Learning sparse graphons and the generalized Kesten–Stigum threshold
Emmanuel Abbe, Shuangping Li, Allan Sly
The Annals of Statistics · 2023 · Volume 51 · Issue 2
Abstract
The problem of learning graphons has attracted considerable attention across several scientific communities, with significant progress over the recent years in sparser regimes. Yet, the current techniques still require diverging degrees in order to succeed with efficient algorithms in the challenging cases where the local structure of the graph is homogeneous. This paper provides an efficient algorithm to learn graphons in the constant expected degree regime. The algorithm is shown to succeed in estimating the rank-k projection of a graphon in the L2 metric if the top k eigenvalues of the graphon satisfy a generalized Kesten–Stigum condition.
Keywords
62H22, graphon, Inference on networks, spectral algorithm
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