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How to Get a Perfectly Random Sample from a Generic Markov Chain and Generate a Random Spanning Tree of a Directed Graph

James Gary Propp, David Bruce Wilson
1998 Journal of Algorithms  
A general problem in computational probability theory is that of generating a random sample from the state space of a Markov chain in accordance with the steady-state probability law of the chain.  ...  Another problem is that of generating a random spanning tree of a graph or spanning arborescence of a directed graph in accordance with the uniform distribution, or more generally in accordance with a  ...  The answer is ''yes,'' to within constant factors; Section 5 shows how to use coupling from the past to generate random arborescences from a general directed graph within 18 cover times of G.  ... 
doi:10.1006/jagm.1997.0917 fatcat:kg4dpk5g65dtnn6evz57qtmgbu

Page 7778 of Mathematical Reviews Vol. , Issue 96m [page]

1996 Mathematical Reviews  
and sample a random spanning tree from a directed graph, both within the cover time.  ...  Using the techniques from the sampling algorithm, we also show how to sample random directed spanning trees from a weighted directed graph, with arcs directed to a root, and probability proportional to  ... 

Metropolized Forest Recombination for Monte Carlo Sampling of Graph Partitions [article]

Eric Autrey and Daniel Carter and Gregory Herschlag and Zach Hunter and Jonathan C. Mattingly
2021 arXiv   pre-print
We develop a new Markov chain on graph partitions that makes relatively global moves yet is computationally feasible to be used as the proposal in the Metropolis-Hastings method.  ...  Our resulting algorithm can be made reversible and able to sample from a specified measure on partitions.  ...  We also thank the Rhodes Information Intiative and the Duke Provost and Deans office for financial support and creating a productive working environment.  ... 
arXiv:1911.01503v2 fatcat:2grqc24l2jbfhcguhosbrww3pq

A closed-form approach to Bayesian inference in tree-structured graphical models [article]

Loïc Schwaller, Stéphane Robin, Michael Stumpf
2017 arXiv   pre-print
Under these conditions, we derive a fast an exact algorithm to compute the posterior probability for an edge to belong to the tree model using an algebraic result called the Matrix-Tree theorem.  ...  More specifically we aim at achieving the inference with close-form posteriors, avoiding any sampling step. To this aim, we restrict the set of considered graphs to mixtures of spanning trees.  ...  Acknowledgments The authors thank Sophie Donnet for her helpful comments and remarks.  ... 
arXiv:1504.02723v4 fatcat:l6tzpgahfjcp5ftymtenaq7aza

Exact sampling with coupled Markov chains and applications to statistical mechanics

James Gary Propp, David Bruce Wilson
1996 Random structures & algorithms (Print)  
We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution.  ...  One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M su  ...  Acknowledgements We thank David Aldous, Persi Diaconis, and Jim Fill for their useful suggestions.  ... 
doi:10.1002/(sici)1098-2418(199608/09)9:1/2<223::aid-rsa14>3.0.co;2-o fatcat:xav4i5knujdpjp5lh77hvrss6u

Exact sampling with coupled Markov chains and applications to statistical mechanics

James Gary Propp, David Bruce Wilson
1996 Random structures & algorithms (Print)  
We describe a simple variant of this method that determines on its own when to stop, and that outputs samples in exact accordance with the desired distribution.  ...  One approach is to run an ergodic (i.e., irreducible aperiodic) Markov chain whose stationary distribution is the desired distribution on this set; after the Markov chain has run for M steps, with M su  ...  Acknowledgements We thank David Aldous, Persi Diaconis, and Jim Fill for their useful suggestions.  ... 
doi:10.1002/(sici)1098-2418(199608/09)9:1/2<223::aid-rsa14>3.3.co;2-r fatcat:3nc3ro3qefckffm7ackemkeauu

A Distributed Laplacian Solver and its Applications to Electrical Flow and Random Spanning Tree Computation [article]

Iqra Altaf Gillani, Amitabha Bagchi
2020 arXiv   pre-print
This marks a significant departure from the existing techniques, mostly based on graph-theoretic constructions and sampling.  ...  As a result, our Laplacian solver can be used to adapt the approach by Kelner and Mądry (2009) to give the first distributed algorithm to compute approximate random spanning trees efficiently.  ...  Random Spanning Tree Generation Given an undirected graph G = (V, E) with |V | = n vertices and |E| = m edges each having unit weight, the random spanning tree generation problem requires us to find an  ... 
arXiv:1905.04989v4 fatcat:nw7jppxkmvdp7lo7otpj4zvhbi

Randomization algorithms for large sparse networks

Kai Puolamäki, Andreas Henelius, Antti Ukkonen
2019 Physical review. E  
These two types of constraints cover a wide variety of practical use cases. The method is applicable to both undirected and directed graphs.  ...  In this paper we present an efficient property-preserving Markov chain Monte Carlo method termed CycleSampler for generating surrogate networks in which (1) edge weights are constrained to intervals and  ...  Indeed, by taking a spanning tree of a graph and adding an edge not in the graph we always get a unique graph cycle. Those graph cycles form the cycle basis of the graph.  ... 
doi:10.1103/physreve.99.053311 fatcat:4bmdjcwb4fgv3hyeqemi7kvfmm

Graphical Models in a Nutshell [chapter]

2007 Introduction to Statistical Relational Learning  
Graphical models have enjoyed a surge of interest in the last two decades, due both to the flexibility and power of the representation and to the increased ability to effectively learn and perform inference  ...  The framework is quite general in that many of the commonly proposed statistical models (Kalman filters, hidden Markov models, Ising models) can be described as graphical models.  ...  We can transform the undirected spanning tree into a directed spanning tree by choosing an arbitrary root, and directing edges away from the root.  ... 
doi:10.7551/mitpress/7432.003.0004 fatcat:wbhjah7qczdftaiod5jg4ok2xe

The Looping Rate and Sandpile Density of Planar Graphs

Adrien Kassel, David B. Wilson
2016 The American mathematical monthly  
We give a simple formula for the looping rate of loop-erased random walk on a finite planar graph.  ...  The looping rate formula is well-suited to taking limits where the graph tends to an infinite lattice, and we use it to give an elementary derivation of the (previously computed) looping rate and sandpile  ...  Wilson [40] described further connections between random spanning trees and random walk, giving an exact sampling algorithm (this is how Figure 1 was produced) with implications for the analysis of spanning  ... 
doi:10.4169/amer.math.monthly.123.1.19 fatcat:ohrq6shikjezfhp22fj4zyvu3q

Exact Mixing in an Unknown Markov Chain

Laszlo Lovasz, Peter Winkler
1995 Electronic Journal of Combinatorics  
We give a simple stopping rule which will stop an unknown, irreducible $n$-state Markov chain at a state whose probability distribution is exactly the stationary distribution of the chain.  ...  The expected stopping time of the rule is bounded by a polynomial in the maximum mean hitting time of the chain.  ...  The authors are indebted to David Aldous and Eric Denardo for many useful comments and corrections.  ... 
doi:10.37236/1209 fatcat:jfvyjh52eray3cyynovflh6fsa

Random Forests and Networks Analysis

Luca Avena, Fabienne Castell, Alexandre Gaudillière, Clothilde Mélot
2018 Journal of statistical physics  
Wilson [Wi] in the 1990's described a simple and efficient algorithm based on loop-erased random walks to sample uniform spanning trees and more generally weighted trees or forests spanning a given graph  ...  A first foundational part on determinantal structures and efficient sampling procedures is followed by four main applications: 1) a random-walk-based notion of well-distributed points in a graph 2) how  ...  The project leading to this publication has received funding from Excellence Initiative of Aix-Marseille University -A*MIDEX -and Excellence Laboratory Archimède (ANR-11-LABX-0033), a French "Investissements  ... 
doi:10.1007/s10955-018-2124-8 fatcat:wqqbjef63rcs7azcduux2limti

Conditional random fields for multi-agent reinforcement learning

Xinhua Zhang, Douglas Aberdeen, S. V. N. Vishwanathan
2007 Proceedings of the 24th international conference on Machine learning - ICML '07  
They are actions that update the environment and affect the next observation. From an RL point of view, CRFs provide a natural way to model joint actions in a decentralized Markov decision process.  ...  They define how agents can communicate with each other to choose the optimal joint action.  ...  Acknowledgements NICTA is funded by the Australian Government's Backing Australia's Ability program and the Centre of Excellence program.  ... 
doi:10.1145/1273496.1273640 dblp:conf/icml/ZhangAV07 fatcat:qm5uqf4emzgvbdlhzvssrgwgge

Generalized loop-erased random walks and approximate reachability

Igor Gorodezky, Igor Pak
2012 Random structures & algorithms (Print)  
The sampling of random trees is a well-studied problem with connections to graph polynomials and their complexity (see [Wel]).  ...  In this paper we extend the loop-erased random walk (LERW) to the directed hypergraph setting. We then generalize Wilson's algorithm for uniform sampling of spanning trees to directed hypergraphs.  ...  This work was initiated and completed during a special program at the Institute for Pure and Applied Mathematics (IPAM) at UCLA; we are thankful to IPAM and the program organizers for their hospitality  ... 
doi:10.1002/rsa.20460 fatcat:e4g66vwmbrdptmvo4ueuuvzziu

Probabilistic Independence Networks for Hidden Markov Probability Models

Padhraic Smyth, David Heckerman, Michael I. Jordan
1997 Neural Computation  
In this paper we explore hidden Markov models (HMMs) and related structures within the general framework of probabilistic independence networks (PINs).  ...  Examples of relatively complex models to handle sensor fusion and coarticulation in speech recognition are introduced and treated within the graphical model framework to illustrate the advantages of the  ...  The research described in this article was carried out in part by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration  ... 
doi:10.1162/neco.1997.9.2.227 pmid:9117903 fatcat:es5rdtx6t5dorcta7lplgu7k74
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