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Metropolis-Hastings Algorithms for Estimating Betweenness Centrality Talel Abdessalem

Abstract

Recently, an optimal probability distribution was proposed to sample vertices for estimating betweenness centrality, that yields the minimum approximation error. However, it is computation-ally expensive to directly use it. In this paper, we investigate exploiting Metropolis-Hastings technique to sample based on this distribution. As a result, first given a network G and a vertex r ∈ V (G), we propose a Metropolis-Hastings MCMC algorithm that samples from the space V (G) and estimates betweenness score of r. The stationary distribution of our MCMC sampler is the optimal distribution. We also show that our MCMC sampler provides an (ϵ, δ)-approximation. Then, given a network G and a set R ⊂ V (G), we present a Metropolis-Hastings MCMC sam-pler that samples from the joint space R and V (G) and estimates relative betweenness scores of the vertices in R. We show that for any pair r i , r j ∈ R, the ratio of the expected values of the estimated relative betweenness scores of r i and r j with respect to each other is equal to the ratio of their betweenness scores. We also show that our joint-space MCMC sampler provides an (ϵ, δ)-approximation of the relative betweenness score of r i with respect to r j .
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Dates and versions

hal-02339557 , version 1 (30-10-2019)

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Mostafa Haghir Chehreghani, Talel Abdessalem, Albert Bifet. Metropolis-Hastings Algorithms for Estimating Betweenness Centrality Talel Abdessalem. 22nd International Conference on Extending Database Technology EDBT 2019, Mar 2019, Lisbon, Portugal. ⟨10.5441/002/edbt.2019.87⟩. ⟨hal-02339557⟩
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