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

2016
*
arXiv
*
pre-print

We examine

arXiv:1602.01162v1
fatcat:4wmyzpabi5b73fu2622sp6e4vq
*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 ...##
###
Distribution and Dependence of Extremes in Network Sampling Processes

2014
*
2014 Tenth International Conference on Signal-Image Technology and Internet-Based Systems
*

We consider

doi:10.1109/sitis.2014.91
dblp:conf/sitis/AvrachenkovMS14
fatcat:j7ktcne5ffas3cqj3pcb7omraa
*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. ...##
###
Distribution and dependence of extremes in network sampling processes

2015
*
Computational Social Networks
*

We consider

doi:10.1186/s40649-015-0018-3
fatcat:kpzk2hwvlrc35cqgp2xfhbuctm
*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. ...##
###
Urban sensing as a random search process
[article]

2020
*
arXiv
*
pre-print

In particular,

arXiv:1901.08678v2
fatcat:h7srnsbxvnekpov3cde5tjl5ua
*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 ...##
###
Walk, not wait

2015
*
Proceedings of the VLDB Endowment
*

Specifically, unlike traditional

doi:10.14778/2735703.2735707
fatcat:l4qgzngbdrbnbboj5zzmmanh7a
*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*. ...##
###
Potential induced random teleportation on finite graphs

2015
*
Computational optimization and applications
*

We present a continuous time analogue

doi:10.1007/s10589-015-9727-7
fatcat:xve2b4m3vvbs3ehxcqzv35si3m
*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*. ...##
###
Leveraging history for faster sampling of online social networks

2015
*
Proceedings of the VLDB Endowment
*

A problem with

doi:10.14778/2794367.2794373
fatcat:amr2zx7wofhwnnxff7nmia27hi
*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*. ...##
###
Distribution and Dependence of Extremes in Network Sampling Processes
[article]

2015
*
arXiv
*
pre-print

We consider

arXiv:1408.2529v2
fatcat:5hujht4qbvfa7btvrky77nplje
*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, ∞] ...##
###
Leveraging History for Faster Sampling of Online Social Networks
[article]

2015
*
arXiv
*
pre-print

baseline

arXiv:1505.00079v3
fatcat:h4jxlvajxjcovbqz3s4els4yya
*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*. ...##
###
Arc-Community Detection via Triangular Random Walks

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 , . . . ...

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

2014
*
arXiv
*
pre-print

Specifically, unlike traditional

arXiv:1410.7833v2
fatcat:pnfslqrijvholc6deegqgcpiw4
*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*. ...##
###
Concentration of the Stationary Distribution on General Random Directed Graphs
[article]

2013
*
arXiv
*
pre-print

Using perturbation bounds as well as Chernoff inequalities, we show that

arXiv:1309.4811v1
fatcat:37mytb7bx5blvigvee3hji73dm
*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*. ...##
###
When Simple Exploration is Sample Efficient: Identifying Sufficient Conditions for Random Exploration to Yield PAC RL Algorithms
[article]

2019
*
arXiv
*
pre-print

In this work we propose problem specific sample complexity bounds

arXiv:1805.09045v4
fatcat:m3qh5wty4zamzkkvw2uuu36kfq
*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) . ...##
###
Distributed Averaging Via Lifted Markov Chains

2010
*
IEEE Transactions on Information Theory
*

As

doi:10.1109/tit.2009.2034777
fatcat:s46nkx2vdnhxzey2qeebmemjvq
*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. ...##
###
Distributed Averaging via Lifted Markov Chains
[article]

2009
*
arXiv
*
pre-print

As

arXiv:0908.4073v1
fatcat:qme34amqjbgmdnx6zckgp66q64
*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. ...
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