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Extreme values of the stationary distribution of random walks on directed graphs [article]

Sinan Aksoy, Fan Chung, Xing Peng
2016 arXiv   pre-print
We examine the stationary distribution of random walks on directed graphs.  ...  In particular, we focus on the principal ratio, which is the ratio of maximum to minimum values of vertices in the stationary distribution.  ...  This has immediate implications for the central question of bounding the rate of convergence of a random walk on a directed graph where extreme values of the stationary distribution play an important role  ... 
arXiv:1602.01162v1 fatcat:4wmyzpabi5b73fu2622sp6e4vq

Distribution and Dependence of Extremes in Network Sampling Processes

Konstantin Avrachenkov, Natalia M. Markovich, Jithin K. Sreedharan
2014 2014 Tenth International Conference on Signal-Image Technology and Internet-Based Systems  
We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like node degrees, number of followers, or income  ...  Several useful extremes of the sampled sequence like the kth largest value, clusters of exceedances over a threshold, and first hitting time of a large value are investigated.  ...  Acknowledgements The work of the first and third authors is partly supported by ADR "Network Science" of the Alcatel-Lucent Inria joint lab.  ... 
doi:10.1109/sitis.2014.91 dblp:conf/sitis/AvrachenkovMS14 fatcat:j7ktcne5ffas3cqj3pcb7omraa

Distribution and dependence of extremes in network sampling processes

Konstantin Avrachenkov, Natalia M. Markovich, Jithin K. Sreedharan
2015 Computational Social Networks  
We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like node degrees, number of followers, or income  ...  Several useful extremes of the sampled sequence like the kth largest value, clusters of exceedances over a threshold, and first hitting time of a large value are investigated.  ...  Acknowledgements The work of the first and third authors is partly supported by ADR "Network Science" of the Alcatel-Lucent Inria joint lab.  ... 
doi:10.1186/s40649-015-0018-3 fatcat:kpzk2hwvlrc35cqgp2xfhbuctm

Urban sensing as a random search process [article]

Kevin O'Keeffe, Paolo Santi, Brandon Wang, Carlo Ratti
2020 arXiv   pre-print
In particular, on certain graph topologies it offers reduced cover times compared to persistent random walks.  ...  Inspired by the movements of real taxis, the taxi-drive is composed of both random and regular parts; passengers are brought to randomly chosen locations via deterministic (i.e. shortest paths) routes.  ...  for Natural Resources and the Environment, Shenzhen, Singapore-MIT Alliance for Research and Technology (SMART), UBER, Vitoria State Government, Volkswagen Group America, and all the members of the MIT  ... 
arXiv:1901.08678v2 fatcat:h7srnsbxvnekpov3cde5tjl5ua

Walk, not wait

Azade Nazi, Zhuojie Zhou, Saravanan Thirumuruganathan, Nan Zhang, Gautam Das
2015 Proceedings of the VLDB Endowment  
Specifically, unlike traditional random walks which wait for the convergence of sampling distribution to a predetermined target distribution -a waiting process that incurs a high query cost -we develop  ...  We present a novel backward random walk technique which provides provably unbiased estimations for the sampling probability, and demonstrate the superiority of WALK-ESTIMATE over traditional random walks  ...  One can see that Z → 0 when the random walk converges to the stationary distribution.  ... 
doi:10.14778/2735703.2735707 fatcat:l4qgzngbdrbnbboj5zzmmanh7a

Potential induced random teleportation on finite graphs

Shui-Nee Chow, Xiaojing Ye, Haomin Zhou
2015 Computational optimization and applications  
We present a continuous time analogue of the random walk and teleportation, and derive the lower bound on the order of its exponential convergence rate to stationary distribution.  ...  We propose and analyze a potential induced random walk and its modification called random teleportation on finite graphs.  ...  The value of β determines how much the random walk relies on graph structure and potential distribution.  ... 
doi:10.1007/s10589-015-9727-7 fatcat:xve2b4m3vvbs3ehxcqzv35si3m

Leveraging history for faster sampling of online social networks

Zhuojie Zhou, Nan Zhang, Gautam Das
2015 Proceedings of the VLDB Endowment  
A problem with random walks, however, is the "burn-in" period which requires a large number of transitions/queries before the sampling distribution converges to a stationary value that enables the drawing  ...  than baseline random walks while achieving the same stationary distribution.  ...  One can see that all the three random walks converge to the same stationary distribution.  ... 
doi:10.14778/2794367.2794373 fatcat:amr2zx7wofhwnnxff7nmia27hi

Distribution and Dependence of Extremes in Network Sampling Processes [article]

Konstantin Avrachenkov, Natalia M. Markovich, Jithin K. Sreedharan
2015 arXiv   pre-print
We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like node degrees, number of followers or income  ...  We abstract the dependence and the statistics of extremes into a single parameter that appears in Extreme Value Theory, called extremal index (EI).  ...  In this algorithm we follow random walk on a modified graph which is a superposition of the given graph and complete graph on same vertex set of the given graph with weight α/N on each edge, α ∈ [0, ∞]  ... 
arXiv:1408.2529v2 fatcat:5hujht4qbvfa7btvrky77nplje

Leveraging History for Faster Sampling of Online Social Networks [article]

Zhuojie Zhou, Nan Zhang, Gautam Das
2015 arXiv   pre-print
baseline random walks while achieving the same stationary distribution.  ...  A problem with random walks, however, is the "burn-in" period which requires a large number of transitions/queries before the sampling distribution converges to a stationary value that enables the drawing  ...  One can see that all the three random walks converge to the same stationary distribution.  ... 
arXiv:1505.00079v3 fatcat:h4jxlvajxjcovbqz3s4els4yya

Arc-Community Detection via Triangular Random Walks

Paolo Boldi, Marco Rosa
2012 2012 Eighth Latin American Web Congress  
stationary distribution will depend on the damping factor as well • The stationary distribution of RWR is PageRank From nodes to arcs • The stationary distribution of RWR associates a probability to  ...  Nature, 2010. • Random walks (RW) on a graph • Standard random walk: a sequence of r.v. such that • The surfer moves around, choosing every time an arc to follow uniformly at random X 0 , X 1 , . . .  ... 
doi:10.1109/la-web.2012.19 dblp:conf/la-web/BoldiR12 fatcat:ceifmbb3z5fohjqtbvbhxlq34y

Walk, Not Wait: Faster Sampling Over Online Social Networks [article]

Azade Nazi, Zhuojie Zhou, Saravanan Thirumuruganathan, Nan Zhang, Gautam Das
2014 arXiv   pre-print
Specifically, unlike traditional random walk which wait for the convergence of sampling distribution to a predetermined target distribution - a waiting process that incurs a high query cost - we develop  ...  We present a novel backward random walk technique which provides provably unbiased estimations for the sampling probability, and demonstrate the superiority of WALK-ESTIMATE over traditional random walks  ...  One can see that Z → 0 when the random walk converges to the stationary distribution.  ... 
arXiv:1410.7833v2 fatcat:pnfslqrijvholc6deegqgcpiw4

Concentration of the Stationary Distribution on General Random Directed Graphs [article]

Franklin H. J. Kenter
2013 arXiv   pre-print
Using perturbation bounds as well as Chernoff inequalities, we show that the stationary distribution of a Markov process on a random graph is concentrated near that of the "expected" process under mild  ...  These conditions involve the ratio between the minimum and maximum in- and out-degrees, the ratio of the minimum and maximum entry in the stationary distribution, and the smallest singu- lar value of the  ...  In this paper, we give criteria as to when the stationary distribution of a Markov chain on a general random directed graph is close to the "expected" stationary distribution.  ... 
arXiv:1309.4811v1 fatcat:37mytb7bx5blvigvee3hji73dm

When Simple Exploration is Sample Efficient: Identifying Sufficient Conditions for Random Exploration to Yield PAC RL Algorithms [article]

Yao Liu, Emma Brunskill
2019 arXiv   pre-print
In this work we propose problem specific sample complexity bounds of Q learning with random walk exploration that rely on several structural properties.  ...  Efficient exploration is one of the key challenges for reinforcement learning (RL) algorithms. Most traditional sample efficiency bounds require strategic exploration.  ...  Our result relies on some key results about convergence of a lazy random walk on directed graph in Chung (2005) .  ... 
arXiv:1805.09045v4 fatcat:m3qh5wty4zamzkkvw2uuu36kfq

Distributed Averaging Via Lifted Markov Chains

Kyomin Jung, Devavrat Shah, Jinwoo Shin
2010 IEEE Transactions on Information Theory  
As the main result of this paper, we design an algorithm with the fastest possible rate of convergence using a non-reversible Markov chain on the given network graph.  ...  Motivated by applications of distributed linear estimation, distributed control and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average  ...  For a given graph G = (V, E) and distribution π on V , the goal is to produce a random walk P on G whose stationary distribution is π.  ... 
doi:10.1109/tit.2009.2034777 fatcat:s46nkx2vdnhxzey2qeebmemjvq

Distributed Averaging via Lifted Markov Chains [article]

Kyomin Jung, Devavrat Shah, Jinwoo Shin
2009 arXiv   pre-print
As the main result of this paper, we design an algorithm with the fastest possible rate of convergence using a non-reversible Markov chain on the given network graph.  ...  Motivated by applications of distributed linear estimation, distributed control and distributed optimization, we consider the question of designing linear iterative algorithms for computing the average  ...  For example, failure of "root" node can increase the mixing time drastically. To address this, one may alternatively use a "hierarchical expander" based pseudo-lifting.  ... 
arXiv:0908.4073v1 fatcat:qme34amqjbgmdnx6zckgp66q64
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