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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

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. ...

##
###
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]

2021
*
arXiv
*
pre-print

We develop

arXiv:1911.01503v2
fatcat:2grqc24l2jbfhcguhosbrww3pq
*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. ...##
###
A closed-form approach to Bayesian inference in tree-structured graphical models
[article]

2017
*
arXiv
*
pre-print

Under these conditions, we derive

arXiv:1504.02723v4
fatcat:l6tzpgahfjcp5ftymtenaq7aza
*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. ...##
###
Exact sampling with coupled Markov chains and applications to statistical mechanics

1996
*
Random structures & algorithms (Print)
*

We describe

doi:10.1002/(sici)1098-2418(199608/09)9:1/2<223::aid-rsa14>3.0.co;2-o
fatcat:xav4i5knujdpjp5lh77hvrss6u
*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. ...##
###
Exact sampling with coupled Markov chains and applications to statistical mechanics

1996
*
Random structures & algorithms (Print)
*

We describe

doi:10.1002/(sici)1098-2418(199608/09)9:1/2<223::aid-rsa14>3.3.co;2-r
fatcat:3nc3ro3qefckffm7ackemkeauu
*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. ...##
###
A Distributed Laplacian Solver and its Applications to Electrical Flow and Random Spanning Tree Computation
[article]

2020
*
arXiv
*
pre-print

This marks

arXiv:1905.04989v4
fatcat:nw7jppxkmvdp7lo7otpj4zvhbi
*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*...##
###
Randomization algorithms for large sparse networks

2019
*
Physical review. E
*

These two types of constraints

doi:10.1103/physreve.99.053311
fatcat:4bmdjcwb4fgv3hyeqemi7kvfmm
*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*. ...##
###
Graphical Models in a Nutshell
[chapter]

2007
*
Introduction to Statistical Relational Learning
*

Graphical models have enjoyed

doi:10.7551/mitpress/7432.003.0004
fatcat:wbhjah7qczdftaiod5jg4ok2xe
*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. ...##
###
The Looping Rate and Sandpile Density of Planar Graphs

2016
*
The American mathematical monthly
*

We give

doi:10.4169/amer.math.monthly.123.1.19
fatcat:ohrq6shikjezfhp22fj4zyvu3q
*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*...##
###
Exact Mixing in an Unknown Markov Chain

1995
*
Electronic Journal of Combinatorics
*

We give

doi:10.37236/1209
fatcat:jfvyjh52eray3cyynovflh6fsa
*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. ...##
###
Random Forests and Networks Analysis

2018
*
Journal of statistical physics
*

Wilson [Wi] in

doi:10.1007/s10955-018-2124-8
fatcat:wqqbjef63rcs7azcduux2limti
*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 ...##
###
Conditional random fields for multi-agent reinforcement learning

2007
*
Proceedings of the 24th international conference on Machine learning - ICML '07
*

They are actions that update

doi:10.1145/1273496.1273640
dblp:conf/icml/ZhangAV07
fatcat:qm5uqf4emzgvbdlhzvssrgwgge
*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. ...##
###
Generalized loop-erased random walks and approximate reachability

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 ...

##
###
Probabilistic Independence Networks for Hidden Markov Probability Models

1997
*
Neural Computation
*

In this paper we explore hidden

doi:10.1162/neco.1997.9.2.227
pmid:9117903
fatcat:es5rdtx6t5dorcta7lplgu7k74
*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 ...
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