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Related papers: Perfect sampling from rapidly mixing Markov chains

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In this paper we propose a perfect simulation algorithm for the Exponential Random Graph Model, based on the Coupling From The Past method of Propp & Wilson (1996). We use a Glauber dynamics to construct the Markov Chain and we prove the…

Computation · Statistics 2017-10-04 Andressa Cerqueira , Aurélien Garivier , Florencia Leonardi

In the $G$-sampling problem, the goal is to output an index $i$ of a vector $f \in\mathbb{R}^n$, such that for all coordinates $j \in [n]$, \[\textbf{Pr}[i=j] = (1 \pm \epsilon) \frac{G(f_j)}{\sum_{k\in[n]} G(f_k)} + \gamma,\] where…

Data Structures and Algorithms · Computer Science 2021-08-30 Rajesh Jayaram , David P. Woodruff , Samson Zhou

The problem of efficiently sampling from a set of(undirected) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the sampling. The…

Data Structures and Algorithms · Computer Science 2014-12-18 Catherine Greenhill

Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the…

Machine Learning · Computer Science 2014-11-13 Xianghang Liu , Justin Domke

This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…

Data Structures and Algorithms · Computer Science 2020-03-10 Feras A. Saad , Cameron E. Freer , Martin C. Rinard , Vikash K. Mansinghka

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…

Probability · Mathematics 2013-12-17 Jose Blanchet , Jing Dong

We show that any application of the technique of unbiased simulation becomes perfect simulation when coalescence of the two coupled Markov chains can be practically assured in advance. This happens when a fixed number of iterations is high…

Computation · Statistics 2023-08-15 George M. Leigh , Wen-Hsi Yang , Montana E. Wickens , Amanda R. Northrop

Markov chains are an important tool for modelling and evaluating systems in computer science, economics, biology and numerous other fields. Thus, approximating Markov chains is a useful tool for decreasing the computational effort needed…

Probability · Mathematics 2025-07-16 Patrick Sonnentag

The problem of efficiently sampling from a set of (undirected, or directed) graphs with a given degree sequence has many applications. One approach to this problem uses a simple Markov chain, which we call the switch chain, to perform the…

Discrete Mathematics · Computer Science 2017-09-13 Catherine Greenhill , Matteo Sfragara

We provide a perfect sampling algorithm for the hard-sphere model on subsets of $\mathbb{R}^d$ with expected running time linear in the volume under the assumption of strong spatial mixing. A large number of perfect and approximate sampling…

Data Structures and Algorithms · Computer Science 2024-08-22 Konrad Anand , Andreas Göbel , Marcus Pappik , Will Perkins

We show that the ratio of the number of near perfect matchings to the number of perfect matchings in $d$-regular strong expander (non-bipartite) graphs, with $2n$ vertices, is a polynomial in $n$, thus the Jerrum and Sinclair Markov chain…

Data Structures and Algorithms · Computer Science 2021-03-17 Farzam Ebrahimnejad , Ansh Nagda , Shayan Oveis Gharan

Counting perfect matchings has played a central role in the theory of counting problems. The permanent, corresponding to bipartite graphs, was shown to be #P-complete to compute exactly by Valiant (1979), and a fully polynomial randomized…

Data Structures and Algorithms · Computer Science 2017-12-21 Daniel Štefankovič , Eric Vigoda , John Wilmes

Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…

Computation · Statistics 2015-10-30 Christophe Andrieu , Matti Vihola

The target measure $\mu$ is the distribution of a random vector in a box $\cB$, a Cartesian product of bounded intervals. The Gibbs sampler is a Markov chain with invariant measure $\mu$. A ``coupling from the past'' construction of the…

Probability · Mathematics 2007-09-25 Pedro J. Fernandez , Pablo A. Ferrari , Sebastian Grynberg

We give an efficient perfect sampling algorithm for weighted, connected induced subgraphs (or graphlets) of rooted, bounded degree graphs. Our algorithm utilizes a vertex-percolation process with a carefully chosen rejection filter and…

Data Structures and Algorithms · Computer Science 2023-11-17 Antonio Blanca , Sarah Cannon , Will Perkins

Generating random variates from high-dimensional distributions is often done approximately using Markov chain Monte Carlo. In certain cases, perfect simulation algorithms exist that allow one to draw exactly from the stationary…

Data Structures and Algorithms · Computer Science 2017-01-05 Mark Huber

We prove that Broder's Markov chain for approximate sampling near-perfect and perfect matchings is not rapidly mixing for Hamiltonian, regular, threshold and planar bipartite graphs, filling a gap in the literature. In the second part we…

Discrete Mathematics · Computer Science 2014-04-17 Annabell Berger , Steffen Rechner

In this work, we propose a first-order sampling method called the Metropolis-adjusted Preconditioned Langevin Algorithm for approximate sampling from a target distribution whose support is a proper convex subset of $\mathbb{R}^{d}$. Our…

Computation · Statistics 2025-02-27 Vishwak Srinivasan , Andre Wibisono , Ashia Wilson

Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…

Statistics Theory · Mathematics 2025-11-14 Erik Jansson , Moritz Schauer , Ruben Seyer , Akash Sharma

It is known that the simple slice sampler has robust convergence properties, however the class of problems where it can be implemented is limited. In contrast, we consider hybrid slice samplers which are easily implementable and where…

Methodology · Statistics 2026-01-14 Krzysztof Łatuszyński , Daniel Rudolf