Asymptotic uncertainty quantification for communities in sparse planted bi-section models

B. J.K. Kleijn, J. van Waaij*

*Corresponding author for this work

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Abstract

Posterior distributions for community structure in sparse planted bi-section models are shown to achieve exact (resp. almost-exact) recovery, with sharp bounds for the sparsity regimes where edge probabilities decrease as O(log(n)/n) (resp. O(1/n)). Assuming posterior recovery, one may interpret credible sets (resp. enlarged credible sets) as asymptotically consistent confidence sets; the diameters of those credible sets are controlled by the rate of posterior concentration. If credible levels are chosen to grow to one quickly enough, corresponding credible sets can be interpreted as frequentist confidence sets without conditions on posterior concentration. In the regimes with O(1/n) edge sparsity, or when within-community and between-community edge probabilities are very close, credible sets may be enlarged to achieve frequentist asymptotic coverage, also without conditions on posterior concentration.

Original languageEnglish
JournalJournal of Statistical Planning and Inference
Volume227
Pages (from-to)112-128
ISSN0378-3758
DOIs
Publication statusPublished - 2023

Keywords

  • Community detection
  • Posterior consistency
  • Sparse random graph
  • uncertainty quantification

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