Related papers: A note on perfect simulation for exponential rando…
Generation of deviates from random graph models with non-trivial edge dependence is an increasingly important problem. Here, we introduce a method which allows perfect sampling from random graph models in exponential family form…
We describe a new algorithm for the perfect simulation of variable length Markov chains and random systems with perfect connections. This algorithm, which generalizes Propp and Wilson's simulation scheme, is based on the idea of coupling…
This note extends the work of Foss and Tweedie (1997), who showed that availability of the classic Coupling from The Past algorithm of Propp and Wilson (1996) is essentially equivalent to uniform ergodicity for a Markov chain (see also…
In this paper we consider the problem of sampling from the low-temperature exponential random graph model (ERGM). The usual approach is via Markov chain Monte Carlo, but Bhamidi et al. showed that any local Markov chain suffers from an…
Exponential random graphs are used extensively in the sociology literature. This model seeks to incorporate in random graphs the notion of reciprocity, that is, the larger than expected number of triangles and other small subgraphs.…
We show that efficient approximate sampling algorithms, combined with a slow exponential time oracle for computing its output distribution, can be combined into constructing efficient perfect samplers, which sample exactly from a target…
We present the first algorithm for generating random variates exactly uniformly from the set of perfect matchings of a bipartite graph with a polynomial expected running time over a nontrivial set of graphs. Previous Markov chain approaches…
Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible…
This paper generalizes the work of Kendall [Electron. Comm. Probab. 9 (2004) 140--151], which showed that perfect simulation, in the form of dominated coupling from the past, is always possible (although not necessarily practical) for…
The Exponential-family Random Graph Model (ERGM) is a powerful model to fit networks with complex structures. However, for dynamic valued networks whose observations are matrices of counts that evolve over time, the development of the ERGM…
We study a simple Markov chain, the switch chain, on the set of all perfect matchings in a bipartite graph. This Markov chain was proposed by Diaconis, Graham and Holmes as a possible approach to a sampling problem arising in Statistics. We…
In this paper, we consider a one-dimensional random geometric graph process with the inter-nodal gaps evolving according to an exponential AR(1) process, which may serve as a mobile wireless network model. The transition probability matrix…
Exponential random graph models (ERGMs), also known as p* models, have been utilized extensively in the social science literature to study complex networks and how their global structure depends on underlying structural components. However,…
We present the first class of perfect sampling (also known as exact simulation) algorithms for the steady-state distribution of non-Markovian loss networks. We use a variation of Dominated Coupling From The Past for which we simulate a…
Many applications in the field of statistics require Markov chain Monte Carlo methods. Determining appropriate starting values and run lengths can be both analytically and empirically challenging. A desire to overcome these problems has led…
Exponential random graph models have become increasingly important in the study of modern networks ranging from social networks, economic networks, to biological networks. They seek to capture a wide variety of common network tendencies…
Perfect sampling is a technique that uses coupling arguments to provide a sample from the stationary distribution of a Markov chain in a finite time without ever computing the distribution. This technique is very efficient if all the events…
Exponential Random Graph Models (ERGMs) have gained increasing popularity over the years. Rooted into statistical physics, the ERGMs framework has been successfully employed for reconstructing networks, detecting statistically significant…
We give an efficient algorithm to generate a graph from a distribution $\epsilon$-close to $G(n,p)$, in the sense of total variation distance. In particular, if $p$ is represented with $O(\log n)$-bit accuracy, then, with high probability,…
Bounding chains are a technique that offers three benefits to Markov chain practitioners: a theoretical bound on the mixing time of the chain under restricted conditions, experimental bounds on the mixing time of the chain that are provably…