Estimating Stochastic Block Models in the Presence of Covariates
arxiv(2024)
摘要
In the standard stochastic block model for networks, the probability of a
connection between two nodes, often referred to as the edge probability,
depends on the unobserved communities each of these nodes belongs to. We
consider a flexible framework in which each edge probability, together with the
probability of community assignment, are also impacted by observed covariates.
We propose a computationally tractable two-step procedure to estimate the
conditional edge probabilities as well as the community assignment
probabilities. The first step relies on a spectral clustering algorithm applied
to a localized adjacency matrix of the network. In the second step, k-nearest
neighbor regression estimates are computed on the extracted communities. We
study the statistical properties of these estimators by providing
non-asymptotic bounds.
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