Related papers: A note on perfect simulation for exponential rando…
This paper considers a Markov-modulated duplication-deletion random graph where at each time instant, one node can either join or leave the network; the probabilities of joining or leaving evolve according to the realization of a finite…
The configuration model is a standard tool for uniformly generating random graphs with a specified degree sequence, and is often used as a null model to evaluate how much of an observed network's structure can be explained by its degree…
We provide an extension of the perfect sampling algorithm of Fill (1998) to general chains, and describe how use of bounding processes can ease computational burden. Along the way, we unearth a simple connection between the Coupling From…
We propose two algorithms for simulating continuous time Markov chains in the presence of metastability. We show that the algorithms correctly estimate, under the ergodicity assumption, stationary averages of the process. Both algorithms,…
A number of algorithms have been developed to solve probabilistic inference problems on belief networks. These algorithms can be divided into two main groups: exact techniques which exploit the conditional independence revealed when the…
Exponential random graph models, or ERGMs, are a flexible and general class of models for modeling dependent data. While the early literature has shown them to be powerful in capturing many network features of interest, recent work…
Exponential Random Graph Models (ERGM) behave peculiar in large networks with thousand(s) of actors (nodes). Standard models containing two-star or triangle counts as statistics are often unstable leading to completely full or empty…
We develop a forward-reverse EM (FREM) algorithm for estimating parameters that determine the dynamics of a discrete time Markov chain evolving through a certain measurable state space. As a key tool for the construction of the FREM method…
We show that contiguity relations of hypergeometric functions of several variables give a direct sampling algorithm from the conditional distribution of toric models in statistics. The algorithm is based on a Markov chain on a lattice…
We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of…
Infinite Hidden Markov Models (iHMM's) are an attractive, nonparametric generalization of the classical Hidden Markov Model which can automatically infer the number of hidden states in the system. However, due to the infinite-dimensional…
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…
Synthetic power grids enable secure, real-world energy system simulations and are crucial for algorithm testing, resilience assessment, and policy formulation. We propose a novel method for the generation of synthetic transmission power…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…
We present an exclusion process based approach for sampling densest $k$-sub-graphs from regular graphs $L$ with connected complement. By interpreting an exclusion process as a Markov chain on a corresponding Token Graph $\mathfrak{L}_k$, we…
We prove an optimal mixing time bound on the single-site update Markov chain known as the Glauber dynamics or Gibbs sampling in a variety of settings. Our work presents an improved version of the spectral independence approach of Anari et…
The exponential family random graph modeling (ERGM) framework provides a flexible approach for the statistical analysis of networks. As ERGMs typically involve normalizing factors that are costly to compute, practical inference relies on a…
We develop approximate estimation methods for exponential random graph models (ERGMs), whose likelihood is proportional to an intractable normalizing constant. The usual approach approximates this constant with Monte Carlo simulations,…
Given a graph $G$, the hard-core model defines a probability distribution over its independent sets, assigning to each set of size $k$ a probability of $\frac{\lambda^k}{Z}$, where $\lambda>0$ is a parameter known as the \emph{fugacity} and…
We propose a novel exact algorithm for generating connected Erdos-Renyi random graphs $G(n,p)$. The method couples the graph exploration process to an inhomogeneous Poisson random walk, which yields an exact sampler that runs in $O(n)$ time…