Markov random fields form a natural class of models to represent images and spatial data sets. The use of such models is, however, hampered by a computationally intractable normalising constant. This makes parameter estimation and…

Normalizing flows have emerged as an important family of deep neural networks for modelling complex probability distributions. In this note, we revisit their coupling and autoregressive transformation layers as probabilistic graphical…

We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…

In this paper, we present a simple non-parametric method for learning the structure of undirected graphs from data that drawn from an underlying unknown distribution. We propose to use Brownian distance covariance to estimate the…

Current concepts of neural networks have emerged over two centuries of progress beginning with the neural doctrine to the idea of neural cell assemblies. Presently the model of neural networks involves distributed neural circuits of nodes,…

We present an information-based uncertainty quantification method for general Markov Random Fields. Markov Random Fields (MRF) are structured, probabilistic graphical models over undirected graphs, and provide a fundamental unifying…

Big networks express various large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big…

Random matrices are used in fields as different as the study of multi-orthogonal polynomials or the enumeration of discrete surfaces. Both of them are based on the study of a matrix integral. However, this term can be confusing since the…

A new family of tree-structured Markov random fields for a vector of discrete counting random variables is introduced. According to the characteristics of the family, the marginal distributions of the Markov random fields are all Poisson…