Generalized PageRank on directed configuration networks

Chen, Ningyuan; Litvak, Nelly; Olvera–Cravioto, Mariana

doi:10.1002/rsa.20700

Cited by 44 publications

(114 citation statements)

References 75 publications

(136 reference statements)

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“…where (a) follows from triangular inequality of norms, in (b) we used submultiplicativity of matrix norms, and (c) follows from (10), (11) and the fact that (1)). By Lemma 3 we have for any i,…”

Section: Proof Of Lemmamentioning

confidence: 99%

PageRank in undirected random graphs

Avrachenkov¹,

Kadavankandy²,

Prokhorenkova³

et al. 2017

Internet Mathematics

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Abstract. PageRank has numerous applications in information retrieval, reputation systems, machine learning, and graph partitioning. In this paper, we study PageRank in undirected random graphs with an expansion property. The Chung-Lu random graph is an example of such a graph. We show that in the limit, as the size of the graph goes to infinity, PageRank can be approximated by a mixture of the restart distribution and the vertex degree distribution. We also extend the result to Stochastic Block Model (SBM) graphs, where we show that there is a correction term that depends on the community partitioning.

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Section: Proof Of Lemmamentioning

confidence: 99%

PageRank in undirected random graphs

Avrachenkov¹,

Kadavankandy²,

Prokhorenkova³

et al. 2017

Internet Mathematics

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“…We remark that in addition to computing the hopcount distribution, we are now also faced with the challenge of determining P (H n > k), since the distributions of W ± are not known. In order to simulate W ± we use another advanced numerical approach from [27], which describes a bootstrap algorithm for simulating the endogenous solutions of branching linear recursions. For this we first observe that W + and W − satisfy the following stochastic fixed-point equations: Figure 10.1: Hopcount probability mass function compared to the approximation provided by Theorem 10.9 for: (a) a 3-regular bi-degree sequence; (b) a bi-degree sequence generated by the IID algorithm with indpendent in-and out-degrees; and (c) a bi-degree sequence generated by the IID algorithm with dependent inand out-degrees.…”

Section: Results For Different Bi-degree Sequencesmentioning

confidence: 99%

“…We used a Zeta distribution here since then, the sized-bias distribution will again be a Zeta distribution, with exponent 5/2. The W ± were again simulated using the approach from [27] with the same parameters as for the independent case above, but with the appropriate sizedbiased distribution and the corresponding delay for the first generation of the tree. The results for the hopcount are shown in Figure 10.1(c), and the KolmogorovSmirnov distance is 0.0353.…”

Section: Iid Bi-degree Sequence With Dependent In-and Out-degreesmentioning

confidence: 99%

Asymptotic analysis of network structures: degree-degree correlations and directed paths

Hoorn

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Opgedragen aan mijn neefje Wouter: Iter tibi prosperitate scientiaque obseratur et aetas amore sapientiaque plena sit. VoorwoordGeen enkele uitzonderlijke prestatie is het werk van slechts één persoon. En hoewel ik, met betrekking tot dit proefschrift, geen uitspraak zal doen over het eerste deel van dit statement, is het tweede deel absoluut waar. Ik wil dan ook graag iedereen bedanken die hieraan op een of andere manier heeft bijgedragen. Sommige mensen wil ik in het bijzonder noemen en daarvoor zal ik deze pagina's gebruiken. Toen ik, iets meer dan vier jaar geleden, in de zomer van 2012 besloot om een PhD te doen, was ik niet helemaal zeker van mij zaak, gezien het feit dat ik al een jaar geen wiskunde meer bedreven had. Voor mijn interview in Enschede was ik dan ook erg zenuwachtig. Helemaal omdat het hier zelfs over een onderwerp ging waar ik nog nooit iets mee gedaan had gedurende mijn tijd als student. Richard, dank je dat je mij deze kans hebt gegeven, voor je vertrouwen in mij als onderzoeker en het opnemen van mij in je groep. Ik zal altijd met veel plezier terugdenken aan mijn tijd in Twente.Voor mijn dagelijkse begeleiding kon ik terecht bij Nelly. Ik weet nog goed dat ze mij tijdens ons eerste overleg meteen vertelde dat ze hele hoge verwachtingen van me had. Ik kan alleen maar hopen dat ik daar ergens in de buurt van ben gekomen. Maar Nelly, jij bent mijn verwachtingen als begeleider meer dan overstegen. Het voelt ergens vreemd om dit in het Nederlands te schrijven. Ondanks het feit dat je deze taal goed beheerst communiceren wij namelijk altijd met elkaar in het Engels. De stewardess van de KLM begreep er in ieder geval niets van. Jij was altijd heel duidelijk in wat je van me verwachtte en had altijd een plan klaar, hoewel dit laatste vaak erg flexibel was. Je gaf me de vrijheid om mijn onderzoek in te richten en liet me vaak mijn gang gaan, waar je hulp bood als ik dat nodig had. Maar je was ook streng, direct en ondubbelzinnig op de momenten dat dit moest. Naast een meer dan uitstekende begeleider ben je een ook een hele goede vriendin van me geworden. Ik heb ontzettend genoten van de conferenties die wij samen hebben bezocht en alle avonturen die wij hebben beleefd. Ik hoop dan ook dat wij nog heel lang vrienden zullen blijven. Maar nu zal ik verder gaan, voordat je me weer vertelt dat ik als een meisje schrijf.Gedurende mijn PhD heb ik de mogelijkheid gehad om twee onderzoeksstages in het buitenland te doen en daar ben ik heel dankbaar voor.Mariana, thank you for inviting me to Columbia. It was my first time collaborating with someone other than my supervisor and I more than appreciated the opportunity you gave me. When writing this thesis, especially when dealing with some technical proofs, I realized how much I learned from you in only these vii Asymptotic analysis of network structures: degree-degree correlations and directed paths two weeks. I also want to thank you for being part of my defense committee and reading my thesis. I hope to continue our collaboration in the future and learn ...

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“…, where the inequality is Jensen's and the approximate equality is (12). The final expression exceeds T n by (A2), i.e.…”

Section: Related Workmentioning

confidence: 96%

“…Finally, we note that the random graph model we consider was proposed and analyzed in [13]. As mentioned in Appendix A, our analysis uses a branching process approximation of this model that draws from the analysis of [12]. The directed configuration model is a natural extension of the undirected configuration model, the study of which originated in [7,8,31].…”

Section: Related Workmentioning

confidence: 99%

Local Non-Bayesian Social Learning with Stubborn Agents

Vial

Subramanian

2019

Proceedings of the 2019 ACM Conference on Economics and Computation

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In this work, we study a mathematical model for the spread of fake news on social networks. The model includes a large number of agents attempting to learn an underlying true state of the world in an iterative fashion. At each iteration, agents update their beliefs about the true state in a non-Bayesian fashion, using noisy observations of the true state and the beliefs of a subset of other agents. These subsets may include stubborn agents, who attempt to convince others of an erroneous true state (modeling users spreading fake news). This process continues for a finite number of iterations we call the learning horizon.In the first part of the paper, we characterize the learning outcome in terms of the learning horizon and a quantity that describes the "density" of stubborn agents, assuming a certain generative model for the underlying social network. Among other conclusions, our analysis shows that the learning outcome exhibits a phase transition, wherein agents learn the true state on short horizons but suddenly forget the true state on slightly longer horizons, and that adversaries deploying stubborn agents experience diminishing returns.In the second part of the paper, we leverage our learning outcome analysis to devise optimal strategies for seeding stubborn agents so as to disrupt learning. While our proofs of optimality rely on the same generative graph model, we show empirically that these seeding strategies outperform intuitive heuristics on real social networks not conforming to the generative model. Furthermore, the form of our proposed strategies is non-obvious and yields novel insights into vulnerabilities of non-Bayesian learning models.

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Generalized PageRank on directed configuration networks

Cited by 44 publications

References 75 publications

PageRank in undirected random graphs

PageRank in undirected random graphs

Asymptotic analysis of network structures: degree-degree correlations and directed paths

Local Non-Bayesian Social Learning with Stubborn Agents

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